All Times EDT
Keywords: Logrank test, sequential analysis, survival analysis, type 1 error, power
Survival studies are concerned with the time to an event over an observation time. The benefit of one treatment over another may not extend to the end of the observation time, yet the benefit over a shorter time interval may still be medically important. If the analysis using all events over the observation time did not show a significant benefit, then post hoc analyses at earlier times, which showed nominal significance, would only be viewed as suggestive of a benefit. Therefore, it would be advantageous to incorporate the possibility of shorter duration of benefit into the study design. One method would be to plan to conduct sequential logrank tests at the end of the study and, if not significant, at pre-specified earlier time points with a prespecified distribution of Type-1 error a. This paper examines the method of backwards significance testing compared to a single logrank test at the end of the study when there is loss of treatment benefit before the end of the observation period. Critical values and power are obtained by simulation for repeated logrank tests at prespecified times and a distribution. The results show that when the benefit does not extend over the entire observation period the gain in power for the backwards logrank testing procedure compared to the power of a single logrank test at the end of the study outweighs the loss of power when the treatment effect extends to the end of the observation period.