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Abstract:
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We consider comparison of two hazard rates that may cross each other. A number of existing procedures for handling this problem only consider the alternative hypothesis with crossing hazard rates; many other realistic cases 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 logrank test. We show that the two-stage procedure, with the logrank test and the suggested procedure for handling the crossing hazard rates problem used in its two stages, perform well in applications in comparing two hazard rates.
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