A Two-Stage Procedure for Comparing Hazard Rate Functions

Abstract

SummaryComparison of two hazard rates is important in applications that are related to times to occurrence of a specific event. Conventional comparison procedures, such as the log-rank, Gehan–Wilcoxon and Peto–Peto tests, are powerful only when the two hazard rates do not cross each other. Because crossing hazard rates are common in practice, several procedures have been proposed in the literature for comparing such rates. However, most of these procedures consider only the alternative hypothesis with crossing hazard rates; many other realistic cases, including those when the two hazard rates run parallel to each other, are excluded from consideration. We propose a two-stage procedure that considers all possible alternatives, including ones with crossing or running parallel hazard rates. To define its significance level and p-value properly, a new procedure for handling the crossing hazard rates problem is suggested, which has the property that its test statistic is asymptotically independent of the test statistic of the log-rank test. We show that the two-stage procedure, with the log-rank test and the suggested procedure for handling the crossing hazard rates problem used in its two stages, performs well in applications in comparing two hazard rates.