Efficient exposure-response analysis for time-to-event endpoints: beyond the use of time-static exposure metrics
Alexandra Lavalley-morelle1, Félicien Le Louedec1, Richard Anziano1, France Mentré1,2,3, Martin Bergstrand1
1Pharmetheus, 2Department of Epidemiology, Biostatistics and Clinical Research, AP-HP, Bichat-Claude Bernard University Hospital, 3Université Paris Cité, IAME, INSERM
Introduction: Analyzing exposure–response (E-R) relationships for time-to-event (TTE) endpoints is an important part of model-informed drug development. Though exposure often changes systematically over time (e.g. due to dose titration and/or accumulation), it is common practice to approximate the longitudinal exposure with time-static metrics [1,2]. The objective of this work is to demonstrate, across an extensive and varied set of clinical trial simulations, how time-varying exposure metrics can be efficiently applied for E-R analysis of TTE endpoints and the value it offers over different time-static exposure metrics. Methods: PK exposures were simulated from a one-compartment model, with doses administrated weekly during 30 weeks. TTE data were simulated from a parametric proportional hazard model, involving the weekly average PK concentration (Cavg) as a time-varying covariate. Twenty-four main scenarios were considered crossing two dosing designs (fixed or adaptive), two levels of drug accumulation (low or strong), three E-R relationships (absence, positive or negative relationship), and two timings of event onset (early or late). For adaptive dosing simulations, additional scenarios were generated with correlation between the probability of dose reduction and the hazard of the event. For each scenario, 100 data sets of 300 patients were simulated. For the analysis of the main scenarios, parametric TTE models involving a time-static or a time-varying exposure metric were estimated. Three time-static metrics (Cavg during week 1, Cavg during the week before the event and Cavg at steady state based on starting dose) and one time-varying metric (weekly Cavg) were explored. Hazard ratios (HRs) for the exposure effect with associated Wald test p-values were derived. For each scenario and exposure metric, the power (resp. specificity, if no ER relationship simulated) was estimated as the proportion of significant (resp. non-significant) HRs across the 100 replicates using a type I error of 0.05. For the analysis of the additional scenarios, dose reduction probability (logistic model) and event hazard (parametric TTE model) were jointly estimated, correctly handling correlation (denoted as true models). Mis-specified correlation models were also estimated. Relative estimation errors (REEs) on the exposure effect were reported and compared between true and mis-specified models. Estimation was performed in R, using flexsurv package [3] for parametric TTE modelling, and saemix package [4,5] for joint estimation of the logistic and TTE models. Results: Overall, type-I error was controlled for time-varying metric and time-static metrics based on initial exposure. However, only the time-varying metric showed high power whatever the main scenario considered (power of 100%). The use of Cavg before the week of event had a poor power especially with strong accumulation and early events. The use of Cavg at week 1 or at steady state showed a weaker power in the presence of adaptive dosing, with low accumulation and late events (power of 64% versus 100% when dosing design is fixed). For the additional scenarios, the mis-specification of the correlation between the dose reduction process and the hazard of event introduced a bias in the exposure effect parameter. Most of the time, this parameter was underestimated, indicating that the power to identify a significant E-R could be decreased. As an illustration, in a scenario when E-R relationship was positive, events were late and drug accumulation was low, mean REE = 3.9% for the true model versus -57.7% for the model where correlation is mis-specified. Conclusion: Although current recommendations [6,7] suggest using metrics based on initial exposure for time-static metrics in E-R analysis of TTE endpoints, we showed that this approach can weaken the power to detect a signal in some situations where the dosing design is adapted during the study. Time-varying exposure metrics are recommended and can be efficiently implemented in a prespecified R based workflow. Potential correlation between the dose reduction and the TTE processes reflects pharmacodynamic sensitivity, where the variability in drug target sensitivity can increase efficacy for some patients but also the risk of adverse events, often requiring dose adjustments. If such a correlation is suspected, incorporating it into the model is necessary to avoid bias in the E-R relationship, despite longer run times.
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