Efficacy Assessment in Trials of Complex and Rare Diseases: A Comparison Between the Meta-Analytic Global Statistical Test and Co-Primary Analysis

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Dickson, Abe Durrant, Caleb W. Dayley, Joshua R. Christensen, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5194792/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Background: Complex and rare diseases often have heterogeneous symptoms, which complicates the selection of an appropriate primary outcome because outcome assessments rarely capture all aspects of disease. Disease-modifying treatments (DMTs) are expected to affect all disease domains, and even symptomatic treatments can affect multiple aspects of disease; therefore, a single outcome will rarely be sufficient to measure the success of a treatment. To address this issue, regulatory bodies often suggest co-primary endpoints. However, obtaining statistical significance on two outcomes is a much stricter requirement, which could create additional hurdles for effective treatments. Global statistical test (GST) combines multiple outcomes into a single score and could provide a viable alternative to the co-primary approach. Importantly for rare diseases, combining multiple assessments reduces the risk of selecting a poor outcome simply because it has not been studied as extensively as those for more common diseases. Here we compare GST to single primary and co-primary methodologies using simulations of a crossover study with two outcomes that may be moderately or highly correlated using several effect sizes. Results: For the same effect size on both outcomes, GST had greater power than single primary and co-primary approaches, regardless of the correlation level between outcomes. This was also true with different effect size combinations at the same correlation level. With an effect observed on one outcome only, GST was more likely to yield statistical significance than theco-primary approach. Unlike the co-primary approach, The GST yielded lower p-values in scenarios with lower correlation between the outcomes. Conclusions: GST favors independent information (ie, outcomes with moderate or poor correlation), does not reduce statistical power, and is not overtly permissible in cases of null effect on one of the outcomes. Compared to co-primary endpoints, the higher statistical power of GST is especially suited for rare diseases withsample size limitation. GST is a viable approach in analyzing data from heterogeneous outcomes and should be considered over co-primary approaches, especially for treatments that target multiple aspects of the disease or multiple symptoms. Clinical trials rare disease complex disease Global Statistical Test (GST) co-primary endpoints Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Background Numerous conditions, both common and rare, present with a variety of clinically relevant signs and symptoms, posing a challenge in selecting the most appropriate primary outcome for a clinical trial. A common form of addressing this challenge is to designate two or more outcomes as co-primary, requiring a statistically significant result for each outcome in order to declare success [ 1 , 2 ]. This approach, while convenient when making labeling decisions for treatments that can only alleviate specific symptoms, requires a significant burden on the patient population in the form of larger sample sizes, longer development times, and an increased risk of failure to receive otherwise promising treatments. The difficulty of showing a successful treatment effect in a trial with co-primary outcomes is compounded when the selected outcomes evaluate relatively independent aspects of the disease. This may be desirable when a highly comprehensive assessment of the treatment effect is needed, but it is also similar to the requirement of conducting independent trials, one for each primary outcome. There are several disease-specific scenarios in which it is justified to combine outcomes into a single composite measure, with the benefit of preserving statistical power. In diseases with a slowly progressing pathology, earlier administration of a disease-modifying therapy (DMT) has a greater potential to provide clinical benefit. However, by definition, measurable signs and symptoms at the earliest stages of the disease are the weakest, which translates into effect sizes that can be modest at best. In addition, disease presentation can vary substantially between individuals. Therefore, use of co-primary outcomes in these trials may result in unjustified trial failures and in dismissal of actual promising treatments. Similarly, in rare diseases with a multitude of clinically relevant signs and symptoms and a heterogeneous presentation across affected individuals, it can be challenging to select the best assessment to capture the benefits of a candidate treatment. Even for symptomatic treatments, the treatment may be expected to benefit aspects of the disease that cannot be captured adequately by a single assessment. Additionally, a candidate treatment can affect domains of the disease in ways that cannot be anticipated without conducting a dedicated, well-controlled clinical trial. Therefore, studies in patient populations with these attributes could benefit from a carefully selected composite outcome, which would maximize the probability of capturing the effect of a treatment in most participants. Global statistical tests (GSTs) were introduced in 1984 [ 3 ] and combine results from multiple endpoints into a single estimate, single confidence interval, and a single p-value. In a GST, the assumption is that the outcomes being combined are caused by the same pathology and that they all contribute to the strength of evidence. Therefore, with properly selected component outcomes (which could include various primary, secondary, and exploratory measures, or their subsets), a GST could be an objective way to aggregate the information and assess the total level of evidence for a treatment effect [ 4 ]. Commonly used versions of the GST reduce the contribution of items that are correlated or measure overlapping information, which reduces the risk of inflating the strength of evidence. The extent of this correlation can be parameter- or disease-specific and should be known in advance. For example, in healthy individuals, the correlation coefficient between forced expiratory volume in 1 second (FEV1) and forced vital capacity (FVC) can be as high as 0.96 [ 5 ]. In comparison, correlation coefficients between plasma and brain biomarkers in a recent trial in early Alzheimer’s disease (AD) ranged from approximately 0.2 to 0.5 [ 6 ]. The purpose of this simulation study was to compare a GST model comprising two outcomes versus a co-primary analysis of the same outcomes in terms of changes in statistical power and the permissible type I error. Methods Global statistical tests The original GST (O’Brien 1984) was non-parametric and used a summed rank score across endpoints, resulting in a range of scores that increased with additional endpoints and with larger sample sizes. Parametric versions have also been developed, based on ordinary least squares and generalized least squares [ 5 , 8 ]. A meta-analytic GST (MGST) has also been proposed [ 8 ], in which evidence is combined by calculating the joint probability of observing two test statistics simultaneously after accounting for the average correlation between each pair of endpoints. This approach allows the integration of results from different analytic approaches (eg, response rate, mean change, or survival time), provided a correlation, or another measure of overlapping information, is established. The formula for the MGST follows a standard normal distribution: \(\:MGST=\frac{\underset{\_}{z}}{{\left\{\right[1+\left(k-1\right)\rho\:]/k\}\:}^{1/2}}\sim\:N(0,\:1)\) , where \(\:\underset{\_}{z}\) is the average of the z-score test statistics from the hypothesis test for each endpoint, after ensuring that the directionality of all endpoints is the same, \(\:\rho\:\) is the average correlation across each pair of outcomes, and \(\:k\) is the number of outcomes being combined The one-sided p-value for the MGST is calculated as the cumulative probability associated with the test statistic in the direction of the alternative hypothesis. In contrast, co-primary analysis involves a separate assessment of statistical significance on each endpoint, and evidence of efficacy is typically based on statistical significance on both co-primary endpoints. Simulation study To compare GST analysis to co-primary analysis, a simulation was performed to mimic a theoretical clinical trial that evaluates an investigational therapy in patients with a rare, complex, and heterogenous disease. This theoretical clinical trial has a crossover design that includes two treatment sequences, placebo-to-active and active-to-placebo, with 16 participants in each (N = 32), and two outcomes. Washout between treatments was assumed to be fully effective. Each treatment assumed a single observation per outcome. For each outcome, correlation between observations of the same patient within a treatment sequence was assumed to be 0.5. In the null hypothesis scenario, the effect size for each co-primary outcome was assumed to be 0. Since effect sizes can differ substantially between the co-primary outcomes, we examined various Cohen’s d values (drug versus placebo) at various mean-to-standard-deviation ratios (MSDRs) of placebo treatment. For our simulation, we selected Cohen’s d values in the range from 0.27 to 0.54 and simplified them into approximate values of 0.3, 0.4, and 0.5 (Table 1 ). Table 1 Cohen’s d values (drug versus placebo) versus different MSDRs during placebo treatment. MSDR Improvement in symptoms, drug vs placebo, % 20 30 40 50 60 70 80 90 100 0.3 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27 0.30 0.4 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.5 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.6 0.12 0.18 0.24 0.30 0.36 0.42 0.48 0.54 0.60 0.7 0.14 0.21 0.28 0.35 0.42 0.49 0.56 0.63 0.70 0.8 0.16 0.24 0.32 0.40 0.48 0.56 0.64 0.72 0.80 0.9 0.18 0.27 0.36 0.45 0.54 0.63 0.72 0.81 0.90 1.0 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 MSDR, mean-to-standard-deviation ratio. Highlighted values represent low-middle to high-middle range values, which aggregate around 0.3 (blue), 0.4 (orange), and 0.5 (green). Within each combination of effect sizes, two levels of correlation between outcomes were used: 0.9 (strong) and 0.4 (moderate). Overall, this resulted in 32 scenarios, based on two co-primary outcomes, four effect sizes (0, 0.3, 0.4, and 0.5), and two correlation levels between the outcomes (0.9 and 0.4). For each scenario, we generated 10,000 simulated data sets. Data Analysis Data obtained using simulation procedures were analyzed for a single primary endpoint, for the co-primary endpoints, and for the composite MGST endpoint, all with a 2-sided alpha of 0.10. The main analysis considered the entire treatment sequence. We also conducted an auxiliary analysis, which only considered the first treatment period in each sequence. Note that while this analysis uses a 2-sided alpha of 0.10 in the crossover design, all results presented generalize to a 2-sided alpha of 0.05. In the main analysis, test statistics and p-values were obtained from a mixed-effects model with repeated measures (MMRM), the standard analytic approach for trials with longitudinal continuous outcomes, and then used it to derive the MGST estimates via the formula above. The MMRM used to obtain the T-ratios included treatment (not treatment sequence) as a fixed effect and random intercepts by participant. In the auxiliary analysis, test statistics for the single primary endpoint and for the co-primary analysis were calculated via t-test, because there were no repeated measures. The MGST was derived using the formula above. For each scenario, we calculated the power of observing a treatment effect as well as the adjustment needed for the type I error, based on the percentage of simulated data sets in which the result was statistically significant. Results No correlation scenario In an extreme case of zero correlation between outcomes, the true alpha level for a co-primary analysis could be calculated by multiplying the one-sided alpha levels from each test (eg, 0.05 x 0.05 = 0.0025). In a study powered at 80% for a single endpoint, a co-primary analysis would have the power of only 64% for the same effect size on both endpoints. Main analysis: Highly correlated outcomes (r = 0.9), Cohen’s d = 0.5 First, we examined the spread of our simulated data when a significant result was required on a single primary outcome only (x-axis). As expected, with no effect, the T-ratios were symmetrically distributed around the zero value, with a compressed distribution cloud, indicative of a high correlation (0.9; Fig. 1 A) with the other outcome (y-axis). With a 2-sided alpha of 0.10, there was a 5% probability of declaring a significant treatment benefit by chance, which corresponds with the dots in the blue-shaded area. When a significant result was required for the other outcome, too (ie, when the two outcomes were co-primary), the pool of possible significant results declared by chance was reduced below 5%, corresponding with stricter standards (Fig. 1 B). In the null scenario, the pool of significant benefit outcomes declared by chance using MGST methodology was equal to the number permissible with a single primary outcome (Fig. 1 C, yellow-shaded area). With a true and similar effect on both outcomes (Cohen’s d = 0.5), the distribution of simulated datasets shifted up and to the right from the zero point. With a high correlation, most of the outcomes considered significant in MGST were also significant in the co-primary analysis (Fig. 2 ), ie, with a small difference in power (88% vs 83%) and with a small adjustment in Type I error (0.05 to 0.03) (Table 2 ). Main Analysis: Moderately Correlated Outcomes (r = 0.4), Cohen’s d = 0.5 In this scenario, the distribution cloud was notably more dispersed, resulting in substantially more inconsistencies between the two endpoints (Fig. 3 A), even when they both had a relatively strong true treatment effect (Fig. 3 B). Statistical significance in a co-primary analysis required a Type I error adjustment from 0.05 to 0.007, and the power (versus MGST) was reduced from 95–77% (Table 2 ). Table 2 Power and Type 1 error (alpha) for co-primary and MGST analysis, by correlation level (full treatment duration, Cohen’s d = 0.5 for both outcomes) Correlation (r) Co-primary endpoints MGST 0.9 Power 83% 88% α 0.03 0.05 0.4 Power 77% 95% α 0.007 0.05 Main Analysis: High Correlation, True Treatment Effect on a Single Outcome Only (Cohen’s d = 0.5) With only a single outcome showing a true effect, and with a Cohen’s d of 0.5, we would reject null hypothesis, in favor of treatment benefit, 87% of the time (Fig. 4 ). For the other outcome, with zero effect, the null hypothesis in favor of treatment benefit would be rejected 5% of the time, according to the two-sided alpha of 0.10. A coprimary analysis would consider such a trial a success in 5% of simulated datasets, compared with 41% of datasets in the MGST analysis (Fig. 4 ). Main Analysis: Moderate Correlation, Varied Treatment Effects In simulations in which treatment effects differed between the outcomes, power of the co-primary analysis was consistently lower than the power of the individual outcome with a lower effect size, whereas with MGST, power of the individual outcomes was either preserved or increased (Table 3 ). Table 3 Power at different effect sizes (full treatment duration, r = 0.4) Effect size (Cohen’s d ) Power Outcome 1 Outcome 2 Outcome 1 Outcome 2 Co-primary MGST 0.5 0.4 86% 72% 66% 91% 0.5 0.3 87% 51% 47% 85% 0.4 0.4 72% 72% 56% 85% 0.4 0.3 72% 50% 41% 75% Auxiliary Analysis: Moderate Correlation, Varied Treatment Effects When comparing just the first treatment periods of the two sequences (analyzed via t-test), we noticed the same pattern of power reduction with the co-primary analysis and preservation or increase of power when using MGST (Table 4 ). Of note, power in these scenarios was overall lower, because of the shorter treatment duration and the absence of repeated measures. Table 4 Power at different effect sizes (first treatment period only, r = 0.4) Effect size (Cohen’s d ) Power Outcome 1 Outcome 2 Outcome 1 Outcome 2 Co-primary MGST 0.5 0.5 40% 41% 22% 51% 0.5 0.4 39% 30% 17% 44% 0.5 0.3 40% 21% 13% 37% 0.4 0.4 30% 29% 14% 37% 0.4 0.3 29% 21% 10% 31% MGST: Relationship between outcome correlation and p-value Different levels of correlation between the outcomes change the amount of unique information each outcome contributes to the MGST, which affects the p-value calculated in a statistical test. For example, if the p-value calculated separately for each outcome is 0.07, the p-values calculated using MGST would range from 0.0681 for a nearly perfect correlation (r = 0.98) to 0.017 when a correlation is entirely absent (r = 0) (Fig. 5 ). In other words, by its design, an MGST-based hypothesis test “awards” a lower p-value to the evidence obtained from more independent outcomes, which aligns with the way evidence is usually judged, and which is a feature that the co-primary analysis does not possess. Discussion In this simulation study, we explored the relationship between outcome correlation, statistical power, and type I error control when evaluating two study outcomes simultaneously. In line with previous findings, our MGST approach preserved the power, compared with the overly restrictive type I error control of a co-primary analysis approach. We also illustrated how hypothesis testing via MGST considers the degree of correlation between outcomes and provides a differentiation (via p-value) between stronger and weaker aggregated evidence (ie, the one obtained from more versus less independent outcomes). Because of its combining of standardized z-scores across two or more outcomes, GST can be viewed as an assessment of a global treatment effect, which describes the disease, or a treatment effect, from the perspective of a single score. We argue that this is a key strength of GST, which, if deployed properly, should go hand in hand with the analysis of specific symptoms or disease domains. With multifaceted medical conditions, both common and rare, it may be too restrictive to impose the requirements of a co-primary analysis, which can severely limit the permissible level of type I error and substantially increase the demand for study participants, because of a reduction in power. This requirement for very high specificity (ie, very low type I error) in combination with a loss of power can be particularly challenging for the study of rare diseases, which are often multifaceted in symptoms and have a very small pool of potential trial participants. In addition, small samples are more prone to mean values being affected by extreme results, both high and low, thereby making it even more challenging to observe a true treatment effect. Outcomes like GST can temper these extreme results into a single summary that, compared with the co-primary approach, can be better in both detecting effective treatments and rejecting ineffective ones, especially when endpoints have low correlation. For these reasons, we advocate for incorporating, or at the very least thoroughly considering a GST model in the statistical plan of trials in which assessing multiple outcomes as primary would be appropriate. Such a prespecified analysis, combined with a sequential testing of individual outcomes, may strike an optimal balance between type I and type II error, between preventing ineffective therapies from reaching the market and approving those that would address patients’ needs. This approach can be envisioned for treatments developed for rare or certain complex diseases, in which simultaneous assessment of two or more outcomes is deemed appropriate. Of course, strict requirements regarding study design and conduct would always apply, and sensitivity analyses could be deployed to test the GST assumptions or utility in a specific situation. Of note, statistical studies using data from published trials on Parkinson’s disease (PD), rheumatoid arthritis, and stroke all came to a conclusion that the GST was well suited for analyzing multiple outcomes [ 9 , 10 , 11 ]. In all three cases, the underlying hypothesis is that the treatment has an overall impact on the disease, which would be better reflected on a composite scale of multiple outcomes. The PD study group emphasized that the multidimensional nature of PD impairments makes multivariate statistical methods ideal for evaluating treatment effects on long-term decline. Their comparison of GST to other multivariate approaches using data from two PD trials concluded that GST is particularly effective in conditions that affect multiple systems and functions, and in which both disease and treatment side effects impact quality of life [ 9 ]. In an acute stroke trial, the definition of treatment success was based on consistent and persuasive differences in the proportion of patients achieving favorable outcomes on 4 different scales, supporting GSTs appropriateness for such trials [ 11 ]. In 2012, a long-term PD trial, the National Institute of Neurological Disorders and Stroke exploratory trials in Parkinson's Disease Long-Term Study–1, announced the use of the GST approach in its design, which encompasses five clinical rating scales for the assessment of disease progression [ 12 ]. Furthermore, composite outcomes like GSTs have been used in early AD clinical trials. The recently approved DMTs donanemab and lecanemab both used composite scores, which are conceptually similar to GSTs, as primary outcomes in their clinical trials: donanemab used the composite score, iADRS, as its primary outcome in its phase 2 and 3 trials [ 13 ], [ 14 ] and lecanemab used the composite score ADCOMS as its primary outcome for its phase 2 trial [ 15 ]. A key limitation of GSTs could be formulated as granting an unfair advantage: it inflates the power of individual outcomes, and the more outcomes are included in the model, the likelier it will be to declare a significant treatment effect. Indeed, this would be the case when each outcome is picking up a signal of similar magnitude (eg, Table 2 ), but not in the situation when outcomes show treatment effects of different magnitude (Table 3 ), or, importantly, when a significant effect can be observed on a single outcome only. In these situations, adding outcomes without a true treatment effect would make it less likely for a GST to detect a statistically significant result. Finally, it is important to align the outcomes selected for the GST with the prespecified outcome hierarchy. A GST combining primary and key secondary endpoints would be a reasonable first step, followed by another GST, combining primary, key secondary, and other secondary endpoints. Combining primary endpoints across studies could also be a useful GST application, even with primary endpoints that arose from different analytic approaches. Conclusion Using GST as a prespecified statistical tool in trials where assessing multiple primary outcomes is warranted could provide a formal and objective approach to aggregating evidence for a treatment effect. This would be of particular importance for multidimensional and heterogeneous rare diseases, or those that have prodromal stages with small initial decline. While regulatory authorities may feel greater responsibility to protect type I error, thus preventing ineffective treatments from reaching market, it should be kept in mind that this doesn’t come without a cost, in form of unjustified dismissal of truly promising therapeutics. In our opinion, further exploration of this statistical approach is both merited and needed. Abbreviations AD: Alzheimer’s disease DMT: Disease-modifying therapy GST: Global statistical test MGST: Meta-analytic global statistical test OLS: Ordinary least squares GLS: Generalized least squares FEV1: Forced expiratory volume in 1 second FVC: Forced vital capacity MSDR: Mean-to-standard-deviation ratio MMRM: Mixed-effects model with repeated measures PD: Parkinson’s disease Declarations Ethics approval and consent to participate Not applicable Consent for publication Not applicable Availability of data and materials All data generated or analyzed during this study are included in this published article. Competing interests All the authors are employees of Pentara Corporation. SBH is also the CEO and owner of Pentara Corporation, which provides statistical consulting and clinical data management services to pharmaceutical companies, especially in neurodegenerative disease area. Funding This project was funded by Tisento Therapeutics. Authors' contributions SPD and AD wrote the first draft. AD, CWD, and JRC performed the stimulation study and generated the data tables and figures. SPD, CHM, and SBH validated the results, revised the manuscript. SPD and SBH supervised this project. All authors read and approved the final manuscript. Acknowledgements Vojislav Pejovic, PhD (Clef Communications) and Chenge Zhang, PhD (Pentara Corporation) provided medical writing and editorial support for the preparation of this manuscript. Patrick O’Keefe and Angie Goldsberry from Pentara Corporation reviewed and revised this manuscript. 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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-5194792","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":431723764,"identity":"31856b03-c858-4f6f-a0b2-24c951a530ce","order_by":0,"name":"Samuel P. Dickson","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3ElEQVRIiWNgGAWjYFCCxAbGBiDFT7oWSRBxgDgtCQxgLQYHiNUi357c+HHGH5s849vNxx5/qLknz8B++OgGfFoMzjxsltzYllZsdudYusGBY8WGDTxpaTfwapFIbGN82HA4cduNHDOJA2wJjA0SPGZ4tcjPAGp58Odw4uYZ+d8kDvxLsCeoheEGUMsGtsOJGyRy2CQOtiUkEtQC9svMtrTEGXeOmUmc7UtIbiPkF/n29Icfe/7YJPbPbn4mUfEtwbaf/fAx/A6DAwkozUaccmQto2AUjIJRMArQAQCMi1O/uzp3TgAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-4622-1349","institution":"Pentara Corporation","correspondingAuthor":true,"prefix":"","firstName":"Samuel","middleName":"P.","lastName":"Dickson","suffix":""},{"id":431723765,"identity":"ab324ece-e804-4436-b551-5c70e664b097","order_by":1,"name":"Abe Durrant","email":"","orcid":"","institution":"Pentara Corporation","correspondingAuthor":false,"prefix":"","firstName":"Abe","middleName":"","lastName":"Durrant","suffix":""},{"id":431723766,"identity":"1c7e1b00-08db-414e-9d7b-67bb6b59b2f6","order_by":2,"name":"Caleb W. Dayley","email":"","orcid":"","institution":"Pentara Corporation","correspondingAuthor":false,"prefix":"","firstName":"Caleb","middleName":"W.","lastName":"Dayley","suffix":""},{"id":431723767,"identity":"9bf23dc7-7255-449f-a0dd-0085b0f427ca","order_by":3,"name":"Joshua R. Christensen","email":"","orcid":"","institution":"Pentara Corporation","correspondingAuthor":false,"prefix":"","firstName":"Joshua","middleName":"R.","lastName":"Christensen","suffix":""},{"id":431723768,"identity":"9b54573e-2e46-43e7-91e5-e2f59f99d35c","order_by":4,"name":"Craig H. Mallinckrodt","email":"","orcid":"","institution":"Pentara Corporation","correspondingAuthor":false,"prefix":"","firstName":"Craig","middleName":"H.","lastName":"Mallinckrodt","suffix":""},{"id":431723769,"identity":"ab66e359-c25b-4654-9a56-0f7753169af3","order_by":5,"name":"Suzanne B. Hendrix","email":"","orcid":"","institution":"Pentara Corporation","correspondingAuthor":false,"prefix":"","firstName":"Suzanne","middleName":"B.","lastName":"Hendrix","suffix":""}],"badges":[],"createdAt":"2024-10-02 20:18:51","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5194792/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5194792/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":79660204,"identity":"823fdceb-e775-447b-b1de-4cd86ae47b09","added_by":"auto","created_at":"2025-04-01 09:30:36","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":915065,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of simulated outcomes with no treatment effect on either outcome (full treatment duration, r=0.9)\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5194792/v1/1eb95f363f78ee2fed786488.png"},{"id":79660209,"identity":"4b05e1e9-5c32-4e29-8d11-d1172afc9ed6","added_by":"auto","created_at":"2025-04-01 09:30:36","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":225252,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of simulated outcomes with strong treatment effect on both outcomes (full treatment duration, r=0.9)\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5194792/v1/3f6264931a46463ab1e03008.png"},{"id":79660210,"identity":"2590bb42-a45b-4505-9738-59154c3ebdb6","added_by":"auto","created_at":"2025-04-01 09:30:36","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":609302,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of simulated outcomes with moderate correlation (full treatment duration, r=0.4)\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5194792/v1/23b53dcc757fbead86f5d964.png"},{"id":79660207,"identity":"4e3477a2-ba1e-4ab4-97e8-7947d1011e86","added_by":"auto","created_at":"2025-04-01 09:30:36","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":291325,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of simulated outcomes with treatment effect on a single outcome only (full treatment duration, r=0.9)\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5194792/v1/0199ac6d30c892044009cd15.png"},{"id":79661132,"identity":"ed63950b-5b4e-459e-b7e6-7f2cf7e2e269","added_by":"auto","created_at":"2025-04-01 09:38:36","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":132871,"visible":true,"origin":"","legend":"\u003cp\u003eImpact of outcome correlation on statistical testing using MGST\u003c/p\u003e\n\u003cp\u003eMGST, meta-analytic global statistical test.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-5194792/v1/2f47c3ea4dd09473925135cb.png"},{"id":81610188,"identity":"a0136891-baba-4583-bfe0-76d7830dfe60","added_by":"auto","created_at":"2025-04-29 06:53:51","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2971376,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5194792/v1/f2784567-115c-46ae-b96c-99a05ad9d54e.pdf"}],"financialInterests":"","formattedTitle":"Efficacy Assessment in Trials of Complex and Rare Diseases: A Comparison Between the Meta-Analytic Global Statistical Test and Co-Primary Analysis","fulltext":[{"header":"Background","content":"\u003cp\u003eNumerous conditions, both common and rare, present with a variety of clinically relevant signs and symptoms, posing a challenge in selecting the most appropriate primary outcome for a clinical trial. A common form of addressing this challenge is to designate two or more outcomes as co-primary, requiring a statistically significant result for each outcome in order to declare success [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. This approach, while convenient when making labeling decisions for treatments that can only alleviate specific symptoms, requires a significant burden on the patient population in the form of larger sample sizes, longer development times, and an increased risk of failure to receive otherwise promising treatments. The difficulty of showing a successful treatment effect in a trial with co-primary outcomes is compounded when the selected outcomes evaluate relatively independent aspects of the disease. This may be desirable when a highly comprehensive assessment of the treatment effect is needed, but it is also similar to the requirement of conducting independent trials, one for each primary outcome.\u003c/p\u003e \u003cp\u003eThere are several disease-specific scenarios in which it is justified to combine outcomes into a single composite measure, with the benefit of preserving statistical power. In diseases with a slowly progressing pathology, earlier administration of a disease-modifying therapy (DMT) has a greater potential to provide clinical benefit. However, by definition, measurable signs and symptoms at the earliest stages of the disease are the weakest, which translates into effect sizes that can be modest at best. In addition, disease presentation can vary substantially between individuals. Therefore, use of co-primary outcomes in these trials may result in unjustified trial failures and in dismissal of actual promising treatments.\u003c/p\u003e \u003cp\u003eSimilarly, in rare diseases with a multitude of clinically relevant signs and symptoms and a heterogeneous presentation across affected individuals, it can be challenging to select the best assessment to capture the benefits of a candidate treatment. Even for symptomatic treatments, the treatment may be expected to benefit aspects of the disease that cannot be captured adequately by a single assessment. Additionally, a candidate treatment can affect domains of the disease in ways that cannot be anticipated without conducting a dedicated, well-controlled clinical trial. Therefore, studies in patient populations with these attributes could benefit from a carefully selected composite outcome, which would maximize the probability of capturing the effect of a treatment in most participants.\u003c/p\u003e \u003cp\u003eGlobal statistical tests (GSTs) were introduced in 1984 [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] and combine results from multiple endpoints into a single estimate, single confidence interval, and a single p-value. In a GST, the assumption is that the outcomes being combined are caused by the same pathology and that they all contribute to the strength of evidence. Therefore, with properly selected component outcomes (which could include various primary, secondary, and exploratory measures, or their subsets), a GST could be an objective way to aggregate the information and assess the total level of evidence for a treatment effect [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eCommonly used versions of the GST reduce the contribution of items that are correlated or measure overlapping information, which reduces the risk of inflating the strength of evidence.\u003c/p\u003e \u003cp\u003eThe extent of this correlation can be parameter- or disease-specific and should be known in advance. For example, in healthy individuals, the correlation coefficient between forced expiratory volume in 1 second (FEV1) and forced vital capacity (FVC) can be as high as 0.96 [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. In comparison, correlation coefficients between plasma and brain biomarkers in a recent trial in early Alzheimer\u0026rsquo;s disease (AD) ranged from approximately 0.2 to 0.5 [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe purpose of this simulation study was to compare a GST model comprising two outcomes versus a co-primary analysis of the same outcomes in terms of changes in statistical power and the permissible type I error.\u003c/p\u003e"},{"header":"Methods","content":"\n\u003ch3\u003eGlobal statistical tests\u003c/h3\u003e\n\u003cp\u003eThe original GST (O\u0026rsquo;Brien 1984) was non-parametric and used a summed rank score across endpoints, resulting in a range of scores that increased with additional endpoints and with larger sample sizes. Parametric versions have also been developed, based on ordinary least squares and generalized least squares [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. A meta-analytic GST (MGST) has also been proposed [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], in which evidence is combined by calculating the joint probability of observing two test statistics simultaneously after accounting for the average correlation between each pair of endpoints. This approach allows the integration of results from different analytic approaches (eg, response rate, mean change, or survival time), provided a correlation, or another measure of overlapping information, is established.\u003c/p\u003e \u003cp\u003eThe formula for the MGST follows a standard normal distribution:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:MGST=\\frac{\\underset{\\_}{z}}{{\\left\\{\\right[1+\\left(k-1\\right)\\rho\\:]/k\\}\\:}^{1/2}}\\sim\\:N(0,\\:1)\\)\u003c/span\u003e \u003c/span\u003e, where\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:\\underset{\\_}{z}\\)\u003c/span\u003e \u003c/span\u003e is the average of the z-score test statistics from the hypothesis test for each endpoint, after ensuring that the directionality of all endpoints is the same,\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:\\rho\\:\\)\u003c/span\u003e \u003c/span\u003e is the average correlation across each pair of outcomes, and\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:k\\)\u003c/span\u003e \u003c/span\u003e is the number of outcomes being combined\u003c/p\u003e \u003cp\u003eThe one-sided p-value for the MGST is calculated as the cumulative probability associated with the test statistic in the direction of the alternative hypothesis. In contrast, co-primary analysis involves a separate assessment of statistical significance on each endpoint, and evidence of efficacy is typically based on statistical significance on both co-primary endpoints.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eSimulation study\u003c/h2\u003e \u003cp\u003eTo compare GST analysis to co-primary analysis, a simulation was performed to mimic a theoretical clinical trial that evaluates an investigational therapy in patients with a rare, complex, and heterogenous disease. This theoretical clinical trial has a crossover design that includes two treatment sequences, placebo-to-active and active-to-placebo, with 16 participants in each (N\u0026thinsp;=\u0026thinsp;32), and two outcomes. Washout between treatments was assumed to be fully effective. Each treatment assumed a single observation per outcome. For each outcome, correlation between observations of the same patient within a treatment sequence was assumed to be 0.5.\u003c/p\u003e \u003cp\u003eIn the null hypothesis scenario, the effect size for each co-primary outcome was assumed to be 0. Since effect sizes can differ substantially between the co-primary outcomes, we examined various Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e values (drug versus placebo) at various mean-to-standard-deviation ratios (MSDRs) of placebo treatment. For our simulation, we selected Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e values in the range from 0.27 to 0.54 and simplified them into approximate values of 0.3, 0.4, and 0.5 (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\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\u003eCohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e values (drug versus placebo) versus different MSDRs during placebo treatment.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\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=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eMSDR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"9\" nameend=\"c10\" namest=\"c2\"\u003e \u003cp\u003eImprovement in symptoms, drug vs placebo, 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\u003cp\u003e\u003cb\u003e0.5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.50\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.6\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.60\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.7\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.70\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.8\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.9\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e1.0\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"10\" nameend=\"c10\" namest=\"c1\"\u003e \u003cp\u003eMSDR, mean-to-standard-deviation ratio.\u003c/p\u003e \u003cp\u003eHighlighted values represent low-middle to high-middle range values, which aggregate around 0.3 (blue), 0.4 (orange), and 0.5 (green).\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\u003eWithin each combination of effect sizes, two levels of correlation between outcomes were used: 0.9 (strong) and 0.4 (moderate). Overall, this resulted in 32 scenarios, based on two co-primary outcomes, four effect sizes (0, 0.3, 0.4, and 0.5), and two correlation levels between the outcomes (0.9 and 0.4). For each scenario, we generated 10,000 simulated data sets.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eData Analysis\u003c/h2\u003e \u003cp\u003eData obtained using simulation procedures were analyzed for a single primary endpoint, for the co-primary endpoints, and for the composite MGST endpoint, all with a 2-sided alpha of 0.10. The main analysis considered the entire treatment sequence. We also conducted an auxiliary analysis, which only considered the first treatment period in each sequence. Note that while this analysis uses a 2-sided alpha of 0.10 in the crossover design, all results presented generalize to a 2-sided alpha of 0.05.\u003c/p\u003e \u003cp\u003eIn the main analysis, test statistics and p-values were obtained from a mixed-effects model with repeated measures (MMRM), the standard analytic approach for trials with longitudinal continuous outcomes, and then used it to derive the MGST estimates via the formula above. The MMRM used to obtain the T-ratios included treatment (not treatment sequence) as a fixed effect and random intercepts by participant.\u003c/p\u003e \u003cp\u003eIn the auxiliary analysis, test statistics for the single primary endpoint and for the co-primary analysis were calculated via t-test, because there were no repeated measures. The MGST was derived using the formula above. For each scenario, we calculated the power of observing a treatment effect as well as the adjustment needed for the type I error, based on the percentage of simulated data sets in which the result was statistically significant.\u003c/p\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec6\"\u003e\n \u003ch2\u003eNo correlation scenario\u003c/h2\u003e\n \u003cp\u003eIn an extreme case of zero correlation between outcomes, the true alpha level for a co-primary analysis could be calculated by multiplying the one-sided alpha levels from each test (eg, 0.05 x 0.05\u0026thinsp;=\u0026thinsp;0.0025). In a study powered at 80% for a single endpoint, a co-primary analysis would have the power of only 64% for the same effect size on both endpoints.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv\u003e\u003cem\u003eMain analysis: Highly correlated outcomes (r\u0026thinsp;=\u0026thinsp;0.9), Cohen\u0026rsquo;s\u003c/em\u003e d\u0026thinsp;\u003cem\u003e=\u0026thinsp;0.5\u003c/em\u003e\u003c/div\u003e\n\u003cp\u003eFirst, we examined the spread of our simulated data when a significant result was required on a single primary outcome only (x-axis). As expected, with no effect, the T-ratios were symmetrically distributed around the zero value, with a compressed distribution cloud, indicative of a high correlation (0.9; Fig. \u003cspan\u003e1\u003c/span\u003eA) with the other outcome (y-axis). With a 2-sided alpha of 0.10, there was a 5% probability of declaring a significant treatment benefit by chance, which corresponds with the dots in the blue-shaded area.\u003c/p\u003e\n\u003cp\u003eWhen a significant result was required for the other outcome, too (ie, when the two outcomes were co-primary), the pool of possible significant results declared by chance was reduced below 5%, corresponding with stricter standards (Fig. \u003cspan\u003e1\u003c/span\u003eB). In the null scenario, the pool of significant benefit outcomes declared by chance using MGST methodology was equal to the number permissible with a single primary outcome (Fig. \u003cspan\u003e1\u003c/span\u003eC, yellow-shaded area).\u003c/p\u003e\n\u003cdiv\u003eWith a true and similar effect on both outcomes (Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.5), the distribution of simulated datasets shifted up and to the right from the zero point. With a high correlation, most of the outcomes considered significant in MGST were also significant in the co-primary analysis (Fig. \u003cspan\u003e2\u003c/span\u003e), ie, with a small difference in power (88% vs 83%) and with a small adjustment in Type I error (0.05 to 0.03) (Table \u003cspan\u003e2\u003c/span\u003e).\u003c/div\u003e\n\u003cdiv id=\"Sec8\"\u003e\n \u003ch2\u003e\u003cem\u003eMain Analysis: Moderately Correlated Outcomes (r\u0026thinsp;=\u0026thinsp;0.4), Cohen\u0026rsquo;s\u003c/em\u003e d\u0026thinsp;\u003cem\u003e=\u0026thinsp;0.5\u003c/em\u003e\u003c/h2\u003e\n \u003cp\u003eIn this scenario, the distribution cloud was notably more dispersed, resulting in substantially more inconsistencies between the two endpoints (Fig. \u003cspan\u003e3\u003c/span\u003eA), even when they both had a relatively strong true treatment effect (Fig. \u003cspan\u003e3\u003c/span\u003eB).\u003c/p\u003e\n \u003cdiv\u003eStatistical significance in a co-primary analysis required a Type I error adjustment from 0.05 to 0.007, and the power (versus MGST) was reduced from 95\u0026ndash;77% (Table \u003cspan\u003e2\u003c/span\u003e).\u003c/div\u003e\n \u003cdiv\u003e\u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 2\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003ePower and Type 1 error (alpha) for co-primary and MGST analysis, by correlation level (full treatment duration, Cohen\u0026rsquo;s d\u0026thinsp;=\u0026thinsp;0.5 for both outcomes)\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCorrelation (r)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCo-primary\u003c/p\u003e\n \u003cp\u003eendpoints\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMGST\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.9\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003ePower\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e83%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e88%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026alpha;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.4\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003ePower\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e77%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e95%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026alpha;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.007\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003e\u003cem\u003eMain Analysis: High Correlation, True Treatment Effect on a Single Outcome Only (Cohen\u0026rsquo;s\u003c/em\u003e d\u0026thinsp;\u003cem\u003e=\u0026thinsp;0.5)\u003c/em\u003e\u003c/p\u003e\n\u003c/div\u003e\n \u003cp\u003eWith only a single outcome showing a true effect, and with a Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e of 0.5, we would reject null hypothesis, in favor of treatment benefit, 87% of the time (Fig. \u003cspan\u003e4\u003c/span\u003e). For the other outcome, with zero effect, the null hypothesis in favor of treatment benefit would be rejected 5% of the time, according to the two-sided alpha of 0.10. A coprimary analysis would consider such a trial a success in 5% of simulated datasets, compared with 41% of datasets in the MGST analysis (Fig. \u003cspan\u003e4\u003c/span\u003e).\u003c/p\u003e\n \n\u003ch3\u003eMain Analysis: Moderate Correlation, Varied Treatment Effects\u003c/h3\u003e\n\u003cp\u003eIn simulations in which treatment effects differed between the outcomes, power of the co-primary analysis was consistently lower than the power of the individual outcome with a lower effect size, whereas with MGST, power of the individual outcomes was either preserved or increased (Table\u0026nbsp;\u003cspan\u003e3\u003c/span\u003e).\u003c/p\u003e\n\u003cdiv\u003e\n \u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 3\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003ePower at different effect sizes (full treatment duration, r\u0026thinsp;=\u0026thinsp;0.4)\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eEffect size (Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"4\"\u003e\n \u003cp\u003ePower\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eOutcome 1\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eOutcome 2\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eOutcome 1\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eOutcome 2\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCo-primary\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMGST\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e86%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e72%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e66%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e91%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e87%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e51%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e47%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e85%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e72%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e72%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e56%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e85%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e72%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e50%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e41%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e75%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003ch3\u003eAuxiliary Analysis: Moderate Correlation, Varied Treatment Effects\u003c/h3\u003e\n\u003cp\u003eWhen comparing just the first treatment periods of the two sequences (analyzed via t-test), we noticed the same pattern of power reduction with the co-primary analysis and preservation or increase of power when using MGST (Table\u0026nbsp;\u003cspan\u003e4\u003c/span\u003e). Of note, power in these scenarios was overall lower, because of the shorter treatment duration and the absence of repeated measures.\u003c/p\u003e\n\u003cdiv\u003e\n \u003ctable id=\"Tab4\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 4\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003ePower at different effect sizes (first treatment period only, r\u0026thinsp;=\u0026thinsp;0.4)\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eEffect size (Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"4\"\u003e\n \u003cp\u003ePower\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eOutcome 1\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eOutcome 2\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eOutcome 1\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eOutcome 2\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCo-primary\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMGST\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e40%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e41%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e22%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e51%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e39%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e17%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e44%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e40%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e21%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e37%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e29%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e37%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e29%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e21%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e31%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec11\"\u003e\n \u003ch2\u003eMGST: Relationship between outcome correlation and p-value\u003c/h2\u003e\n \u003cp\u003eDifferent levels of correlation between the outcomes change the amount of unique information each outcome contributes to the MGST, which affects the p-value calculated in a statistical test. For example, if the p-value calculated separately for each outcome is 0.07, the p-values calculated using MGST would range from 0.0681 for a nearly perfect correlation (r\u0026thinsp;=\u0026thinsp;0.98) to 0.017 when a correlation is entirely absent (r\u0026thinsp;=\u0026thinsp;0) (Fig.\u0026nbsp;\u003cspan\u003e5\u003c/span\u003e). In other words, by its design, an MGST-based hypothesis test \u0026ldquo;awards\u0026rdquo; a lower p-value to the evidence obtained from more independent outcomes, which aligns with the way evidence is usually judged, and which is a feature that the co-primary analysis does not possess.\u003c/p\u003e\n \n\u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eIn this simulation study, we explored the relationship between outcome correlation, statistical power, and type I error control when evaluating two study outcomes simultaneously. In line with previous findings, our MGST approach preserved the power, compared with the overly restrictive type I error control of a co-primary analysis approach. We also illustrated how hypothesis testing via MGST considers the degree of correlation between outcomes and provides a differentiation (via p-value) between stronger and weaker aggregated evidence (ie, the one obtained from more versus less independent outcomes).\u003c/p\u003e \u003cp\u003eBecause of its combining of standardized z-scores across two or more outcomes, GST can be viewed as an assessment of a global treatment effect, which describes the disease, or a treatment effect, from the perspective of a single score. We argue that this is a key strength of GST, which, if deployed properly, should go hand in hand with the analysis of specific symptoms or disease domains. With multifaceted medical conditions, both common and rare, it may be too restrictive to impose the requirements of a co-primary analysis, which can severely limit the permissible level of type I error and substantially increase the demand for study participants, because of a reduction in power.\u003c/p\u003e \u003cp\u003eThis requirement for very high specificity (ie, very low type I error) in combination with a loss of power can be particularly challenging for the study of rare diseases, which are often multifaceted in symptoms and have a very small pool of potential trial participants. In addition, small samples are more prone to mean values being affected by extreme results, both high and low, thereby making it even more challenging to observe a true treatment effect. Outcomes like GST can temper these extreme results into a single summary that, compared with the co-primary approach, can be better in both detecting effective treatments and rejecting ineffective ones, especially when endpoints have low correlation.\u003c/p\u003e \u003cp\u003eFor these reasons, we advocate for incorporating, or at the very least thoroughly considering a GST model in the statistical plan of trials in which assessing multiple outcomes as primary would be appropriate. Such a prespecified analysis, combined with a sequential testing of individual outcomes, may strike an optimal balance between type I and type II error, between preventing ineffective therapies from reaching the market and approving those that would address patients\u0026rsquo; needs. This approach can be envisioned for treatments developed for rare or certain complex diseases, in which simultaneous assessment of two or more outcomes is deemed appropriate.\u003c/p\u003e \u003cp\u003eOf course, strict requirements regarding study design and conduct would always apply, and sensitivity analyses could be deployed to test the GST assumptions or utility in a specific situation. Of note, statistical studies using data from published trials on Parkinson\u0026rsquo;s disease (PD), rheumatoid arthritis, and stroke all came to a conclusion that the GST was well suited for analyzing multiple outcomes [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. In all three cases, the underlying hypothesis is that the treatment has an overall impact on the disease, which would be better reflected on a composite scale of multiple outcomes. The PD study group emphasized that the multidimensional nature of PD impairments makes multivariate statistical methods ideal for evaluating treatment effects on long-term decline. Their comparison of GST to other multivariate approaches using data from two PD trials concluded that GST is particularly effective in conditions that affect multiple systems and functions, and in which both disease and treatment side effects impact quality of life [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. In an acute stroke trial, the definition of treatment success was based on consistent and persuasive differences in the proportion of patients achieving favorable outcomes on 4 different scales, supporting GSTs appropriateness for such trials [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. In 2012, a long-term PD trial, the National Institute of Neurological Disorders and Stroke exploratory trials in Parkinson's Disease Long-Term Study\u0026ndash;1, announced the use of the GST approach in its design, which encompasses five clinical rating scales for the assessment of disease progression [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Furthermore, composite outcomes like GSTs have been used in early AD clinical trials. The recently approved DMTs donanemab and lecanemab both used composite scores, which are conceptually similar to GSTs, as primary outcomes in their clinical trials: donanemab used the composite score, iADRS, as its primary outcome in its phase 2 and 3 trials [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] and lecanemab used the composite score ADCOMS as its primary outcome for its phase 2 trial [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eA key limitation of GSTs could be formulated as granting an unfair advantage: it inflates the power of individual outcomes, and the more outcomes are included in the model, the likelier it will be to declare a significant treatment effect. Indeed, this would be the case when each outcome is picking up a signal of similar magnitude (eg, Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), but not in the situation when outcomes show treatment effects of different magnitude (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), or, importantly, when a significant effect can be observed on a single outcome only. In these situations, adding outcomes without a true treatment effect would make it less likely for a GST to detect a statistically significant result.\u003c/p\u003e \u003cp\u003eFinally, it is important to align the outcomes selected for the GST with the prespecified outcome hierarchy. A GST combining primary and key secondary endpoints would be a reasonable first step, followed by another GST, combining primary, key secondary, and other secondary endpoints. Combining primary endpoints across studies could also be a useful GST application, even with primary endpoints that arose from different analytic approaches.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eUsing GST as a prespecified statistical tool in trials where assessing multiple primary outcomes is warranted could provide a formal and objective approach to aggregating evidence for a treatment effect. This would be of particular importance for multidimensional and heterogeneous rare diseases, or those that have prodromal stages with small initial decline. While regulatory authorities may feel greater responsibility to protect type I error, thus preventing ineffective treatments from reaching market, it should be kept in mind that this doesn\u0026rsquo;t come without a cost, in form of unjustified dismissal of truly promising therapeutics. In our opinion, further exploration of this statistical approach is both merited and needed.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cp\u003eAD: Alzheimer\u0026rsquo;s disease\u003c/p\u003e\n\u003cp\u003eDMT: Disease-modifying therapy\u003c/p\u003e\n\u003cp\u003eGST: Global statistical test\u003c/p\u003e\n\u003cp\u003eMGST: Meta-analytic global statistical test\u003c/p\u003e\n\u003cp\u003eOLS: Ordinary least squares\u003c/p\u003e\n\u003cp\u003eGLS: Generalized least squares\u003c/p\u003e\n\u003cp\u003eFEV1: Forced\u0026nbsp;expiratory volume in 1 second\u003c/p\u003e\n\u003cp\u003eFVC: Forced vital capacity\u003c/p\u003e\n\u003cp\u003eMSDR: Mean-to-standard-deviation ratio\u003c/p\u003e\n\u003cp\u003eMMRM: Mixed-effects model with repeated measures\u0026nbsp;\u003c/p\u003e\n\u003cp\u003ePD: Parkinson\u0026rsquo;s disease\u003c/p\u003e\n"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003e\u003cem\u003eEthics approval and consent to participate\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eConsent for publication\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eAvailability of data and materials\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll data generated or analyzed during this study are included in this published article.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eCompeting interests\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll the authors are employees of Pentara Corporation. SBH is also the CEO and owner of Pentara Corporation, which provides statistical consulting and clinical data management services to pharmaceutical companies, especially in neurodegenerative disease area.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eFunding\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis project was funded by\u0026nbsp;Tisento Therapeutics.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eAuthors\u0026apos; contributions\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSPD and AD wrote the first draft. AD, CWD, and JRC performed the stimulation study and generated the data tables and figures. SPD, CHM, and SBH validated the results, revised the manuscript. SPD and SBH supervised this project. All authors read and approved the final manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eAcknowledgements\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eVojislav Pejovic, PhD (Clef Communications) and Chenge Zhang, PhD (Pentara Corporation) provided medical writing and editorial support for the preparation of this manuscript. Patrick O\u0026rsquo;Keefe and Angie Goldsberry from Pentara Corporation reviewed and revised this manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eFDA, \u0026ldquo;Multiple Endpoints in Clinical Trials.\u0026rdquo; Accessed: Aug. 29, 2024. [Online]. Available: https://www.fda.gov/regulatory-information/search-fda-guidance-documents/multiple-endpoints-clinical-trials\u003c/li\u003e\n\u003cli\u003e\u0026ldquo;draft-guideline-multiplicity-issues-clinical-trials_en.pdf.\u0026rdquo; Accessed: Aug. 29, 2024. [Online]. Available: https://www.ema.europa.eu/en/documents/scientific-guideline/draft-guideline-multiplicity-issues-clinical-trials_en.pdf\u003c/li\u003e\n\u003cli\u003eP. C. O\u0026rsquo;Brien, \u0026ldquo;Procedures for comparing samples with multiple endpoints,\u0026rdquo; \u003cem\u003eBiometrics\u003c/em\u003e, vol. 40, no. 4, pp. 1079\u0026ndash;1087, Dec. 1984.\u003c/li\u003e\n\u003cli\u003eP. Huan, R. Woolson, and A.-C. Granholm, \u0026ldquo;The Use of a Global Statistical Approach for the Design and Data Analysis of Clinical Trials with Multiple Primary Outcomes,\u0026rdquo; in \u003cem\u003eExperimental Stroke\u003c/em\u003e, 2008, pp. 100\u0026ndash;108. doi: 10.2174/97816080500171080101000108.\u003c/li\u003e\n\u003cli\u003eT. G\u0026oacute;lczewski, W. Lubiński, and A. Chciałowski, \u0026ldquo;A mathematical reason for FEV1/FVC dependence on age,\u0026rdquo; \u003cem\u003eRespir. Res.\u003c/em\u003e, vol. 13, no. 1, p. 57, Jul. 2012, doi: 10.1186/1465-9921-13-57.\u003c/li\u003e\n\u003cli\u003eM. J. Pontecorvo \u003cem\u003eet al.\u003c/em\u003e, \u0026ldquo;Association of Donanemab Treatment With Exploratory Plasma Biomarkers in Early Symptomatic Alzheimer Disease: A Secondary Analysis of the TRAILBLAZER-ALZ Randomized Clinical Trial,\u0026rdquo; \u003cem\u003eJAMA Neurol.\u003c/em\u003e, vol. 79, no. 12, pp. 1250\u0026ndash;1259, Dec. 2022, doi: 10.1001/jamaneurol.2022.3392.\u003c/li\u003e\n\u003cli\u003eD. I. Tang, N. L. Geller, and S. J. Pocock, \u0026ldquo;On the design and analysis of randomized clinical trials with multiple endpoints,\u0026rdquo; \u003cem\u003eBiometrics\u003c/em\u003e, vol. 49, no. 1, pp. 23\u0026ndash;30, Mar. 1993.\u003c/li\u003e\n\u003cli\u003eS. P. Dickson, N. Knowlton, and S. B. Hendrix, \u0026ldquo;Combining evidence across multiple endpoints with a global statistical test: Comparison of z-scores versus ranks,\u0026rdquo; \u003cem\u003eAlzheimers Dement.\u003c/em\u003e, vol. 16, no. S9, p. e046771, 2020, doi: 10.1002/alz.046771.\u003c/li\u003e\n\u003cli\u003eP. Huang \u003cem\u003eet al.\u003c/em\u003e, \u0026ldquo;Using Global Statistical Tests in Long-Term Parkinson\u0026rsquo;s Disease Clinical Trials,\u0026rdquo; \u003cem\u003eMov. Disord. Off. J. Mov. Disord. Soc.\u003c/em\u003e, vol. 24, no. 12, p. 1732, Sep. 2009, doi: 10.1002/mds.22645.\u003c/li\u003e\n\u003cli\u003eB. C. Tilley, S. R. Pillemer, S. P. Heyse, S. Li, D. O. Clegg, and G. S. Alarćon, \u0026ldquo;Global statistical tests for comparing multiple outcomes in rheumatoid arthritis trials,\u0026rdquo; \u003cem\u003eArthritis Rheum.\u003c/em\u003e, vol. 42, no. 9, pp. 1879\u0026ndash;1888, 1999, doi: 10.1002/1529-0131(199909)42:9\u0026lt;1879::AID-ANR12\u0026gt;3.0.CO;2-1.\u003c/li\u003e\n\u003cli\u003eB. C. Tilley \u003cem\u003eet al.\u003c/em\u003e, \u0026ldquo;Use of a Global Test for Multiple Outcomes in Stroke Trials With Application to the National Institute of Neurological Disorders and Stroke t-PA Stroke Trial,\u0026rdquo; \u003cem\u003eStroke\u003c/em\u003e, vol. 27, no. 11, pp. 2136\u0026ndash;2142, Nov. 1996, doi: 10.1161/01.STR.27.11.2136.\u003c/li\u003e\n\u003cli\u003eJ. J. Elm and NINDS NET-PD Investigators, \u0026ldquo;Design innovations and baseline findings in a long-term Parkinson\u0026rsquo;s trial: the National Institute of Neurological Disorders and Stroke Exploratory Trials in Parkinson\u0026rsquo;s Disease Long-Term Study-1,\u0026rdquo; \u003cem\u003eMov. Disord. Off. J. Mov. Disord. Soc.\u003c/em\u003e, vol. 27, no. 12, pp. 1513\u0026ndash;1521, Oct. 2012, doi: 10.1002/mds.25175.\u003c/li\u003e\n\u003cli\u003eM. A. Mintun \u003cem\u003eet al.\u003c/em\u003e, \u0026ldquo;Donanemab in Early Alzheimer\u0026rsquo;s Disease,\u0026rdquo; \u003cem\u003eN. Engl. J. Med.\u003c/em\u003e, vol. 384, no. 18, pp. 1691\u0026ndash;1704, May 2021, doi: 10.1056/NEJMoa2100708.\u003c/li\u003e\n\u003cli\u003eJ. R. Sims \u003cem\u003eet al.\u003c/em\u003e, \u0026ldquo;Donanemab in Early Symptomatic Alzheimer Disease: The TRAILBLAZER-ALZ 2 Randomized Clinical Trial,\u0026rdquo; \u003cem\u003eJAMA\u003c/em\u003e, vol. 330, no. 6, pp. 512\u0026ndash;527, Aug. 2023, doi: 10.1001/jama.2023.13239.\u003c/li\u003e\n\u003cli\u003eC. J. Swanson \u003cem\u003eet al.\u003c/em\u003e, \u0026ldquo;A randomized, double-blind, phase 2b proof-of-concept clinical trial in early Alzheimer\u0026rsquo;s disease with lecanemab, an anti-A\u0026beta; protofibril antibody,\u0026rdquo; \u003cem\u003eAlzheimers Res. Ther.\u003c/em\u003e, vol. 13, no. 1, p. 80, Apr. 2021, doi: 10.1186/s13195-021-00813-8.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Clinical trials, rare disease, complex disease, Global Statistical Test (GST), co-primary endpoints","lastPublishedDoi":"10.21203/rs.3.rs-5194792/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5194792/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eBackground:\u003c/strong\u003e Complex and rare diseases often have heterogeneous symptoms, which complicates the selection of an appropriate primary outcome because outcome assessments rarely capture all aspects of disease. Disease-modifying treatments (DMTs) are expected to affect all disease domains, and even symptomatic treatments can affect multiple aspects of disease; therefore, a single outcome will rarely be sufficient to measure the success of a treatment. To address this issue, regulatory bodies often suggest co-primary endpoints. However, obtaining statistical significance on two outcomes is a much stricter requirement, which could create additional hurdles for effective treatments. Global statistical test (GST) combines multiple outcomes into a single score and could provide a viable alternative to the co-primary approach. Importantly for rare diseases, combining multiple assessments reduces the risk of selecting a poor outcome simply because it has not been studied as extensively as those for more common diseases. Here we compare GST to single primary and co-primary methodologies using simulations of a crossover study with two outcomes that may be moderately or highly correlated using several effect sizes.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResults:\u003c/strong\u003e For the same effect size on both outcomes, GST had greater power than single primary and co-primary approaches, regardless of the correlation level between outcomes. This was also true with different effect size combinations at the same correlation level. With an effect observed on one outcome only, GST was more likely to yield statistical significance than theco-primary approach. Unlike the co-primary approach, The GST yielded lower p-values in scenarios with lower correlation between the outcomes.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConclusions:\u003c/strong\u003e GST favors independent information (ie, outcomes with moderate or poor correlation), does not reduce statistical power, and is not overtly permissible in cases of null effect on one of the outcomes. Compared to co-primary endpoints, the higher statistical power of GST is especially suited for rare diseases withsample size limitation. GST is a viable approach in analyzing data from heterogeneous outcomes and should be considered over co-primary approaches, especially for treatments that target multiple aspects of the disease or multiple symptoms.\u003c/p\u003e","manuscriptTitle":"Efficacy Assessment in Trials of Complex and Rare Diseases: A Comparison Between the Meta-Analytic Global Statistical Test and Co-Primary Analysis","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-01 09:30:31","doi":"10.21203/rs.3.rs-5194792/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"e594337b-0c5f-425d-9ab3-60d936e9440f","owner":[],"postedDate":"April 1st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-04-29T06:53:20+00:00","versionOfRecord":[],"versionCreatedAt":"2025-04-01 09:30:31","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5194792","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5194792","identity":"rs-5194792","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}