Time-dependent dynamics of noncompliance and risk in clinical trials: Methods of assessment and sample size calculation

Most existing methods of sample size calculation for survival trials adjust the estimated outcome event rates for noncompliance assuming that noncompliance is independent of the endpoint risk although there has been published evidence (e.g., Coronary Drug Project Research Group, 1980; Snapinn et al., 2004) that noncompliers are often at a higher risk than compliers. More recent work (e.g., Jiang et al., 2004; Porcher et al., 2002) has started to consider the situations of informative noncompliance and different risks for noncompliers. However, the possibility of a time-varying association between noncompliance and risk has been ignored. Our analysis indicated a strong time-varying relationship between permanent withdrawal from study treatments and endpoint risk in the CONVINCE trial. In this dissertation, we introduce a method of sample size calculation which can account for a wide variety of relationships between the time dynamics of noncompliance and risk. The method is based on Lakatos Markov models. Using our method, we are able to study the impact of various assumptions on sample size calculation. Results show that sample size can vary dramatically with different assumptions about noncompliance and risk. Power can be seriously reduced if the assumed association does not agree with the real situation.; Our method requires trial planners to specify the potential time-varying pattern for the association between noncompliance and risk. In chapter 5, we study some methods including a new method for modeling a time-varying effect associated with a binary non-reversible time-dependent covariate in Cox regression. We first study the Zph method (Therneau and Grambsch, 1994) and show that it may not be the optimum method for the covariate of our interest. We then study a simple continuous approach using spline techniques and a simple discrete approach using partitioning the time axes related to the covariate. For the discrete approach, we introduce a Bayesian model with CAR priors to smooth the coefficient estimates. We also consider the penalized partial likelihood approach for smoothing, which is similar to but not exactly the same as the penalized likelihood approach of Heisey and Foong (1998). Our study show that all methods are reasonably effective.