Causal modelling of survival data with informative noncompliance

Noncompliance to treatment allocation is likely to complicate estimation of causal effects in clinical trials. The ubiquitous nonrandom phenomenon of noncompliance renders per-protocol and as-treated analyses or even simple regression adjustments for noncompliance inadequate for causal inference. For survival data, several specialist methods have been developed when noncompliance is related to risk. The Causal Accelerated Life Model (CALM) allows time-dependent departures from randomized treatment in either arm and relates each observed event time to a potential event time that would have been observed if the control treatment had been given throughout the trial. Alternatively, the structural Proportional Hazards (C-Prophet) model accounts for all-or-nothing noncompliance in the treatment arm only while the CHARM estimator allows time-dependent departures from randomized treatment by considering survivaloutcome as a sequence of binary outcomes to provide an `approximate' overall hazard ratio estimate which is adjusted for compliance. The problem of efficacy estimation is compounded for two-active treatment trials (additional noncompliance) where the ITT estimate provides a biased estimator for the true hazard ratio even under homogeneous treatment effects assumption. Using plausible arm-specific predictors of compliance, principal stratification methods can be applied to obtain principal effects for each stratum. The present work applies the above methods to data from the Esprit trials study which was conducted to ascertain whether or not unopposed oestrogen (hormone replacement therapy-HRT) reduced the risk of further cardiac events in postmenopausal women who survive a first myocardial infarction. We use statistically designed simulation studies to evaluate the performance of these methods in terms of bias and 95% confidence interval coverage. We also apply a principal stratification method to adjust for noncompliance in two treatment arms trial originally developed for binary data for survival analysis in terms of causal risk ratio. In a Bayesian framework, we apply the method to Esprit data to account for noncompliance in both treatment arms and estimate principal effects. We apply statistically designed simulation studies to evaluate the performance of the method in terms of bias in the causal effect estimates for each stratum. ITT analysis of the Esprit data showed the effects of taking HRT tablets was not statistically significantly different from placebo for both all-cause mortality and myocardial reinfarction outcomes. Average compliance rate for HRT treatment was 43% and compliance rate decreased as the study progressed. CHARM and C-Prophet methods produced similar results but CALM performed best for Esprit: suggesting HRT would reduce risk of death by 50%. Simulation studies comparing the methods suggested that while both C-Prophet and CHARM methods performed equally well in terms of bias, the CALM method performed best in terms of both bias and 95% confidence interval coverage albeit with the largest RMSE. The principal stratification method failed for the Esprit study possibly due to the strong distribution assumption implicit in the method and lack of adequate compliance information in the data which produced large 95% credible intervals for the principal effect estimates. For moderate value of sensitivity parameter, principal stratification results suggested compliance with HRT tablets relative to placebo would reduce risk of mortality by 43% among the most compliant. Simulation studies on performance of this method showed narrower corresponding mean 95% credible intervals corresponding to the the causal risk ratio estimates for this subgroup compared to other strata. However, the results were sensitive to the unknown sensitivity parameter.