MMRM vs joint modeling of longitudinal responses and time to study drug discontinuation in clinical trials using a “de jure” estimand

In pre-marketing stages of drug development, trialists focus on drug efficacy rather than effectiveness, and observations collected after study drug discontinuation are excluded from the analysis, following the so-called “de jure” estimand. In this setting, mixed models for repeated measures (MMRM) are becoming the benchmark to analyze normally distributed longitudinal responses. We have compared the performance of MMRM against shared parameter models (SPM) that jointly fit the longitudinal response and time to study drug discontinuation. Our simulations have first confirmed that MMRM lead to biased treatment effect estimates when longitudinal and event processes are associated via latent shared parameters, especially if the relationship is heterogeneous across treatment groups. SPM produced unbiased estimates with SPM data but faced two important obstacles: (a) SPM led to considerable bias when treatment discontinuation and response were associated with models of the time-varying covariates (TVC) family, and (b) SPM were rather sensitive to the choice of the parameterization to model the relationship between longitudinal and time-to-event processes. When we simulated SPM data but used an incorrect equation to relate the random effects and time-to-event response, SPM led to a bigger bias than that seen with MMRM. We have finally evaluated a methodology to choose between MMRM and SPM consisting of expanding the MMRM density into the likelihood of both longitudinal and time-to-event data by plugging in the likelihood of a parametric TVC model. This approach allowed us to accurately select the optimal tool (MMRM or SPM) with sample sizes typical of phases 2b and 3.

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