Targeting a hypothetical estimand based on adherence with the parametric g-formula: A post hoc secondary analysis of the MET-PREVENT randomised controlled trial

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Methods We viewed the targeting of this hypothetical estimand as a type of causal mediation problem, where randomisation is a binary exposure, adherence is a binary mediator, there is an exposure-mediator interaction, and mediator-outcome confounders that are caused by the exposure (e.g., gastrointestinal symptoms) are present. We used the parametric g-formula to estimate the average controlled direct effect (CDE) of metformin (versus placebo) on 4-metre walk speed, which is interpreted as the average treatment effect under the hypothetical scenario that all trial participants adhered to assigned treatment. Variables identified as confounders were informed by a literature review and discussions with an expert; assumptions about the causal structure were represented in a directed acyclic graph. We applied a probabilistic bias analysis (PBA) to understand the potential for bias assuming adherence had been misclassified; observed adherence based on returned tablet count may be an inaccurate version of “true adherence” based on actual consumption. Results Our sample size was 70 trial participants (34 metformin, 36 placebo). Our estimate of the CDE was 0.072 [percentile-based bootstrap 95% CI -0.292, 0.445]. Results from PBA indicated that the greater the extent of misclassification, the more the CDE may be estimated with bias and with over-optimistic precision. Conclusions Our study provided supporting information on metformin’s potential role as a repurposed medication to improve physical performance in nondiabetic older adult patients with physical prefrailty/frailty and probable sarcopenia. Unlike the main trial results, our results do not rule out the possibility of a meaningful benefit of metformin, provided that full adherence can be assured. We highlighted the parametric g-formula as a useful method in trials to target hypothetical estimands that are concerned with treatment adherence. Trial registration ISRCTN29932357, registered 21st January 2021 Estimands Causal inference G-formula Mediation Secondary analysis Quantitative bias analysis Figures Figure 1 Figure 2 Background The de facto position of randomised placebo-controlled superiority trials is to make conclusions from effects that preserve the intention to treat (ITT) principle, which is analogous to the treatment policy estimand, followed by accompanying per-protocol analyses whereby non-adherers are either excluded or censored. It is known that such ITT effects are particularly sensitive to intercurrent events since any event occurring after randomisation is essentially ignored in the analysis ( 1 ). Treatment adherence may be one such intercurrent event, and differential adherence rates between arms (whereby the intervention arm usually has the lower adherence rate possibly due to the adverse effects of the new treatment) make it challenging to separate between two propositions for observed null findings from ITT results: either the treatment regime under investigation is inefficacious in the target population or it is efficacious but was observed to be inefficacious due to low adherence. Making this distinction is important because adherence is a behaviour that can be improved through intervention. In this study, we conducted a post hoc secondary analysis of the MET-PREVENT trial to target a hypothetical estimand with the parametric g-formula to estimate the average controlled direct effect (CDE) of metformin (versus placebo) on 4-metre walk speed under the hypothetical scenario that all participants adhered ( 2 ). We viewed the targeting of this hypothetical estimand as a type of causal mediation problem, where randomisation is a binary exposure, adherence is a binary mediator, there is an exposure-mediator interaction (because adhering to metformin may matter more than adhering to placebo), and presence of mediator-outcome confounders that are caused by the exposure (e.g., gastrointestinal symptoms). The parametric g-formula (also known as g-computation) overcomes limitations of conventional methods in investigating causal effects when adherence plays the role of a mediator. Traditional per-protocol analyses that involve restricting the sample to those who are adherent (effectively censoring non-adherers) are at-risk of selection bias as an event that happens after randomisation is conditioned upon. Valid estimation of per-protocol (PP) effects requires controlling for factors that influence adherence (i.e. mediator-outcome confounders) ( 3 , 4 ). However, where there is exposure-mediator interaction and mediator-outcome confounders are caused by the exposure, there is a need to turn to a family of methods known as “g-methods” of which the g-formula is a member ( 5 ). Methods Details of the trial MET-PREVENT was a multicentre, proof-of-concept, superiority randomised controlled trial (RCT) of older adults with probable sarcopenia and frailty or prefrailty, but without diabetes mellitus, to investigate if metformin, a glucose-lowering therapy, was efficacious in improving physical performance in this population. The primary analysis was an intention-to-treat (ITT) analysis which found no statistically significant difference between arms (0.001 [95% CI -0.06, 0.06] m/s). The primary results have recently been accepted for publication ( 6 ). Adherence to medication was observed only at the end of the trial when tablets were returned and counted; a participant was defined as adherent if they consumed ≥ 80% of the expected number of tablets they should have taken by the final four-month visit. There was a noticeable difference in adherence rates between the intervention (53%) and placebo (78%) arms respectively. Seventy-two participants were randomised 1:1 (using minimisation with a 30% random element) between metformin and matched placebo. The primary outcome was the 4-metre walk speed test at a four month visit ( 7 ). A minimal clinically important difference (MCID) of 0.1 m/s was pre-specified. One participant withdrew before receiving their medication and one died during follow-up, leaving n = 70 with available data on the primary outcome (4-metre walk speed). Because there was data on only one death and study withdrawal respectively, we could not model these events. Scheduled visits occurred at baseline, one month, two months, and three months after randomisation, with a final visit at four months where the primary outcome was measured. No participant was lost to follow-up. Details on the trial eligibility criteria and design are available in a published protocol ( 7 ). The trial is registered on ISRCTN (ISRCTN29932357). Treatment assignment is regarded as the exposure in our secondary analysis. Participants were randomised to receive metformin 500mg or matching placebo tablets. Dosage was three tablets per day. All participants were supplied with 372 tablets at the point of medication reception to last the entire four-month follow-up duration. True adherence, based on knowledge of actual tablet consumption, was regarded as the mediator. However, in the absence of this knowledge, observed adherence, defined as a medication possession ratio (MPR) ≥ 80% at the final visit when unused tablets were returned and counted, was treated as the closest (but potentially misclassified) surrogate to true adherence in the data. The MPR could not be computed for two participants in the intervention arm as tablets were disposed of by accident. One participant was classified as non-adherent as they experienced gastrointestinal symptoms leading to treatment discontinuation at five days after randomisation. The other participant was classified as adherent based on mean imputation of the MPR. The primary outcome was the 4-metre walk speed (in m/s) measured at the four-month visit. All participants were tasked to walk 4-metres on a measured course and at a pace they normally walk at if they were walking down the street. Participants were allowed to use their walking aid. The faster of two attempts was the primary outcome. Hypothetical estimand Our estimand of interest is the mean difference in physical performance, as measured by the 4-metre walk speed at four months after randomisation between metformin and placebo arms – under the hypothetical scenario that all participants adhered to assigned treatment over a four-month period, amongst physically pre-frail and frail nondiabetic older adults with probable sarcopenia. Assumptions about underlying causal relationships We make explicit our assumptions about the underlying causal relationships in a directed acyclic graph (DAG) (Fig. 1 ); we did not assume unmeasured exposure-outcome confounding owing to randomisation. Variables identified as mediator-outcome confounders were informed by the intersection between literature on factors which influence adherence to medication ( 8 – 11 ) and predictors of walk speed amongst older adults, and discussions with an expert (MDW). Baseline mediator-outcome confounders included age ( 12 , 13 ), sex ( 12 ), obesity (body mass index ≥ 30 kg/m 2 ) ( 14 , 15 ), history of depression ( 16 , 17 ), functional ability as defined by the Nottingham Extended Activities of Daily Living (NEADL) ( 13 ), polypharmacy (≥ 5 concomitant medications) ( 18 ), and baseline 4-metre walk speed. We postulated that individuals who were more impaired on their walk speed may be more motivated to adhere given that participants were informed of the premise of the trial and blinded to treatment allocation. The mediator-outcome confounder caused by the exposure was the number of gastrointestinal adverse events over follow-up (0, 1, or ≥ 2 events). Metformin is known to potentially cause gastrointestinal (GI) symptoms, such as diarrhoea and nausea, which may discourage adherence ( 8 ). We postulated two ways in which GI symptoms may influence walk speed. Participants who experience GI symptoms may perform worse on physical performance measures, especially if the GI side effects made them less active and they became physically deconditioned. Alternatively, if metformin's effect on skeletal muscle is due to a change in the gut microbiome, it may be that only those who do experience GI symptoms achieve benefit. Adverse events were recorded in an adverse events log and GI adverse events are defined as those which were coded under “gastrointestinal disorders” within the Medical Dictionary for Regulatory Activities (MedDRA®) terminology (version 25) ( 19 ). We replaced the missing subscale items on the NEADL with the participant-specific median from the completed items in the subscale, provided less than three items within a subscale were missing. Statistical analysis We used the parametric g-formula to identify the CDE. We refer readers to Appendix A where we introduce the notation for potential outcomes and introduce the g-formula. A stepwise process for the parametric g-formula and our modelling assumptions are described in Appendix B. We reported the estimate of the CDE and a percentile-based 95% confidence interval (CI). We also reported a bias-corrected and accelerated (BCa) bootstrap 95% CI for comparison; the relevance of the BCa bootstrap is included in our discussion but, briefly, it has been proposed to improve the coverage of the parametric g-formula estimator, especially for small sample sizes ( 20 ). The g-formula algorithm is provided in greater detail elsewhere ( 21 ). Analyses were carried out in R version 4.3.0. Sensitivity analyses We assessed how well our model specifications agreed with our assumptions about the underlying causal structure by estimating the natural course ( 22 ). The idea of the natural course is if one were to derive the observed sample mean of the primary outcome through the parametric g-formula, it would require us to specify parametric models for the conditional probability of treatment, adherence, occurrence of GI adverse events, and the conditional mean of the primary outcome. If all these models were correctly specified, then the summary statistics and distributions of the variables that are predicted by the parametric g-formula algorithm should approximately match the observed data. We compared the mean, standard deviation, and empirical cumulative distribution function (eCDF) of the observed primary outcome data against the data predicted by the parametric g-formula, and the means of observed adherence and GI adverse events data against the those predicted by the parametric g-formula. Observed adherence rates based on returned tablet count may overestimate “true adherence” rates based on actual consumption, and there may be concerns over bias due to a misclassified mediator. To understand the impact of misclassifying adherence, we applied a probabilistic bias analysis (PBA) that adjusted the ‘naïve’ estimate of the CDE for misclassification by incorporating information from the literature surrounding the possible extent of misclassification ( 23 ). The aim of a PBA was to gain insight into the impact that misclassification had on the magnitude and direction of bias in our ‘naïve’ CDE estimate, as well as on our uncertainty ( 24 ). We simulated four conditions that represented: 1) a very high certainty in our beliefs that there is a low degree of misclassification; 2) a very high certainty in our beliefs that there is a severe degree of misclassification; 3) more moderate certainty in our beliefs that there is a low degree of misclassification; and lastly 4) more moderate certainty in our beliefs that there is a severe degree of misclassification. Detailed methodology on the PBA is available in Appendix C. We reported the median and percentile-based 95% simulation interval (95% SI) of the misclassification bias-adjusted CDE. The misclassification bias-adjusted point estimate was compared against the naïve point estimate, as well as the widths of the simulation intervals versus the confidence interval ( 24 ). Results Summary characteristics of our sample are in Table 1 . Thirteen participants in the control arm (36.1%) and 27 participants in the intervention arm (79.4%) experienced at least one GI adverse event over the course of follow-up. Of the 27 in the control arm, 10 discontinued due to GI adverse events (9 participant-led, 1 investigator-led). Of the 13 in the control arm, 1 discontinued due to a GI adverse event which was participant-led. Two participants assigned to metformin discontinued due to elevated lactate concentrations (> 4 mmol/L at the one-month and three-month visits respectively) and one participant assigned to placebo discontinued due to hypoglycaemia (< 4 mmol/L) at the two-month visit. None discontinued due to severe renal impairment. Table 1 Characteristics of the sample Analysis set (n = 70) Treatment arm, n (%) Metformin 34 (48.57) Placebo 36 (51.43) Age, years, mean (SD) 80.49 (5.75) Sex, n (%) Female 41 (58.57) Male 29 (41.43) History of depression, n (%) 19 (27.14) Obesity (body mass index ≥ 30 kg/m 2 ), n (%) 18 (25.71) Nottingham Extended Activities of Daily Living, mean (SD) 15.53 (4.94) Polypharmacy (≥ 5 medications), n (%) 60 (85.71) Baseline 4-metre walk speed, m/s, mean (SD) 0.59 (0.22) Four month 4-metre walk speed, m/s, mean (SD) 0.58 (0.22) Observed adherence, n (%) 47 (67.14) Number of gastrointestinal adverse events over follow-up, n (%) 0 30 (42.86) 1 30 (42.86) 2 2 (5.71) 3 3 (7.14) 4 4 (1.43) Our estimate of the CDE was 0.072 [percentile-based bootstrap 95% CI -0.292, 0.445] m/s. We also reported the BCa bootstrap 95% CI [-0.244, 0.519] for comparison. We conducted a natural course analysis to validate our models used in the parametric g-formula. We observed agreement, to an extent, between the observed data and the data predicted from the parametric g-formula algorithm under the natural course (Table 2 ). The eCDFs of the observed and predicted primary outcome data are presented in Fig. 2 . We observed that there was close agreement on the proportion of GI adverse events, adherence, and the distribution of the primary outcome. Our PBA results are presented in Table 3 . Table 2 Comparison of observed data and data predicted by the parametric g-formula estimator in the natural course analysis Observed data (n = 70) Predicted data (n = 10000) Number of GI adverse events No events, % 42.86% 40.66% One event, % 42.86% 45.04% ≥ 2 events, % 14.29% 14.30% Adherence Observed adherence, % 67.14% 66.80% 4-metre walk speed at four months, m/s Mean (SD) 0.58 (0.22) 0.56 (0.20) 1st percentile 0.20 0.19 2.5th percentile 0.21 0.21 5th percentile 0.22 0.23 25th percentile 0.41 0.41 50th percentile 0.56 0.58 75th percentile 0.75 0.70 95th percentile 0.94 0.94 97.5th percentile 1.02 1.06 99th percentile 1.08 1.07 GI, gastrointestinal; SD, standard deviation. Table 3 Results of probabilistic bias analysis Scenario Description Prior Beta distribution of the FPR Median [95% SI] 1 Very high certainty of low degree of misclassification Beta(33.3, 231) 0.066 [-0.657, 0.818] 2 Very high certainty of severe degree of misclassification Beta(355, 205) 0.020 [-0.744, 0.760] 3 Moderate certainty of low degree of misclassification Beta( 4 , 26 ) 0.069 [-0.687, 0.809] 4 Moderate certainty of low degree of misclassification Beta(39.8, 25) 0.029 [-0.728, 0.779] FPR, false positive rate; SI, simulation interval. Discussion Our post hoc secondary analysis supports the trial’s primary finding of insufficient evidence to conclude a beneficial effect of metformin on older adults with physical pre-frailty/frailty and probably sarcopenia. However, in contrast to the prespecified primary analysis findings, our results do not rule out the possibility of either a meaningful benefit of metformin, provided that the consumption of ≥ 80% of prescribed tablets can be assured. Both the percentile-based and BCa bootstrap CIs of our CDE included zero as well as the MCID on both sides of the null, indicating that a null effect, meaningful benefit, and meaningful harm are all consistent with our analysis ( 25 ). Our main analyses assumed that there was no misclassification of treatment adherence and that observed adherence faithfully reflected true adherence. If on the other hand we suspect there to be misclassification, our sensitivity analyses indicated that the greater the extent of misclassification, the more the CDE may be estimated with bias (estimate would have been closer to the null if true adherence had been collected and used in the parametric g-formula analysis) and with over-optimistic precision (confidence intervals would have been wider if true adherence had been collected and used in the parametric g-formula analysis). Because the actual extent of misclassification is not known, we ran our PBA under multiple scenarios to cover different sets of beliefs about the misclassification. It could be argued that the low misclassification scenarios were more plausible than the severe misclassification scenarios. This is based on the premise that participants on clinical trials are generally motivated to follow trial processes especially if an investigational product has the potential to improve the symptoms of a progressive disorder like sarcopenia. Hence, the plausible source of misclassification may be benign forgetfulness such as accidental disposal as opposed to an active intent to defy protocol. Strengths Methods based on the potential outcome framework have utility in overcoming some of the limitations of traditional per-protocol methods which may unintentionally subject themselves to bias ( 4 ). To illustrate this, we compare our estimates with the those from the trial’s original PP analysis of 0.023 [95% CI -0.053, 0.099] m/s. The noticeable difference between the point estimates may reflect that the original PP analysis was subjected to collider-stratification bias when adherence was conditioned upon (by limiting the analysis to adherers only) ( 26 , 27 ). A collider is variable \(\:C\) that is caused by two other variables \(\:A\) and \(\:B\) (hence the effects of the two variables on \(\:C\) ‘collide’). The effect of A on B is estimated with (collider-stratification) bias when a model regressing \(\:B\) on \(\:A\) also includes \(\:C\) as a covariate. With reference to Fig. 1 , and assuming that it accurately reflects the underlying causal structure, limiting the analysis to adherers only induces a noncausal association between treatment assignment and the outcome through the baseline covariates and number of GI adverse events because adherence is a collider on four backdoor paths through GI adverse events. If one were to adjust for the baseline covariates and number of GI adverse events in a traditional outcome regression model (e.g., analysis of covariance), a portion of the direct effect of treatment assignment on the outcome which goes through number of GI events would be removed. Hence, the need for g-methods to avoid collider-stratification bias, unintended partial subtraction of direct effects, and importantly interpret results as causal effects. A more detailed introduction to directed acyclic graphs, collider-stratification bias, and backdoor paths is available elsewhere ( 27 ). The strength of the parametric g-formula is that parametric models allow investigators to extrapolate beyond the observed data, thus positivity violations due to sparsity of data are less of an issue compared to methods using inverse probability weights ( 28 ). However, this trade-off means the parametric g-formula relies heavily on correct model specification to extrapolate over strata of covariates with sparse data. We attempted to make appropriate model specifications as much as possible by referencing prior literature and seeking expert opinion on potential mediator-outcome confounders, and relaxing modelling assumptions by allowing for interactions between treatment and all covariates and the inclusion of non-linear terms of continuous covariates in the primary outcome model. On the other hand, baseline cognitive functioning ( 8 , 10 , 29 , 30 ) may be an unmeasured mediator-outcome confounder such that higher cognitive functioning may lead to better adherence and walk speed. Under unmeasured confounding, a qualified interpretation of our estimates is necessary. If the confounder(s) exists and it increases the likelihood of adherence and the average value of the outcome simultaneously, then our estimate of the CDE may be interpreted as estimates for the lower bound of the true CDE instead ( 2 ). The impact of this confounder was partially mitigated against as none of the participants was diagnosed with dementia and that baseline walk speed and functional ability are correlated with cognition ( 31 , 32 ). Nevertheless, this means that our estimate of 0.072 m/s may be regarded as our best estimate of this lower bound, and the true effect of metformin under unanimous adherence may be larger than this quantity. However, given the confidence interval, a negative-valued lower bound is consistent with our data, which maintains the possibility of the true CDE being zero. Limitations The use of the parametric g-formula at small sample sizes carries limitations. Few studies have evaluated the performance of the parametric g-formula estimator in small sample sizes (n ≤ 100). Tackney and colleagues ( 20 ) examined the performance of the parametric g-formula estimator of the average treatment effect (ATE) of a point exposure on a continuous outcome. They examined the performance of the estimator when sample size was small (n = 50 and n = 100) and the model for the conditional mean of their outcome included a treatment variable, 17 covariates (which were all predictive of the outcome), and interactions between treatment and all covariates. Provided all confounders have been accounted for, their results indicate that whilst the estimator had a mean bias close to zero, but there was suboptimal coverage (approximately 90% at either sample size) which were due to the model-based standard errors underestimating the empirical standard error. Coverage was further reduced when including four additional covariates that were unpredictive of the outcome. These findings regarding suboptimal coverage are supported by Chatton and colleagues ( 33 ) who evaluated the performance of the parametric g-formula estimator of the average treatment effect of a point exposure when the outcome was binary, sample size was 100, and the outcome model included 9 covariates (6 were predictive of the outcome) and the treatment variable. Assuming correct model specification, their results indicated that the estimator had a mean bias close to zero but coverage was suboptimal at 91.8%; reducing the number of covariates appeared to shift the coverage probability closer towards the desired 95% probability. Small sample corrections such as BCa bootstrap have thus been proposed to improve coverage ( 20 ). A limitation of the CDE is that all participants are always set to adhere through some conceivable intervention. This may not be realistic as interventions should allow treatment to be discontinued at any point when a participant experiences a clinical event that jeopardises their safety. Relevant events in the context of metformin would be elevated lactate concentrations, hypoglycaemia, and severe renal impairment. One strategy would have been to conceive of a dynamic intervention on adherence that allows for non-adherence when participant safety is compromised at any point during follow-up ( 34 ). Given that the incidence rates of elevated lactate concentrations, hypoglycaemia, and severe renal impairment following metformin use are low based from previous reports and our observations ( 35 – 37 ), it may be reasonable to interpret our effect as a close approximation to the effect under this dynamic intervention on adherence. We observed a relatively wider confidence interval of the CDE compared that of the trial’s ITT and PP effects. One possible reason could be that controlled direct effects estimated by the parametric g-formula have greater sample size requirements for the same level of precision because of the added modelling assumptions. A previous study conducted a secondary analysis of a placebo-controlled trial to investigate the per-protocol effect of complete adherence to low-dose aspirin at preconception to improve live births amongst 1,227 women with documented pregnancy losses and were actively trying to conceive ( 38 ). Compared to the trial’s ITT effect of a relative risk of live birth of 1.10 [95% CI 0.98, 1.22], the parametric g-formula estimate of the per-protocol effect in which all participants adhered was 1.33 [95% CI 1.08, 1.64]; an approximately two-fold increase in the width of the confidence interval on the log relative risk scale. Another reason could be that at the given sample size the models were overfitted to the data. However, Tackney and colleagues ( 20 ) showed by simulation that even at a fixed sample size of 50, increasing the number of covariates or even adding interaction terms between treatment all covariates did not substantially change the model-based standard error or empirical standard error of the parametric g-formula estimator of the ATE of a point exposure on a continuous outcome. Further work could be developed to investigate if this also extends to mediation analyses. Conclusions Our study allowed us to draw out lessons for trialists. We highlighted the parametric g-formula as a useful method in trials to target hypothetical estimands that are concerned with treatment adherence. Our study shines a light on two contexts in which targeting a hypothetical estimand based on adherence is meaningful. Firstly, efficacy trials may benefit most whereby maximising adherence is important so as not to miss a possible benefit of treatment. Meeting the threshold for adherence for all participants in an efficacy trial setting could possibly be reached perhaps by introducing an initial titration period ( 39 ) plus raising awareness amongst participants about the nocebo effect i.e. a portion of GI adverse events may be attributable to negative expectations about the medicine rather than a pharmacological effect ( 40 ). Other strategies may also include patient education and counselling ( 8 ), shared decision-making between clinicians and patients ( 8 ), dose adjustment ( 41 ), use of extended release formulations ( 41 ), and lifestyle adaptations (e.g., time medication intake around meals ( 41 )). However, in effectiveness trials, it is much more important that the trial conditions reflect how the drug will be used in the real world, so if low adherence is going to be an issue in clinical practice, seeing this in the trial is preferable and thus there may not be much to be gained from targeting an adherence-based hypothetical estimand. Secondly, while there may be no substitute for efforts to actually maximise adherence at the design and implementation stages, methods such as the parametric g-formula to target adherence-based hypothetical estimands may be the best alternative when maximising adherence is challenging in practice. If there is an a priori interest in the treatment effect under an ideal circumstance of unanimous adherence, then there may be a need to build in an analysis to estimate the CDE at the trial design stage as it may influence sample size. Generally, closed form solutions are not readily available for causal effects thus Monte Carlo simulation will be needed ( 42 , 43 ). Declarations Funding The MET-PREVENT trial was funded by the NIHR Newcastle Biomedical Research Centre. Additional funding for mechanistic analyses were provided as a philanthropic gift by Mr Alan Halsall. MDW, AAS, and CMcD acknowledge support from the NIHR Newcastle Biomedical Research Centre. JMSW is funded by a NIHR Research Professorship (NIHR301614). The views expressed are those of the author(s) and not necessarily those of the NIHR or the Department of Health and Social Care. Ethical approval and consent to participate All participants provided their informed consent. The trial was approved by the UK Health Research Authority North-West - Liverpool Central Research Ethics Committee (20/NW/0470) and the UK Medicines and Healthcare products Regulatory Agency (2020-004023-16). The trial was sponsored by the Newcastle Upon Tyne Hospitals NHS Foundation Trust. The trial complied with the ethical standards laid down in the 1964 Declaration of Helsinki and its later amendments. Competing interests None to declare. Availability of data and materials Data can be shared upon reasonable request to the NIHR Newcastle Biomedical Research Centre by contacting Professor Miles Witham (Chief Investigator): [email protected] . Consent for publication: Not applicable Authors’ contributions : Conception and design : SH, NW, NL, KW, JMSW Acquisition, analysis : SH, NW, MDW Interpretation of data : all authors Drafting : SH Critical revision of draft : all authors All authors have approved the submitted version Acknowledgements : we thank the participants in the MET-PREVENT trial and members of the Trial Management Group who are not in the co-authorship list. References Ye CL, Beyene J, Browne G, Thabane L. 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Applying Quantitative Bias Analysis to Epidemiologic Data [Internet]. Switzerland: Springer Cham; 2021. 2nd. [291–327]. Probabilistic Bias Analysis for Simulation of Record-Level Data. Hunnicutt JN, Ulbricht CM, Chrysanthopoulou SA, Lapane KL. Probabilistic bias analysis in pharmacoepidemiology and comparative effectiveness research: a systematic review. Pharmacoepidem Dr S. 2016;25(12):1343–53. Hawkins AT, Samuels LR. Use of Confidence Intervals in Interpreting Nonstatistically Significant Results. Jama-J Am Med Assoc. 2021;326(20):2068–9. Loeys T, Moerkerke B, Raes A, Rosseel Y, Vansteelandt S. Estimation of Controlled Direct Effects in the Presence of Exposure-Induced Confounding and Latent Variables. Struct Equ Model. 2014;21(3):396–407. Igelström E, Craig P, Lewsey J, Lynch J, Pearce A, Katikireddi SV. Causal inference and effect estimation using observational data. J Epidemiol Commun H. 2022;76(11):960–6. Chatton A, Rohrer JM. The Causal Cookbook: Recipes for Propensity Scores, G-Computation, and Doubly Robust Standardization. Adv Meth Pract Psych. 2024;7(1). Atkinson HH, Rapp SR, Williamson JD, Lovato J, Absher JR, Gass M, et al. The Relationship Between Cognitive Function and Physical Performance in Older Women: Results From the Women's Health Initiative Memory Study. J Gerontol a-Biol. 2010;65(3):300–6. Watson NL, Rosano C, Boudreau RM, Simonsick EM, Ferrucci L, Sutton-Tyrrell K, et al. Executive Function, Memory, and Gait Speed Decline in Well-Functioning Older Adults. J Gerontol a-Biol. 2010;65(10):1093–100. Garcia-Pinillos F, Cozar-Barba M, Munoz-Jimenez M, Soto-Hermoso V, Latorre-Roman P. Gait speed in older people: an easy test for detecting cognitive impairment, functional independence, and health state. Psychogeriatrics. 2016;16(3):165–71. Rodakowski J, Skidmore ER, Reynolds CF, Dew MA, Butters MA, Holm MB, et al. Can Performance on Daily Activities Discriminate Between Older Adults with Normal Cognitive Function and Those with Mild Cognitive Impairment? J Am Geriatr Soc. 2014;62(7):1347–52. Chatton A, Le Borgne F, Leyrat C, Gillaizeau F, Rousseau C, Barbin L et al. G-computation, propensity score-based methods, and targeted maximum likelihood estimator for causal inference with different covariates sets: a comparative simulation study. Sci Rep-Uk. 2020;10(1). Young JG, Cain LE, Robins JM, O'Reilly EJ, Hernan MA. Comparative effectiveness of dynamic treatment regimes: an application of the parametric g-formula. Stat Biosci. 2011;3(1):119–43. Bodmer M, Meier C, Krahenbuhl S, Jick SS, Meier CR. Metformin, sulfonylureas, or other antidiabetes drugs and the risk of lactic acidosis or hypoglycemia: a nested case-control analysis. Diabetes Care. 2008;31(11):2086–91. Christiansen CF, Ehrenstein V, Heide-Jorgensen U, Skovbo S, Norrelund H, Sorensen HT, et al. Metformin initiation and renal impairment: a cohort study in Denmark and the UK. Bmj Open. 2015;5(9):e008531. Salpeter SR, Greyber E, Pasternak GA, Salpeter EE. Risk of fatal and nonfatal lactic acidosis with metformin use in type 2 diabetes mellitus. Cochrane Db Syst Rev. 2010(4). Naimi AI, Perkins NJ, Sjaarda LA, Mumford SL, Platt RW, Silver RM, et al. The Effect of Preconception-Initiated Low-Dose Aspirin on Human Chorionic Gonadotropin-Detected Pregnancy, Pregnancy Loss, and Live Birth Per Protocol Analysis of a Randomized Trial. Ann Intern Med. 2021;174(5):595–. Bonnet F, Scheen A. Understanding and overcoming metformin gastrointestinal intolerance. Diabetes Obes Metab. 2017;19(4):473–81. Michnevich T, Pan Y, Hendi A, Oechsle K, Stein A, Nestoriuc Y. Preventing adverse events of chemotherapy for gastrointestinal cancer by educating patients about the nocebo effect: a randomized-controlled trial. BMC Cancer. 2022;22(1):1008. Flory JH, Keating S, Guelce D, Mushlin AI. Overcoming barriers to the use of metformin: patient and provider perspectives. Patient Prefer Adher. 2019;13:1433–41. Landau S, Stahl D. Sample size and power calculations for medical studies by simulation when closed form expressions are not available. Stat Methods Med Res. 2013;22(3):324–45. Rudolph KE, Goin DE, Stuart EA. The Peril of Power: A Tutorial on Using Simulation to Better Understand When and How We Can Estimate Mediating Effects. Am J Epidemiol. 2020;189(12):1559–67. Supplementary Files SupplementarymaterialHiuetal.docx Cite Share Download PDF Status: Published Journal Publication published 10 Apr, 2026 Read the published version in Trials → Version 1 posted Editorial decision: Minor revision 19 Oct, 2025 Reviewers agreed at journal 29 Aug, 2025 Reviewers invited by journal 26 Aug, 2025 Editor assigned by journal 28 Apr, 2025 First submitted to journal 15 Feb, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6037689","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":505876545,"identity":"4b495da4-34d8-4ad1-99f0-39cb33f7d2ad","order_by":0,"name":"Shaun Hiu","email":"","orcid":"","institution":"University of Oxford Nuffield Department of Primary Care Health Sciences","correspondingAuthor":false,"prefix":"","firstName":"Shaun","middleName":"","lastName":"Hiu","suffix":""},{"id":505876546,"identity":"358a9dfc-2d82-41d3-825c-99999b0e9de7","order_by":1,"name":"Nina Wilson","email":"","orcid":"","institution":"Newcastle University Population Health Sciences Institute","correspondingAuthor":false,"prefix":"","firstName":"Nina","middleName":"","lastName":"Wilson","suffix":""},{"id":505876547,"identity":"124f4862-a7e9-43ef-ad89-3b5c3290f707","order_by":2,"name":"Kevin Wilson","email":"","orcid":"","institution":"Newcastle University School of Mathematics Statistics and Physics","correspondingAuthor":false,"prefix":"","firstName":"Kevin","middleName":"","lastName":"Wilson","suffix":""},{"id":505876548,"identity":"31ce1205-719b-4f3e-a1b5-ce7a2a380e6c","order_by":3,"name":"Nan Lin","email":"","orcid":"","institution":"Newcastle University Population Health Sciences Institute","correspondingAuthor":false,"prefix":"","firstName":"Nan","middleName":"","lastName":"Lin","suffix":""},{"id":505876549,"identity":"3c497c8d-dae4-46fa-9f40-659c587a8c04","order_by":4,"name":"Miles D Witham","email":"","orcid":"","institution":"NIHR Newcastle Biomedical Research Centre","correspondingAuthor":false,"prefix":"","firstName":"Miles","middleName":"D","lastName":"Witham","suffix":""},{"id":505876550,"identity":"2f12a370-194a-4194-bbaf-121d020eaed2","order_by":5,"name":"James Wason","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0002-4691-126X","institution":"Newcastle University","correspondingAuthor":true,"prefix":"","firstName":"James","middleName":"","lastName":"Wason","suffix":""}],"badges":[],"createdAt":"2025-02-15 16:48:39","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6037689/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6037689/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1186/s13063-026-09708-1","type":"published","date":"2026-04-10T15:57:04+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":90473846,"identity":"2a914ce0-d110-4375-8e58-2873ebb7cdcc","added_by":"auto","created_at":"2025-09-03 06:39:48","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":77079,"visible":true,"origin":"","legend":"\u003cp\u003eDirected acyclic graph representing assumptions of causal relationships\u003cem\u003e. \u003c/em\u003eThe observed adherence variable in our data (which is based on returned tablet counts) may be a misclassified version of “true adherence” (which is based on actual consumption and not known to us). The variable U represents unmeasured mediator-outcome confounder(s) that are not available in the data. The bolded paths collectively make up the CDE of treatment assignment on the outcome.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6037689/v1/0a0d6f77475811ce49845d38.png"},{"id":90473845,"identity":"30906246-c122-4492-ab87-72357520c528","added_by":"auto","created_at":"2025-09-03 06:39:48","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":46975,"visible":true,"origin":"","legend":"\u003cp\u003eEmpirical cumulative distribution functions of the observed and predicted primary outcome data\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6037689/v1/5474c15acf32c907a3ca855b.png"},{"id":106809581,"identity":"4a699860-1cba-4f0c-8bcb-0c341852f5bd","added_by":"auto","created_at":"2026-04-13 16:11:39","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":832765,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6037689/v1/ca91becb-a0c9-4c66-aab7-10b9b20d449e.pdf"},{"id":90473854,"identity":"aa24708a-2ebb-4a04-8db7-4b842a5ffb49","added_by":"auto","created_at":"2025-09-03 06:39:48","extension":"docx","order_by":4,"title":"","display":"","copyAsset":false,"role":"supplement","size":301200,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementarymaterialHiuetal.docx","url":"https://assets-eu.researchsquare.com/files/rs-6037689/v1/b68341fd40172312b7edcfc2.docx"}],"financialInterests":"","formattedTitle":"Targeting a hypothetical estimand based on adherence with the parametric g-formula: A post hoc secondary analysis of the MET-PREVENT randomised controlled trial","fulltext":[{"header":"Background","content":"\u003cp\u003eThe de facto position of randomised placebo-controlled superiority trials is to make conclusions from effects that preserve the intention to treat (ITT) principle, which is analogous to the treatment policy estimand, followed by accompanying per-protocol analyses whereby non-adherers are either excluded or censored. It is known that such ITT effects are particularly sensitive to intercurrent events since any event occurring after randomisation is essentially ignored in the analysis (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e). Treatment adherence may be one such intercurrent event, and differential adherence rates between arms (whereby the intervention arm usually has the lower adherence rate possibly due to the adverse effects of the new treatment) make it challenging to separate between two propositions for observed null findings from ITT results: either the treatment regime under investigation is inefficacious in the target population or it is efficacious but was observed to be inefficacious due to low adherence. Making this distinction is important because adherence is a behaviour that can be improved through intervention.\u003c/p\u003e\u003cp\u003eIn this study, we conducted a post hoc secondary analysis of the MET-PREVENT trial to target a hypothetical estimand with the parametric g-formula to estimate the average controlled direct effect (CDE) of metformin (versus placebo) on 4-metre walk speed under the hypothetical scenario that all participants adhered (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eWe viewed the targeting of this hypothetical estimand as a type of causal mediation problem, where randomisation is a binary exposure, adherence is a binary mediator, there is an exposure-mediator interaction (because adhering to metformin may matter more than adhering to placebo), and presence of mediator-outcome confounders that are caused by the exposure (e.g., gastrointestinal symptoms). The parametric g-formula (also known as g-computation) overcomes limitations of conventional methods in investigating causal effects when adherence plays the role of a mediator. Traditional per-protocol analyses that involve restricting the sample to those who are adherent (effectively censoring non-adherers) are at-risk of selection bias as an event that happens after randomisation is conditioned upon. Valid estimation of per-protocol (PP) effects requires controlling for factors that influence adherence (i.e. mediator-outcome confounders) (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e). However, where there is exposure-mediator interaction and mediator-outcome confounders are caused by the exposure, there is a need to turn to a family of methods known as \u0026ldquo;g-methods\u0026rdquo; of which the g-formula is a member (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e).\u003c/p\u003e"},{"header":"Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003eDetails of the trial\u003c/h2\u003e\u003cp\u003eMET-PREVENT was a multicentre, proof-of-concept, superiority randomised controlled trial (RCT) of older adults with probable sarcopenia and frailty or prefrailty, but without diabetes mellitus, to investigate if metformin, a glucose-lowering therapy, was efficacious in improving physical performance in this population. The primary analysis was an intention-to-treat (ITT) analysis which found no statistically significant difference between arms (0.001 [95% CI -0.06, 0.06] m/s). The primary results have recently been accepted for publication (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e). Adherence to medication was observed only at the end of the trial when tablets were returned and counted; a participant was defined as adherent if they consumed\u0026thinsp;\u0026ge;\u0026thinsp;80% of the expected number of tablets they should have taken by the final four-month visit. There was a noticeable difference in adherence rates between the intervention (53%) and placebo (78%) arms respectively.\u003c/p\u003e\u003cp\u003eSeventy-two participants were randomised 1:1 (using minimisation with a 30% random element) between metformin and matched placebo. The primary outcome was the 4-metre walk speed test at a four month visit (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e). A minimal clinically important difference (MCID) of 0.1 m/s was pre-specified. One participant withdrew before receiving their medication and one died during follow-up, leaving n\u0026thinsp;=\u0026thinsp;70 with available data on the primary outcome (4-metre walk speed). Because there was data on only one death and study withdrawal respectively, we could not model these events. Scheduled visits occurred at baseline, one month, two months, and three months after randomisation, with a final visit at four months where the primary outcome was measured. No participant was lost to follow-up. Details on the trial eligibility criteria and design are available in a published protocol (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e). The trial is registered on ISRCTN (ISRCTN29932357).\u003c/p\u003e\u003cp\u003eTreatment assignment is regarded as the exposure in our secondary analysis. Participants were randomised to receive metformin 500mg or matching placebo tablets. Dosage was three tablets per day. All participants were supplied with 372 tablets at the point of medication reception to last the entire four-month follow-up duration.\u003c/p\u003e\u003cp\u003eTrue adherence, based on knowledge of actual tablet consumption, was regarded as the mediator. However, in the absence of this knowledge, observed adherence, defined as a medication possession ratio (MPR)\u0026thinsp;\u0026ge;\u0026thinsp;80% at the final visit when unused tablets were returned and counted, was treated as the closest (but potentially misclassified) surrogate to true adherence in the data. The MPR could not be computed for two participants in the intervention arm as tablets were disposed of by accident. One participant was classified as non-adherent as they experienced gastrointestinal symptoms leading to treatment discontinuation at five days after randomisation. The other participant was classified as adherent based on mean imputation of the MPR.\u003c/p\u003e\u003cp\u003eThe primary outcome was the 4-metre walk speed (in m/s) measured at the four-month visit. All participants were tasked to walk 4-metres on a measured course and at a pace they normally walk at if they were walking down the street. Participants were allowed to use their walking aid. The faster of two attempts was the primary outcome.\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eHypothetical estimand\u003c/h3\u003e\n\u003cp\u003eOur estimand of interest is the mean difference in physical performance, as measured by the 4-metre walk speed at four months after randomisation between metformin and placebo arms \u0026ndash; under the hypothetical scenario that all participants adhered to assigned treatment over a four-month period, amongst physically pre-frail and frail nondiabetic older adults with probable sarcopenia.\u003c/p\u003e\n\u003ch3\u003eAssumptions about underlying causal relationships\u003c/h3\u003e\n\u003cp\u003eWe make explicit our assumptions about the underlying causal relationships in a directed acyclic graph (DAG) (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e); we did not assume unmeasured exposure-outcome confounding owing to randomisation. Variables identified as mediator-outcome confounders were informed by the intersection between literature on factors which influence adherence to medication (\u003cspan additionalcitationids=\"CR9 CR10\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e) and predictors of walk speed amongst older adults, and discussions with an expert (MDW).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eBaseline mediator-outcome confounders included age (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e), sex (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e), obesity (body mass index\u0026thinsp;\u0026ge;\u0026thinsp;30 kg/m\u003csup\u003e2\u003c/sup\u003e) (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e), history of depression (\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e), functional ability as defined by the Nottingham Extended Activities of Daily Living (NEADL) (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e), polypharmacy (\u0026ge;\u0026thinsp;5 concomitant medications) (\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e), and baseline 4-metre walk speed. We postulated that individuals who were more impaired on their walk speed may be more motivated to adhere given that participants were informed of the premise of the trial and blinded to treatment allocation. The mediator-outcome confounder caused by the exposure was the number of gastrointestinal adverse events over follow-up (0, 1, or \u0026ge;\u0026thinsp;2 events). Metformin is known to potentially cause gastrointestinal (GI) symptoms, such as diarrhoea and nausea, which may discourage adherence (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e). We postulated two ways in which GI symptoms may influence walk speed. Participants who experience GI symptoms may perform worse on physical performance measures, especially if the GI side effects made them less active and they became physically deconditioned. Alternatively, if metformin's effect on skeletal muscle is due to a change in the gut microbiome, it may be that only those who do experience GI symptoms achieve benefit. Adverse events were recorded in an adverse events log and GI adverse events are defined as those which were coded under \u0026ldquo;gastrointestinal disorders\u0026rdquo; within the Medical Dictionary for Regulatory Activities (MedDRA\u0026reg;) terminology (version 25) (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e). We replaced the missing subscale items on the NEADL with the participant-specific median from the completed items in the subscale, provided less than three items within a subscale were missing.\u003c/p\u003e\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003eStatistical analysis\u003c/h2\u003e\u003cp\u003eWe used the parametric g-formula to identify the CDE. We refer readers to Appendix A where we introduce the notation for potential outcomes and introduce the g-formula. A stepwise process for the parametric g-formula and our modelling assumptions are described in Appendix B. We reported the estimate of the CDE and a percentile-based 95% confidence interval (CI). We also reported a bias-corrected and accelerated (BCa) bootstrap 95% CI for comparison; the relevance of the BCa bootstrap is included in our discussion but, briefly, it has been proposed to improve the coverage of the parametric g-formula estimator, especially for small sample sizes (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e). The g-formula algorithm is provided in greater detail elsewhere (\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e). Analyses were carried out in R version 4.3.0.\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eSensitivity analyses\u003c/h3\u003e\n\u003cp\u003eWe assessed how well our model specifications agreed with our assumptions about the underlying causal structure by estimating the natural course (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e). The idea of the natural course is if one were to derive the observed sample mean of the primary outcome through the parametric g-formula, it would require us to specify parametric models for the conditional probability of treatment, adherence, occurrence of GI adverse events, and the conditional mean of the primary outcome. If all these models were correctly specified, then the summary statistics and distributions of the variables that are predicted by the parametric g-formula algorithm should approximately match the observed data. We compared the mean, standard deviation, and empirical cumulative distribution function (eCDF) of the observed primary outcome data against the data predicted by the parametric g-formula, and the means of observed adherence and GI adverse events data against the those predicted by the parametric g-formula.\u003c/p\u003e\u003cp\u003eObserved adherence rates based on returned tablet count may overestimate \u0026ldquo;true adherence\u0026rdquo; rates based on actual consumption, and there may be concerns over bias due to a misclassified mediator. To understand the impact of misclassifying adherence, we applied a probabilistic bias analysis (PBA) that adjusted the \u0026lsquo;na\u0026iuml;ve\u0026rsquo; estimate of the CDE for misclassification by incorporating information from the literature surrounding the possible extent of misclassification (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e). The aim of a PBA was to gain insight into the impact that misclassification had on the magnitude and direction of bias in our \u0026lsquo;na\u0026iuml;ve\u0026rsquo; CDE estimate, as well as on our uncertainty (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e). We simulated four conditions that represented: 1) a very high certainty in our beliefs that there is a low degree of misclassification; 2) a very high certainty in our beliefs that there is a severe degree of misclassification; 3) more moderate certainty in our beliefs that there is a low degree of misclassification; and lastly 4) more moderate certainty in our beliefs that there is a severe degree of misclassification. Detailed methodology on the PBA is available in Appendix C. We reported the median and percentile-based 95% simulation interval (95% SI) of the misclassification bias-adjusted CDE. The misclassification bias-adjusted point estimate was compared against the na\u0026iuml;ve point estimate, as well as the widths of the simulation intervals versus the confidence interval (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e).\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eSummary characteristics of our sample are in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Thirteen participants in the control arm (36.1%) and 27 participants in the intervention arm (79.4%) experienced at least one GI adverse event over the course of follow-up. Of the 27 in the control arm, 10 discontinued due to GI adverse events (9 participant-led, 1 investigator-led). Of the 13 in the control arm, 1 discontinued due to a GI adverse event which was participant-led. Two participants assigned to metformin discontinued due to elevated lactate concentrations (\u0026gt;\u0026thinsp;4 mmol/L at the one-month and three-month visits respectively) and one participant assigned to placebo discontinued due to hypoglycaemia (\u0026lt;\u0026thinsp;4 mmol/L) at the two-month visit. None discontinued due to severe renal impairment.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eCharacteristics of the sample\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"2\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eAnalysis set (n\u0026thinsp;=\u0026thinsp;70)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTreatment arm, n (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMetformin\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e34 (48.57)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePlacebo\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e36 (51.43)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAge, years, mean (SD)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e80.49 (5.75)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSex, n (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFemale\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e41 (58.57)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMale\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e29 (41.43)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHistory of depression, n (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e19 (27.14)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eObesity (body mass index\u0026thinsp;\u0026ge;\u0026thinsp;30 kg/m\u003csup\u003e2\u003c/sup\u003e), n (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e18 (25.71)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNottingham Extended Activities of Daily Living, mean (SD)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e15.53 (4.94)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePolypharmacy (\u0026ge;\u0026thinsp;5 medications), n (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e60 (85.71)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBaseline 4-metre walk speed, m/s, mean (SD)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.59 (0.22)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFour month 4-metre walk speed, m/s, mean (SD)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.58 (0.22)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eObserved adherence, n (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e47 (67.14)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNumber of gastrointestinal adverse events over follow-up, n (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e30 (42.86)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e30 (42.86)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2 (5.71)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e3 (7.14)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e4 (1.43)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eOur estimate of the CDE was 0.072 [percentile-based bootstrap 95% CI -0.292, 0.445] m/s. We also reported the BCa bootstrap 95% CI [-0.244, 0.519] for comparison. We conducted a natural course analysis to validate our models used in the parametric g-formula. We observed agreement, to an extent, between the observed data and the data predicted from the parametric g-formula algorithm under the natural course (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The eCDFs of the observed and predicted primary outcome data are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. We observed that there was close agreement on the proportion of GI adverse events, adherence, and the distribution of the primary outcome. Our PBA results are presented in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eComparison of observed data and data predicted by the parametric g-formula estimator in the natural course analysis\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eObserved data (n\u0026thinsp;=\u0026thinsp;70)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003ePredicted data (n\u0026thinsp;=\u0026thinsp;10000)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eNumber of GI adverse events\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNo events, %\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e42.86%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e40.66%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eOne event, %\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e42.86%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e45.04%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u0026ge;\u0026thinsp;2 events, %\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e14.29%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e14.30%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eAdherence\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eObserved adherence, %\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e67.14%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e66.80%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003e4-metre walk speed at four months, m/s\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMean (SD)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.58 (0.22)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.56 (0.20)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1st percentile\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.20\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.19\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2.5th percentile\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.21\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.21\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5th percentile\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.23\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e25th percentile\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e50th percentile\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.56\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.58\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e75th percentile\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.75\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.70\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e95th percentile\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.94\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e97.5th percentile\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.02\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.06\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e99th percentile\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.07\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"3\"\u003eGI, gastrointestinal; SD, standard deviation.\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eResults of probabilistic bias analysis\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\"\u0026minus;\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eScenario\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDescription\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003ePrior Beta distribution of the FPR\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMedian [95% SI]\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eVery high certainty of low degree of misclassification\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eBeta(33.3, 231)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c4\"\u003e\u003cp\u003e0.066 [-0.657, 0.818]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eVery high certainty of severe degree of misclassification\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eBeta(355, 205)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c4\"\u003e\u003cp\u003e0.020 [-0.744, 0.760]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eModerate certainty of low degree of misclassification\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eBeta(\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c4\"\u003e\u003cp\u003e0.069 [-0.687, 0.809]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eModerate certainty of low degree of misclassification\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eBeta(39.8, 25)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c4\"\u003e\u003cp\u003e0.029 [-0.728, 0.779]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"4\"\u003eFPR, false positive rate; SI, simulation interval.\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eOur post hoc secondary analysis supports the trial\u0026rsquo;s primary finding of insufficient evidence to conclude a beneficial effect of metformin on older adults with physical pre-frailty/frailty and probably sarcopenia. However, in contrast to the prespecified primary analysis findings, our results do not rule out the possibility of either a meaningful benefit of metformin, provided that the consumption of \u0026ge;\u0026thinsp;80% of prescribed tablets can be assured. Both the percentile-based and BCa bootstrap CIs of our CDE included zero as well as the MCID on both sides of the null, indicating that a null effect, meaningful benefit, and meaningful harm are all consistent with our analysis (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eOur main analyses assumed that there was no misclassification of treatment adherence and that observed adherence faithfully reflected true adherence. If on the other hand we suspect there to be misclassification, our sensitivity analyses indicated that the greater the extent of misclassification, the more the CDE may be estimated with bias (estimate would have been closer to the null if true adherence had been collected and used in the parametric g-formula analysis) and with over-optimistic precision (confidence intervals would have been wider if true adherence had been collected and used in the parametric g-formula analysis). Because the actual extent of misclassification is not known, we ran our PBA under multiple scenarios to cover different sets of beliefs about the misclassification. It could be argued that the low misclassification scenarios were more plausible than the severe misclassification scenarios. This is based on the premise that participants on clinical trials are generally motivated to follow trial processes especially if an investigational product has the potential to improve the symptoms of a progressive disorder like sarcopenia. Hence, the plausible source of misclassification may be benign forgetfulness such as accidental disposal as opposed to an active intent to defy protocol.\u003c/p\u003e\n\u003ch3\u003eStrengths\u003c/h3\u003e\n\u003cp\u003eMethods based on the potential outcome framework have utility in overcoming some of the limitations of traditional per-protocol methods which may unintentionally subject themselves to bias (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e). To illustrate this, we compare our estimates with the those from the trial\u0026rsquo;s original PP analysis of 0.023 [95% CI -0.053, 0.099] m/s. The noticeable difference between the point estimates may reflect that the original PP analysis was subjected to collider-stratification bias when adherence was conditioned upon (by limiting the analysis to adherers only) (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e). A collider is variable \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:C\\)\u003c/span\u003e\u003c/span\u003e that is caused by two other variables \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:A\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:B\\)\u003c/span\u003e\u003c/span\u003e (hence the effects of the two variables on \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:C\\)\u003c/span\u003e\u003c/span\u003e \u0026lsquo;collide\u0026rsquo;). The effect of A on B is estimated with (collider-stratification) bias when a model regressing \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:B\\)\u003c/span\u003e\u003c/span\u003e on \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:A\\)\u003c/span\u003e\u003c/span\u003e also includes \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:C\\)\u003c/span\u003e\u003c/span\u003e as a covariate. With reference to Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, and assuming that it accurately reflects the underlying causal structure, limiting the analysis to adherers only induces a noncausal association between treatment assignment and the outcome through the baseline covariates and number of GI adverse events because adherence is a collider on four backdoor paths through GI adverse events. If one were to adjust for the baseline covariates and number of GI adverse events in a traditional outcome regression model (e.g., analysis of covariance), a portion of the direct effect of treatment assignment on the outcome which goes through number of GI events would be removed. Hence, the need for g-methods to avoid collider-stratification bias, unintended partial subtraction of direct effects, and importantly interpret results as causal effects. A more detailed introduction to directed acyclic graphs, collider-stratification bias, and backdoor paths is available elsewhere (\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThe strength of the parametric g-formula is that parametric models allow investigators to extrapolate beyond the observed data, thus positivity violations due to sparsity of data are less of an issue compared to methods using inverse probability weights (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e). However, this trade-off means the parametric g-formula relies heavily on correct model specification to extrapolate over strata of covariates with sparse data. We attempted to make appropriate model specifications as much as possible by referencing prior literature and seeking expert opinion on potential mediator-outcome confounders, and relaxing modelling assumptions by allowing for interactions between treatment and all covariates and the inclusion of non-linear terms of continuous covariates in the primary outcome model. On the other hand, baseline cognitive functioning (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e) may be an unmeasured mediator-outcome confounder such that higher cognitive functioning may lead to better adherence and walk speed. Under unmeasured confounding, a qualified interpretation of our estimates is necessary. If the confounder(s) exists and it increases the likelihood of adherence and the average value of the outcome simultaneously, then our estimate of the CDE may be interpreted as estimates for the lower bound of the true CDE instead (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e). The impact of this confounder was partially mitigated against as none of the participants was diagnosed with dementia and that baseline walk speed and functional ability are correlated with cognition (\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e). Nevertheless, this means that our estimate of 0.072 m/s may be regarded as our best estimate of this lower bound, and the true effect of metformin under unanimous adherence may be larger than this quantity. However, given the confidence interval, a negative-valued lower bound is consistent with our data, which maintains the possibility of the true CDE being zero.\u003c/p\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003eLimitations\u003c/h2\u003e\u003cp\u003eThe use of the parametric g-formula at small sample sizes carries limitations. Few studies have evaluated the performance of the parametric g-formula estimator in small sample sizes (n\u0026thinsp;\u0026le;\u0026thinsp;100). Tackney and colleagues (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e) examined the performance of the parametric g-formula estimator of the average treatment effect (ATE) of a point exposure on a continuous outcome. They examined the performance of the estimator when sample size was small (n\u0026thinsp;=\u0026thinsp;50 and n\u0026thinsp;=\u0026thinsp;100) and the model for the conditional mean of their outcome included a treatment variable, 17 covariates (which were all predictive of the outcome), and interactions between treatment and all covariates. Provided all confounders have been accounted for, their results indicate that whilst the estimator had a mean bias close to zero, but there was suboptimal coverage (approximately 90% at either sample size) which were due to the model-based standard errors underestimating the empirical standard error. Coverage was further reduced when including four additional covariates that were unpredictive of the outcome. These findings regarding suboptimal coverage are supported by Chatton and colleagues (\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e) who evaluated the performance of the parametric g-formula estimator of the average treatment effect of a point exposure when the outcome was binary, sample size was 100, and the outcome model included 9 covariates (6 were predictive of the outcome) and the treatment variable. Assuming correct model specification, their results indicated that the estimator had a mean bias close to zero but coverage was suboptimal at 91.8%; reducing the number of covariates appeared to shift the coverage probability closer towards the desired 95% probability. Small sample corrections such as BCa bootstrap have thus been proposed to improve coverage (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eA limitation of the CDE is that all participants are always set to adhere through some conceivable intervention. This may not be realistic as interventions should allow treatment to be discontinued at any point when a participant experiences a clinical event that jeopardises their safety. Relevant events in the context of metformin would be elevated lactate concentrations, hypoglycaemia, and severe renal impairment. One strategy would have been to conceive of a \u003cem\u003edynamic\u003c/em\u003e intervention on adherence that allows for non-adherence when participant safety is compromised at any point during follow-up (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e). Given that the incidence rates of elevated lactate concentrations, hypoglycaemia, and severe renal impairment following metformin use are low based from previous reports and our observations (\u003cspan additionalcitationids=\"CR36\" citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e), it may be reasonable to interpret our effect as a close approximation to the effect under this dynamic intervention on adherence.\u003c/p\u003e\u003cp\u003eWe observed a relatively wider confidence interval of the CDE compared that of the trial\u0026rsquo;s ITT and PP effects. One possible reason could be that controlled direct effects estimated by the parametric g-formula have greater sample size requirements for the same level of precision because of the added modelling assumptions. A previous study conducted a secondary analysis of a placebo-controlled trial to investigate the per-protocol effect of complete adherence to low-dose aspirin at preconception to improve live births amongst 1,227 women with documented pregnancy losses and were actively trying to conceive (\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e). Compared to the trial\u0026rsquo;s ITT effect of a relative risk of live birth of 1.10 [95% CI 0.98, 1.22], the parametric g-formula estimate of the per-protocol effect in which all participants adhered was 1.33 [95% CI 1.08, 1.64]; an approximately two-fold increase in the width of the confidence interval on the log relative risk scale. Another reason could be that at the given sample size the models were overfitted to the data. However, Tackney and colleagues (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e) showed by simulation that even at a fixed sample size of 50, increasing the number of covariates or even adding interaction terms between treatment all covariates did not substantially change the model-based standard error or empirical standard error of the parametric g-formula estimator of the ATE of a point exposure on a continuous outcome. Further work could be developed to investigate if this also extends to mediation analyses.\u003c/p\u003e\u003c/div\u003e"},{"header":"Conclusions","content":"\u003cp\u003eOur study allowed us to draw out lessons for trialists. We highlighted the parametric g-formula as a useful method in trials to target hypothetical estimands that are concerned with treatment adherence. Our study shines a light on two contexts in which targeting a hypothetical estimand based on adherence is meaningful.\u003c/p\u003e\u003cp\u003eFirstly, efficacy trials may benefit most whereby maximising adherence is important so as not to miss a possible benefit of treatment. Meeting the threshold for adherence for all participants in an efficacy trial setting could possibly be reached perhaps by introducing an initial titration period (\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e) plus raising awareness amongst participants about the nocebo effect i.e. a portion of GI adverse events may be attributable to negative expectations about the medicine rather than a pharmacological effect (\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e). Other strategies may also include patient education and counselling (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e), shared decision-making between clinicians and patients (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e), dose adjustment (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e), use of extended release formulations (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e), and lifestyle adaptations (e.g., time medication intake around meals (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e)). However, in effectiveness trials, it is much more important that the trial conditions reflect how the drug will be used in the real world, so if low adherence is going to be an issue in clinical practice, seeing this in the trial is preferable and thus there may not be much to be gained from targeting an adherence-based hypothetical estimand.\u003c/p\u003e\u003cp\u003eSecondly, while there may be no substitute for efforts to actually maximise adherence at the design and implementation stages, methods such as the parametric g-formula to target adherence-based hypothetical estimands may be the best alternative when maximising adherence is challenging in practice. If there is an a priori interest in the treatment effect under an ideal circumstance of unanimous adherence, then there may be a need to build in an analysis to estimate the CDE at the trial design stage as it may influence sample size. Generally, closed form solutions are not readily available for causal effects thus Monte Carlo simulation will be needed (\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e).\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe MET-PREVENT trial was funded by the NIHR Newcastle Biomedical Research Centre. Additional funding for mechanistic analyses were provided as a philanthropic gift by Mr Alan Halsall. MDW, AAS, and CMcD acknowledge support from the NIHR Newcastle Biomedical Research Centre.\u0026nbsp;JMSW is funded by a NIHR Research Professorship (NIHR301614). The views expressed are those of the author(s) and not necessarily those of the NIHR or the Department of Health and Social Care.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthical approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll participants provided their informed consent.\u0026nbsp;The trial was approved by the UK Health Research Authority North-West - Liverpool Central Research Ethics Committee (20/NW/0470) and the UK Medicines and Healthcare products Regulatory Agency (2020-004023-16). The trial was sponsored by the Newcastle Upon Tyne Hospitals NHS Foundation Trust.\u0026nbsp;The trial complied with the ethical standards laid down in the 1964 Declaration of Helsinki and its later amendments.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNone to declare.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eData can be shared upon reasonable request to the NIHR Newcastle Biomedical Research Centre by contacting Professor Miles Witham (Chief Investigator): [email protected].\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication:\u0026nbsp;\u003c/strong\u003eNot applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026rsquo; contributions\u003c/strong\u003e:\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eConception and design\u003c/em\u003e: SH, NW, NL, KW, JMSW\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eAcquisition, analysis\u003c/em\u003e: SH, NW, MDW\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eInterpretation of data\u003c/em\u003e: all authors\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eDrafting\u003c/em\u003e\u003cstrong\u003e:\u0026nbsp;\u003c/strong\u003eSH\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eCritical revision of draft\u003c/em\u003e: all authors\u003c/p\u003e\n\u003cp\u003eAll authors have approved the submitted version\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e: we thank the participants in the MET-PREVENT trial and members of the Trial Management Group who are not in the co-authorship list.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eYe CL, Beyene J, Browne G, Thabane L. Estimating treatment effects in randomised controlled trials with non-compliance: a simulation study. Bmj Open. 2014;4(6).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eVanderweele TJ. Controlled Direct and Mediated Effects: Definition, Identification and Bounds. Scand J Stat. 2011;38(3):551\u0026ndash;63.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBanack HR, Mayeda ER, Naimi A, Fox MP, Whitcomb BW. Collider Stratification Bias I: Principles and Structure. Am J Epidemiol. 2024;193(2):238\u0026ndash;40.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eHern\u0026aacute;n MA, Robins JM. Per-Protocol Analyses of Pragmatic Trials. New Engl J Med. 2017;377(14):1391\u0026ndash;8.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNaimi AI, Cole SR, Kennedy EH. An introduction to g methods. 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Clin Diabetes. 2019;37(3):234\u0026ndash;41.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLee DSU, Lee H. Adherence and persistence rates of major antidiabetic medications: a review. Diabetol Metab Syndr. 2022;14(1).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSmaje A, Weston-Clark M, Raj R, Orlu M, Davis D, Rawle M. Factors associated with medication adherence in older patients: A systematic review. Aging Med (Milton). 2018;1(3):254\u0026ndash;66.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eYap AF, Thirumoorthy T, Kwan YH. Systematic review of the barriers affecting medication adherence in older adults. Geriatr Gerontol Int. 2016;16(10):1093\u0026ndash;101.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eAndrews AW, Vallabhajosula S, Boise S, Bohannon RW. Normal gait speed varies by age and sex but not by geographical region: a systematic review. 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A comparison of covariate adjustment approaches under model misspecification in individually randomized trials. Trials. 2023;24(1).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLin SH, Young J, Logan R, Tchetgen EJT, VanderWeele TJ. Parametric Mediational g-Formula Approach to Mediation Analysis with Time-varying Exposures, Mediators, and Confounders. Epidemiology. 2017;28(2):266\u0026ndash;74.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eRudolph JE, Cartus A, Bodnar LM, Schisterman EF, Naimi AI. The Role of the Natural Course in Causal Analysis. Am J Epidemiol. 2022;191(2):341\u0026ndash;8.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eFox MP, MacLehose RF, Lash TL. Applying Quantitative Bias Analysis to Epidemiologic Data [Internet]. Switzerland: Springer Cham; 2021. 2nd. [291\u0026ndash;327]. Probabilistic Bias Analysis for Simulation of Record-Level Data.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eHunnicutt JN, Ulbricht CM, Chrysanthopoulou SA, Lapane KL. Probabilistic bias analysis in pharmacoepidemiology and comparative effectiveness research: a systematic review. Pharmacoepidem Dr S. 2016;25(12):1343\u0026ndash;53.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eHawkins AT, Samuels LR. Use of Confidence Intervals in Interpreting Nonstatistically Significant Results. Jama-J Am Med Assoc. 2021;326(20):2068\u0026ndash;9.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLoeys T, Moerkerke B, Raes A, Rosseel Y, Vansteelandt S. Estimation of Controlled Direct Effects in the Presence of Exposure-Induced Confounding and Latent Variables. Struct Equ Model. 2014;21(3):396\u0026ndash;407.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eIgelstr\u0026ouml;m E, Craig P, Lewsey J, Lynch J, Pearce A, Katikireddi SV. 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G-computation, propensity score-based methods, and targeted maximum likelihood estimator for causal inference with different covariates sets: a comparative simulation study. Sci Rep-Uk. 2020;10(1).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eYoung JG, Cain LE, Robins JM, O'Reilly EJ, Hernan MA. Comparative effectiveness of dynamic treatment regimes: an application of the parametric g-formula. Stat Biosci. 2011;3(1):119\u0026ndash;43.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBodmer M, Meier C, Krahenbuhl S, Jick SS, Meier CR. Metformin, sulfonylureas, or other antidiabetes drugs and the risk of lactic acidosis or hypoglycemia: a nested case-control analysis. Diabetes Care. 2008;31(11):2086\u0026ndash;91.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eChristiansen CF, Ehrenstein V, Heide-Jorgensen U, Skovbo S, Norrelund H, Sorensen HT, et al. Metformin initiation and renal impairment: a cohort study in Denmark and the UK. Bmj Open. 2015;5(9):e008531.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSalpeter SR, Greyber E, Pasternak GA, Salpeter EE. Risk of fatal and nonfatal lactic acidosis with metformin use in type 2 diabetes mellitus. Cochrane Db Syst Rev. 2010(4).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNaimi AI, Perkins NJ, Sjaarda LA, Mumford SL, Platt RW, Silver RM, et al. The Effect of Preconception-Initiated Low-Dose Aspirin on Human Chorionic Gonadotropin-Detected Pregnancy, Pregnancy Loss, and Live Birth Per Protocol Analysis of a Randomized Trial. Ann Intern Med. 2021;174(5):595\u0026ndash;.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBonnet F, Scheen A. Understanding and overcoming metformin gastrointestinal intolerance. Diabetes Obes Metab. 2017;19(4):473\u0026ndash;81.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eMichnevich T, Pan Y, Hendi A, Oechsle K, Stein A, Nestoriuc Y. 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Am J Epidemiol. 2020;189(12):1559\u0026ndash;67.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"trials","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"trls","sideBox":"Learn more about [Trials](http://trialsjournal.biomedcentral.com/)","snPcode":"13063","submissionUrl":"https://www.editorialmanager.com/trls","title":"Trials","twitterHandle":"MedicalEvidence","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Estimands, Causal inference, G-formula, Mediation, Secondary analysis, Quantitative bias analysis","lastPublishedDoi":"10.21203/rs.3.rs-6037689/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6037689/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eBackground\u003c/h2\u003e\u003cp\u003eWe conducted a post hoc secondary analysis of the MET-PREVENT randomised placebo-controlled trial to target a hypothetical estimand \u0026ndash; the mean difference in physical performance, as measured by the 4-metre walk speed at four months after randomisation, between treatment arms \u0026ndash; under the hypothetical scenario that all participants adhered to assigned treatment.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e\u003cp\u003eWe viewed the targeting of this hypothetical estimand as a type of causal mediation problem, where randomisation is a binary exposure, adherence is a binary mediator, there is an exposure-mediator interaction, and mediator-outcome confounders that are caused by the exposure (e.g., gastrointestinal symptoms) are present. We used the parametric g-formula to estimate the average controlled direct effect (CDE) of metformin (versus placebo) on 4-metre walk speed, which is interpreted as the average treatment effect under the hypothetical scenario that all trial participants adhered to assigned treatment. Variables identified as confounders were informed by a literature review and discussions with an expert; assumptions about the causal structure were represented in a directed acyclic graph. We applied a probabilistic bias analysis (PBA) to understand the potential for bias assuming adherence had been misclassified; observed adherence based on returned tablet count may be an inaccurate version of \u0026ldquo;true adherence\u0026rdquo; based on actual consumption.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e\u003cp\u003e Our sample size was 70 trial participants (34 metformin, 36 placebo). Our estimate of the CDE was 0.072 [percentile-based bootstrap 95% CI -0.292, 0.445]. Results from PBA indicated that the greater the extent of misclassification, the more the CDE may be estimated with bias and with over-optimistic precision.\u003c/p\u003e\u003ch2\u003eConclusions\u003c/h2\u003e\u003cp\u003eOur study provided supporting information on metformin\u0026rsquo;s potential role as a repurposed medication to improve physical performance in nondiabetic older adult patients with physical prefrailty/frailty and probable sarcopenia. Unlike the main trial results, our results do not rule out the possibility of a meaningful benefit of metformin, provided that full adherence can be assured. We highlighted the parametric g-formula as a useful method in trials to target hypothetical estimands that are concerned with treatment adherence.\u003c/p\u003e\u003ch2\u003eTrial registration\u003c/h2\u003e\u003cp\u003eISRCTN29932357, registered 21st January 2021\u003c/p\u003e","manuscriptTitle":"Targeting a hypothetical estimand based on adherence with the parametric g-formula: A post hoc secondary analysis of the MET-PREVENT randomised controlled trial","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-03 06:39:40","doi":"10.21203/rs.3.rs-6037689/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Minor revision","date":"2025-10-19T19:22:59+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"","date":"2025-08-29T06:00:02+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-08-26T13:50:44+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-04-28T10:28:38+00:00","index":"","fulltext":""},{"type":"submitted","content":"Trials","date":"2025-02-15T11:47:34+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"trials","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"trls","sideBox":"Learn more about [Trials](http://trialsjournal.biomedcentral.com/)","snPcode":"13063","submissionUrl":"https://www.editorialmanager.com/trls","title":"Trials","twitterHandle":"MedicalEvidence","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"63e23efa-eecc-4430-90b7-5a3aaed286a5","owner":[],"postedDate":"September 3rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-04-13T16:07:50+00:00","versionOfRecord":{"articleIdentity":"rs-6037689","link":"https://doi.org/10.1186/s13063-026-09708-1","journal":{"identity":"trials","isVorOnly":false,"title":"Trials"},"publishedOn":"2026-04-10 15:57:04","publishedOnDateReadable":"April 10th, 2026"},"versionCreatedAt":"2025-09-03 06:39:40","video":"","vorDoi":"10.1186/s13063-026-09708-1","vorDoiUrl":"https://doi.org/10.1186/s13063-026-09708-1","workflowStages":[]},"version":"v1","identity":"rs-6037689","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6037689","identity":"rs-6037689","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}