Comparison of Two Crossing Hazard Rate Functions
by Peihua Qiu
Abstract: Motivated by a clinical trial in which zinc nasal spray is a primary treatment for viral respiratory illness, we consider comparison of two hazard rate functions which 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 the ones with crossing or running parallel hazard rate functions. 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, performs well in applications. Some recent research on comparison of two crossing hazard rate functions when longitudinal data are present will also be discussed.
This is a joint research with K. Liu, K.Y. Park, and J. Sheng.
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