Comparison of methods to testing for differential treatment effect under non-proportional hazards data.

Many tests for comparing survival curves have been proposed over the last decades. There are two branches, one based on weighted log-rank statistics and other based on weighted Kaplan-Meier statistics. If we carefully choose the weight function, a substantial increase in power of tests against non-proportional alternatives can be obtained. However, it is difficult to specify in advance the types of survival differences that may actually exist between two groups. Therefore, a combination test can simultaneously detect equally weighted, early, late or middle departures from the null hypothesis and can robustly handle several non-proportional hazard types with no a priori knowledge of the hazard functions. In this paper, we focus on the most used and the most powerful test statistics related to these two branches which have been studied separately but not compared between them. Through a simulation study, we compare the size and power of thirteen test statistics under proportional hazards and different types of non-proportional hazards patterns. We illustrate the procedures using data from a clinical trial of bone marrow transplant patients with leukemia.

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.

Outlier detection method in GEEs.

The generalized estimating equations (GEEs) method has become quite useful in modeling correlated data. However, diagnostic tools to check that the selected final model fits the data as accurately as possible have not been explored intensively. In this paper, an outlier detection technique is developed based on the use of the "working" score test statistic to test an appropriate mean-shift model in the context of longitudinal studies based on GEEs. Through a simulation study it has been shown that this method correctly singled out the outlier when the data set had a known outlier. The method is applied to a set of data to illustrate the outlier detection procedure in GEEs.