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In survival studies the treatment effect on the hazard ratio may not extend over the entire observation time, yet the effect over a shorter time may be medically important. If the analysis using all events over the observation time does not show a significant benefit, then post hoc analyses at earlier times, which show nominal significance, would only be viewed as post hoc and suggestive of an effect. Therefore, it would be advantageous to incorporate a shorter duration of treatment effect into the study design. A backward sequential logrank procedure, with testing at the end of study and if not significant then sequentially at prespecified earlier time points with a prespecified distribution of Type I error, is proposed. Critical values and power are obtained by simulation for repeated logrank tests at prespecified times and  α  distribution. When the treatment effect does not extend over the entire observation period the backward logrank testing procedure is more powerful compared to the power of a single logrank test at the end of the study.

Backward Sequential Significance Testing in Survival Trials