Sample size calculation in survival trials accounting for time-varying relationship between noncompliance and risk of outcome event.

Background: Most methods of sample size calculations for survival trials adjust the estimated outcome event rates for noncompliance based on the assumption that non-compliance is independent of the risk of the outcome event although there has been published evidence that noncompliers are often at a higher risk than compliers. More recent work 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 noncompliance defined as permanent discontinuation of study treatments and risk of the outcome event in the CONVINCE trial.

Purpose: The purpose of this research is to develop methods for the log-rank sample size calculations for two-arm clinical trials that allow for the relationship between risk and noncompliance to vary over time and to study how sample size requirements vary with different patterns of the time relationship.

Methods: The method developed takes Lakatos' Markov chain approach as a basis, modifying it to incorporate time dynamics, and emphasizing permanent discontinuation of study medication as the form of noncompliance to be considered.

Results: Results with our method show that sample size depends on the relative rates of noncompliance in the two arms, the hazard for the outcome event following non-compliance, whether it involves switching to the hazard of the opposite arm or is common to both arms, and whether noncompliance occurs early or late in the trial. These factors interact with each other in complex ways, precluding simple summaries.

Limitations: This research focuses on two-arm clinical trials with time to event as primary outcome measure. The method developed is not directly applicable to trials with more complicated designs and/or trials with other types of primary outcome.

Conclusions: The pattern of the relationship between noncompliance and risk can have a dramatic impact on the sample size and power calculations in survival studies. The method introduced provides a useful tool for investigators to explore the optimal sample size accounting for various dynamic associations between noncompliance and risk.