Analysis of Failure Time Data Arising from Studies with Alternating Treatment Schedules

We develop statistical methods for designing and analyzing studies in which treatments are deliberately interrupted and reinitiated, but where interest lies in making inferences about continuous treatment use. We refer to such designs as alternating designs, because subjects alternate between periods in which they are taking the treatment of interest and periods when they are not. Our goals are to determine how to estimate the distribution of time to an event if the treatment were given continuously, to compare the distributions of two such continuously given treatments, and to assess the effects of covariates on the distribution of a continuously given treatment. We examine a nonparametric estimator of the cumulative hazard function for continuous treatment using data from an alternating design and show it to be uniformly consistent and asymptotically normal under certain conditions relating to the effects of interrupting the treatment. We then introduce nonparametric tests for comparing the distributions corresponding to two such continuously given treatments and derive their asymptotic properties under general alternatives to the null and under various conditions related to the interruption of treatment. We compare the properties of the alternating treatment design and the classical parallel group design and present results from a simulation study that assesses the size and power of the test procedures introduced. Finally, we examine partial likelihood methods for assessing the effects of covariates and continuous treatment on time until an event under a proportional hazards model. We illustrate the proposed methods using the results from a recent study in which subjects alternate between taking an active drug and placebo on an annual basis.