Exact Comparision of Hazard Rate Functions of Log-Logistic Survival Distributions

Abstract

A comparison of hazard rates of multiple treatments are compared under the assumption that survival times follow the log-logistic distribution. Exact test procedures are developed for ordered comparisons of the worst case hazard rates of several log-logistic survival functions. In particular, critical constants are computed for testing the null hypothesis that all dose levels give the same maximum hazard rates versus the alternative that the maximum hazard rates are decreasing with increasing dose level. In addition, critical constants are given for comparing equal maximum hazard rates against the alternative of valley ordered hazard rates. A procedure for building simultaneous confidence intervals for certain contrasts is provided. The procedure proposed in this thesis is then compared to two nonparametric simultaneous inference procedures compare it to two nonparametric procedures: the Jonckheere-Terpstra test and the Mack-Wolfe test.