| A two-sample Z test of proportions is often performed in randomized clinical trials designed to assess the superiority of an experimental treatment to a control with respect to a long-term dichotomous primary endpoint, such as 1-year mortality. Due to the staggered entry of participants across the trial's recruitment period, only a portion of enrolled participants have complete follow-up data available at the time of an interim analysis. Typically, the interim evaluation of trial hypotheses is performed using the same test statistic as the test statistic planned for the final analysis. However, application of the Z test of proportions at interim analysis results in a potentially substantial reduction to the number of participants that are able to contribute to the analysis. In this dissertation, methodology for the use of the log-rank test, which incorporates data of all enrolled participants regardless of the amount of time each has been followed, in the interim analysis of trials with a dichotomous final primary endpoint is developed and evaluated. Although the overall power and type I error rates of the newly proposed methodology and the standard methodology are comparable under the assumption of proportional hazards and event rates less than 50%, the efficiency of using the log-rank test during the interim analysis was realized in terms of an increased probability of early trial termination for overwhelming efficacy resulting in potential for shorter trials and smaller sized trials. Methodology for using the log-rank test was also developed for and applied to trials incorporating an adaptation for sample size re-estimation at interim based on the conditional power of achieving a significant result by the end of the trial. In the context of sample size re-estimation, the use of the log-rank test not only increased the probability of declaring superiority of the experimental treatment over the control at the time of interim analysis, but increased the overall power. Regardless of whether or not sample size re-estimation is used, greater efficiency is attained when the log-rank test is performed at interim analysis as the differential between the percentages of subjects enrolled and with complete follow-up at interim analysis increases. |
