Sample size determination in clinical trials with an emphasis on exponentially distributed responses

Sample size determination in clinical trials (and other similar studies) depends on a number of factors including the distribution of patient survival (remission) times, available estimates of the requisite parameters of the distribution under the null and alternative hypotheses, sizes of the Type I and Type II errors, and the length of the clinical trial, which in turn determines whether there are many, few, or no censored observations with regard to patient survival (remission). A further consideration is the patient recruitment period, which is assumed to begin simultaneously with the clinical trial but whose length is less than the length of the clinical trial. The purpose of this article is to explore the optimum lengths of the clinical trial and the recruitment period on the basis of minimizing the expected cost of the trial. A specified cost function, patient entry distribution, and exponential survival distribution are all assumed, primarily for illustrative purposes.