External validation of a dynamic prediction model for repeated predictions of natural conception over time

Approximately 10% of all couples who wish to have a child do not con- ceive within the first year of trying ( Gnoth et al., 2003 ; Wang et al., 2003). For approximately half of these couples, no clear barrier for conception can be found during the workup and these couples are considered unexplained subfertile ( Aboulghar et al., 2009 ; Brandes et al., 2010 ). It is unclear whether these couples should start with ART; first, since observational studies report that 18 –38% of unex- plained subfertile couples will conceive naturally in the year after the fertility workup ( Hunault et al., 2004 ; van der Steeg et al., 2007 ; van Eekelen et al., 2017a ) and second, since there remains uncertainty regarding the effectiveness of ART for unexplained subfertile couples (Pandian et al., 2015 ; Tjon-Kon-Fat et al., 2016 ; Veltman-Verhulst et al., 2016; van Eekelen et al., 2017b ). In the absence of clear evidence on the management of unexplained subfertile couples and when to offer ART, an enticing option is to cal- culate chances of natural conception and to base counselling on this estimated prognosis ( van Eekelen et al., 2017b ). Fundamental to this approach is to identify couples that are expected to bene fit from treat- ment and those who are not. In clinical practice, this would imply that couples with a good prognosis to conceive naturally are advised to continue to try and become pregnant by sexual intercourse, while cou- ples with an unfavourable prognosis are advised to start ART. Several prediction models for natural conception have been published of which the model by Hunault et al., which calculates a prognosis of con- ception leading to live birth over the first year after the completion of the fertility workup, has been externally validated and subsequently implemented in the national guidelines and clinical practice in the Netherlands ( Hunault et al., 2004 ; van der Steeg et al., 2007 ; Leushuis et al., 2009; NVOG, 2010). A practical drawback of the Hunault mod- el is that it cannot give a prediction at later time points when couples who continued expectant management after the fertility workup but did not conceive, return to the clinic. This is because applying the Hunault model at later time points leads to overestimation due to the selection of less fertile couples over time that is not incorporated in the Hunault model ( van Eekelen et al., 2017b ). Van Eekelen et al. recently developed a dynamic prediction model that accommodates the need for repeated predictions ( van Eekelen et al., 2017a ). This model comprises the clinical factors female age, duration of subfertility (both at completion of the fertility workup), percentage of progressively motile sperm, primary or secondary sub- fertility and being referred to the fertility clinic by a general practitioner or a specialist. In addition to these factors, the model uses as an input the number of menstrual cycles that have passed since the completion of the fertility workup, with zero cycles denoting the prediction is made immediately after the workup. The output is the predicted prob- ability to conceive naturally in the following cycle, leading to ongoing pregnancy, which can be extended to predict over any given number of cycles with a maximum of 2.5 years after the workup (~28 –34 cycles). When couples return after a period of expectant manage- ment, the number of cycles that have passed since the workup can be changed to update the predicted probability over subsequent cycles. The model developed by van Eekelen et al. showed promising

in the internal validation, but this in itself is insuf ficient to advise clinical implementation since models tend to perform better in the cohort they were developed on than in another cohort in which the model may be applied ( Steyerberg, 2009). The aim of this study was to externally validate the van Eekelen model on a large cohort that followed couples for natural conception after registration in the fertility clinic of the Grampian region of Scotland, UK. This is the largest contemporary cohort following cou- ples for natural conception, aside from the Dutch cohort on which the dynamic model was developed.

We included couples diagnosed with unexplained subfertility residing in the Grampian region of Scotland who registered with the Aberdeen Fertility Centre (AFC) from 1998 to 2011 ( Pandey et al., 2014 ). Only patients from the Grampian region visiting the AFC were selected because there is no other fertility clinic in the region and it was considered import- ant to have a complete overview of a couple ’s trajectory after the fertility workup, which includes treatment information. We combined the AFC registration database with three other data sources using record-linkage to get the complete follow-up for couples from the registration at the AFC until ongoing pregnancy, treatment or end of the study, which was the 31 March 2012. The AFC database comprises patient characteristics and diagnostic information. Data entry in the AFC database is validated and checked by regular case note audits. First, we record-linked couples registered in the AFC database to the centre ’s Assisted Reproduction Unit database which contained dates when treatment was started. Second, we identi fied natural conceptions leading to an ongoing preg- nancy by record-linkage of the AFC database with the Aberdeen Maternity and Neonatal Databank, which contained gestational age, outcome and delivery date of (early) pregnancies for all women residing in Aberdeen 2269External validation of a dynamic prediction model City District. Third, we performed record-linkage with the national Scottish Morbidity Records Maternity database for identifying gestational age, outcome and delivery date of (early) pregnancies for women who delivered elsewhere in Scotland. The Data Management Team of the University of Aberdeen created a new pseudonomized identi fier for all women by using the Community Health Index identi fier. This new study-speci fic identi fier cannot be used to trace back to individuals and was then used by author D.J.M. to record- link the databases within the Grampian Data Safe Haven environment. This process was carried out according to the Standard Operating Procedures of the Data Management Team, University of Aberdeen. The resulting linked dataset was thus a combination of these four data sources. Ethical approval was provided by the North of Scotland Research Ethics Committee (reference: 12/NS/0120). Access to the Aberdeen Fertility Clinic and the Assisted Reproduction Unit databases was approved by the Aberdeen Fertility Databases Steering Committee. Access to the Aberdeen Maternity and Neonatal Databank was approved by the Aberdeen Maternity and Neonatal Database Steering C ommittee. Access to the Scottish Morbidity Records Maternity database was approved by the Privacy Advisory Committee of Information Services Division Scotland. We de fined unexplained subfertility as couples who tried to conceive for more than 50 weeks before the fertility workup was completed and who had no obvious barriers to conception in terms of uni or bilateral tubal occlusion, anovulation, mild or severe endometriosis according to the revised American Society for Reproductive Medicine (ASRM) score ( ASRM, 1997 ) or impaired semen quality according to World Health Organization (WHO) criteria ( WHO, 1999 , 2010). We used the gesta- tional age at birth or early pregnancy outcome to derive the date of con- ception and included only pregnancies in the analysis that occurred after registration of the couple at the clinic and that were ongoing, de fined as reaching a gestational age of at least 12 weeks. Time to conception was censored at the date of start of IUI, start of IVF, when the woman returned to the fertility centre with a different male partner or at the end of study. Missing data The date of completion of the fertility workup was not reported in the AFC database. The van Eekelen model uses this date as the starting point of follow-up, i.e. the time point from which onwards the model can be used to estimate a prognosis. The date of registration and the diagnosis category were available in the database. Judging from local protocols, we assumed there were 3 months in between registration and completion of the fertility workup for all couples. In a sensitivity analysis, we repeated the validation study assuming 1.5 or 4.5 months between registration and completion of the fertility workup for all couples. Menstrual cycle length is used to determine the number of elapsed men- strual cycles since the fertility workup when updating predictions using the dynamic prediction model. Cycle length was not recorded in the AFC database and we therefore assumed an average cycle length of 28 days for all women. Data on outcomes or at least one prognostic factor were missing for ~4% of couples; 0.5% on pregnancy or follow-up, 0.5% on female age, 2.3% on duration of subfertility, 0.5% on primary or secondary subfertility, 1.9% on the percentage of progressive motile sperm and 0.5% on referral status. We had no reason to believe that couples with missing data differed systematically from couples with complete data and we analysed couples for which data was complete. Analysis We calculated the predicted probabilities of natural conception over 1 year for all couples in the validation cohort using the formula in the Appendix of the paper by van Eekelen et al. ( van Eekelen et al., 2017a ). To test the model ’s ability to not only predict after the completion of the fer- tility workup but also when a couple returns after an unsuccessful period of expectant management, we calculated the prognosis at four time points: directly after completion of the workup, after 0.5, 1 and 1.5 years of expectant management. We evaluated model performance in terms of calibration, i.e. the degree of agreement between observed and predicted natural conception rates, and discrimination, i.e. the ability of the dynamic prediction model to distinguish between couples who do conceive and couples who do not conceive. To assess calibration, we first explored whether the overall prediction of the model was correct by comparing the average predicted probability over a time period with the observed conception rate over that same time period. This is referred to as calibration-in-the-large and assesses whether the model systematically under or overestimates the observed conception rate ( Steyerberg, 2009). Second, we assessed whether the effects of patient characteristics were estimated correctly in three ways: by visuals using calibration plots for risk groups, by calibration within groups with similar patient characteristics and by calculating a calibration slope. For the calibration plots, we ordered the predicted probabilities of couples and divided them in risk groups with similar predictions ( n = 135 per risk group). We compared the mean pre- dicted chances within these groups with the corresponding observed frac- tion of ongoing pregnancy as estimated by the Kaplan –Meier method. We visualized the observed fractions and predicted probabilities per risk group in plots and tabulated the absolute differences. In the plots, the 45 ° line indicates what would be a perfect agreement between the observed frac- tion and average predicted probability within a risk group. We repeated the calibration procedure but instead of grouping based on predicted risks, we grouped couples based on having similar patient characteristics. We again compared the mean predicted chances within these groups with the corresponding observed fraction of ongoing preg- nancy as estimated by the Kaplan –Meier method and tabulated the results. To calculate the calibration slope, we used the prognostic index (i.e. the sum of the multiplication between all patient characteristics and the coef fi- cients from the model) as an explanatory variable in a Cox model for each of the four evaluated time periods ( van Houwelingen, 2000 ). Ideally, the calibration slope is unity, i.e. 1, indicating that the strength of the patient characteristics in the evaluated model perfectly matches the validation data. Third, we used a recalibration procedure as an alternative way to assess the systematic under or overestimation (calibration-in-the-large) and the strength of the patient characteristics (calibration slope) in the model. We did this by using the same coef ficients for the patient characteristics as reported by van Eekelen et al. to calculate a prognostic index but re-estimated the other parameters of the beta-geometric model in the val- idation dataset ( Bongaarts, 1975; Weinberg and Gladen, 1986). The recali- bration model re-estimates three parameters, which we compared to those in the van Eekelen model and tested for the difference between the two using independent samples z-tests. Systematic under or overesti- mation was assessed by comparing the intercept and the variance para- meters. The intercept parameter indicates the estimated pregnancy chances in the first cycle after the fertility workup and the variance param- eter indicates how fast the estimated chances decrease over consecutive failed natural cycles. Similarity in strength of the patient characteristics was assessed by again calculating a calibration slope parameter, which would ideally be 1. We assessed discrimination by calculating Harrel ’s c statistic at the four time points, which we compared to those found at internal validation ( Harrell et al., 1996). Finally, we explored the range of predicted probabilities at the four time points to see if they facilitate meaningful prognostic strati fication of couples (Coppus et al., 2009). 2270 van Eekelen et al. All analyses were conducted in R version 3.4.3 and RStudio ( R Core Team, 2013). A P-value below 0.05 was considered statistically signi ficant.

Data of 1203 couples were included (Fig. 1). The baseline characteris- tics of the couples are shown in Table I. In total, 398 (33%) couples conceived naturally, leading to an ongoing pregnancy. The median follow-up was 1 year and 3 months after the completion of the workup (average follow-up 2 years and 6 months). The observed rates of natural conception up to 2.5 years are depicted in Fig. 2 (upper panel). For couples who did not yet conceive after 0.5, 1 or 1.5 years after the completion of the fertility workup, the observed rates of natural conception over the following year are depicted in Fig. 2 (lower panel). The mean probability of natural con- ception as predicted by the dynamic model over the course of the first year after the fertility workup was 25%, while the observed fraction was 23% (95%CI 20 –25). For couples who did not conceive after 0.5, 1 and 1.5 years of expectant management, the mean estimated prob- ability of conceiving over the course of the following year was esti- mated at 18, 14 and 12%. The observed rates were 15% (13 –18%), 14% (11 –17%) and 12% (9 –15%) for these three time periods, respectively (Fig. 2, lower panel). Except for the second period during which the model slightly overestimated the pregnancy chances by 3% points, the mean predicted probabilities fell within their respective confidence limits of the observed rates, indicating good agreement between the average prediction rendered by the dynamic model and the corresponding observed rate of natural conception. The calibration plots for the four time periods are presented in Fig. 3. The dynamic prediction model was well calibrated based on the upward trends observed in the four plots, indicating that higher pre- dicted probabilities correspond to higher observed rates, and the CIs from the observed rates which all but one cover the ideal 45 ° line. The second calibration plot starting at 0.5 year after the fertility workup showed a slight overestimation since all points are below the 45 ° line. The absolute differences between observed fractions and predicted probabilities of natural conception within risk groups are shown in Table II. This was on average 2.8% points and 9.6 at the highest. The results for the calibration grouping couples by similar character- istics are shown in Supplementary data. Results were similar to those in the calibration using risk groups, with a slight overestimation in the time periods right after the completion of the fertility workup and after 0.5 year of expectant management. The calibration slopes using Cox models were 0.86, 1.01, 1.01 and 0.62 for the four time periods, respectively. None of the correspond- ing P-values were below 0.05, indicating no statistical evidence for under or overfitting. In the recalibration model, the intercept and variance parameters were similar to those reported by van Eekelen et al. (P = 0.69 and P = 0.29 for the difference, respectively), indicating similar underlying chances of pregnancy in the first cycle after the workup and a similar decrease in chances as time progresses. The slope was 0.90 ( P = 0.37), indicating a similar strength of patient characteristics in the valid- ation cohort and no signi ficant difference from 1. The discriminative ability of the model in the validation cohort was moderate and similar to that in the Dutch development cohort, ran- ging over time from a c statistic of 0.61 (95%CI 0.57 –0.64) in the first 5466 couples registered between 1998 and 2011 in the Aberdeen Fer/g415lity Clinic Women excluded with diagnoses other than unexplained subfer/g415lity (n = 3945) 1521 couples with unexplained subfer/g415lity 1203 couples in the final analysis Couples that did not provide consent for treatment data to be used for research (n = 10) Couples conceived before comple/g415on of fer/g415lity workup (n = 234) Couples excluded with missing outcome data (n = 8) Couples excluded with missing predictor values (n = 39) Couples excluded that were followed for less than one cycle of expectant management (n = 6) Couples with a dura/g415on of subfer/g415lity of 50 weeks or less (n = 21) Figure 1 Flow chart of couples with unexplained subfertility who were considered for inclusion in the external validation. 2271External validation of a dynamic prediction model year, 0.62 (95% CI 0.58 –0.67) from 0.5 year, 0.63 (95% CI 0.57 –0.69) from 1 year, to 0.60 (95% CI 0.52 –0.67) for 1.5 years after the com- pletion of the fertility workup, all for conceiving in the following year. The c statistics were around 0.61 for all four time periods and seemed stable over time. The range of predictions varied between 0% and 55% over the course of the first year after the fertility workup. After 0.5, 1 and 1.5 years of expectant management the ranges narrowed to 0 –43%, 0–34% and 0 –29% respectively, all over the course of the following year, facilitating a distinction between couples with a good or poor prognosis. Sensitivity analyses

from the two sensitivity analyses are reported online as Supplementary data. Theanalysis where we assumed 1.5 months between registration and completion of the fertility workup showed a very good performance of the dynamic prediction model (Supplementary Table SI, Supplementary Figs S1 and S2). The analysis assuming 4.5 months between registration and completion of the fertility workup showed similar results to the primary analysis but with slightly more overestimation of chances by the model (Supplementary Table SII, Supplementary Figs S3 and S4).

We conducted an external, geographical validation of the van Eekelen model that can be used for repeated predictions of natural conception when couples return to the clinic after unsuccessful expectant manage- ment. The model performed well in a Scottish cohort of couples with unexplained subfertility that visited a fertility clinic and the model is expected to be generalizable to other fertility centres and countries where the procedure of managing unexplained subfertile couples is comparable to the Netherlands and the UK. In addition, the predicted probabilities varied suf ficiently to aid in distinguishing between couples with a good and poor prognosis in terms of natural conception. The data from the AFC was of high quality, registering every unex- plained subfertile couple in the Grampian region. All natural concep- tions leading to ongoing pregnancy, including after miscarriages and other early pregnancy outcomes, were found using data linkage with maternity records. Indications for the fertility workup and de finitions of censoring and prognostic characteristics in the Scottish cohort were very similar to the Dutch cohort, aiding comparability ( van Eekelen et al., 2017a). The model was well calibrated, which we consider of higher import- ance than discrimination since the c statistics can be expected to be moderate due to the limited range of predicted chances in fertility (Mol et al., 2005 ; Cook, 2007). This restricts the maximum possible c statistics, even if a model was to produce perfect predictions. Recalibration, in which one or more parameters of the prediction model are updated to accommodate better predictions in a different country or clinical setting, was not necessary since the recalibration model showed similar values for all parameters as observed in the development cohort. The main limitation to our study was missing data in terms of dates of completion of the fertility workup and menstrual cycle lengths. Menstrual cycle length was not considered very in fluential since the estimations of the number of cycles per individual are reasonable approximations due to the narrow range of possible cycle lengths in our selection of unexplained subfertile couples, but we did have to make strong assumptions about the date of completion of the fertility workup. We assumed 3 months between registration and completion of the fertility workup, which resulted in ongoing pregnancies before 3 months after registration being excluded. The ‘starting’ moment of follow-up thus differed from the Dutch development cohort since in the latter, the date of last tubal test was used as the end of the workup. Some Dutch clinics did not conduct a visual test of tubal patency, i.e. laparoscopy or hysterosalpingography after a negative

for the chlamydia antibody test. In those Dutch clinics, the workup was thus considered as complete earlier after registration compared to the AFC where visual tests of tubal patency are a part of the standard protocol. This may have led to the observed slight over- estimation in the first year after the fertility workup and after 0.5 year of expectant management but, despite these differences, the dynamic model was still able to estimate a prognosis that was reasonably accur- ate on cohort and risk group level. The results from the sensitivity ana- lysis assuming 1.5 months between registration and completion of the fertility workup were very good because the resulting population more closely resembled that of the Dutch development cohort in which the same average duration was observed between registration and the workup completion. Accordingly, in the analysis assuming 4.5 months between registration and completion of the fertility workup, the per- formance of the dynamic model was poorer because the populations differed more due to additional selection that occurred. The dynamic model is able to reassess the chance of natural con- ception after any given period of expectant management from the completion of the fertility workup onwards. For example, a couple with 1-year secondary subfertility is referred by a general practitioner to the fertility clinic of which the woman is 33 years old at the comple- tion of the fertility workup and the man has 40% progressive motile sperm. Applying our model gives a predicted 38% chance of natural conception over the first year after the workup and they might be advised expectant management. When the couple returns to the clinic after 10 unsuccessful months/cycles, reapplying the model yields 25% chance over the following year, which is a realistic decrease given they have tried for an additional 10 months. This could be a reason to con- sider starting treatment. ........................................................................................ Table I Baseline characteristics at completion of the fertility workup. n = 1203 Mean or n 5th–95th Percentile or % Female age, in years 33.3 25 –41 Duration of subfertility, in years 2.7 1.3 –5.6 Primary female subfertility 697 58% Percentage of progressive motile sperm 51 24 –76 Referral by secondary care 84 7% 2272 van Eekelen et al. Both the Hunault model and the dynamic model performed well in external validations, indicating that the added value of the dynamic model lies in the ability to update predictions at later time points ( van Eekelen et al., 2017a ). This provides clinicians and patients with infor- mation regarding their prognosis of natural conception not only right after the completion of the fertility workup but also when the couple returns after an additional, unsuccessful period of expectant manage- ment, thus aiding in making clinical decisions at multiple time points throughout a couple’s trajectory. The ability to update predictions also aids in studies which include the prognosis of natural conception as an in- or exclusion criterion, since the prognosis of couples who return after unsuccessful expectant management can be updated accurately, leading to the desired homogeneity of the study sample ( van den Boogaard et al., 2014 ). The dynamic model is flexible and can be used to predict over any desired number of menstrual cycles, for instance when the couple is interested in time periods shorter or longer than 1 year. In short, the dynamic model has a wider clinical applicability than the Hunault model and should be the model of choice.

The van Eekelen model is a valid and robust tool that is ready to use in clinical practice to counsel couples with unexplained subfertility on their individualized chances of natural conception at various points in time, notably when couples return to the clinic after a period of unsuc- cessful expectant management. Figure 2 Cumulative chances of natural conception leading to ongoing pregnancy. Cumulative chances after the completion of fertility workup (upper panel) and updated chances of natural conception over the course of 1 year at the completion of the fertility workup or 0.5, 1 and 1.5 years thereafter (lower panel) in the validation cohort. Percentages are Kaplan –Meier estimates of the observed fraction of natural conception leading to ongoing pregnancy. 2273External validation of a dynamic prediction model Supplementary data Supplementary data are available at Human Reproduction online.

The authors would like to thank Prof. Egbert te Velde for all of his efforts regarding development of the dynamic prediction model and the current validation study. The authors acknowledge the data man- agement support of the Grampian Data Safe Haven (DaSH) and the associated financial support of NHS Research Scotland, through NHS Grampian investment in the Grampian DaSH. For more information, Figure 3 Calibration of the predictions of the dynamic prediction model: predicted vs observed 1-year natural conception rates at fourfixed time points. .......................................................................................... Table II Calibration of the dynamic prediction model by risk groups. Mean difference Max difference Number of risk groups After completion of workup 3.2 9.6 9 After 0.5-year EM 3.0 4.7 7 After 1-year EM 2.1 3.5 5 After 1.5-year EM 2.7 4.5 4 Total 2.8 9.6 25 Data are the mean and maximum of the absolute differences (in percentage points) between predicted and observed 1-year natural conception rates per risk group of n = 135, stratified by the elapsed period of expectant management (EM). 2274 van Eekelen et al. visit the DaSH website http://www.abdn.ac.uk/iahs/facilities/grampian- data-safe-haven.php. The authors would like to thank all the staff at Aberdeen Fertility Clinic for their help with database queries. Authors’ roles NvG, MDJ, BS, FvdV, MvW and MJE conceived the study. MDJ per- formed the data linkage, storage in the Safe Haven and cleaned the data. RvE, NvG and MJE designed the statistical analysis plan. RvE, MDJ and NvG analysed the data. RvE drafted the manuscript. All authors contributed critical revision to the paper and approved the final manuscript. Funding Chief Scientist Office postdoctoral training fellowship in health services research and health of the public research (ref PDF/12/06). The views expressed here are those of the authors and not necessarily those of the Chief Scientist Office. The funder did not have any role in the study design; the collection, analysis and interpretation of data; the writing of the report nor the decision to submit the paper for publication. Conflict of interest None declared.

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