Sample size determination under an exponential model in the presence of a confounder and type I censoring

In controlled clinical trials, random assignment of treatments to individuals is usually used to eliminate the effects of confounding variables. When there is censorship in data, however, confounding effects may not be automatically removed solely by random assignment of treatments to individuals under the exponential model. Therefore, it is important to incorporate the confounding effect into the sample size calculation even after randomization of treatments to individuals. In this paper, the discussion is restricted only to the situation where there are two comparison groups and one single Bernoulli confounding variable. Based on an exponential covariate model, an explicit sample size formula considering the confounding effect has been derived for the design of trials with type I censoring, in which an end time is fixed in advance and all responses occurring after that time are censored. The resulting sample size formula can also be applied to nonrandomized clinical trials. Finally, to provide insight into the influence of different factors on sample size calculation, a discussion on the effects of treatments, the confounder, the length of follow-up times for studied individuals, and the joint distribution of the treatment and the confounder has been included.