INFERENCE ON SURVIVAL DATA UNDER NONPROPORTIONAL HAZARDS

The objective of this research is to develop optimal (efficient) test methods for analysis of survival data under random censorship with nonproportional hazards. For the first part we revisit the weighted log-rank test where the weight function was derived by assuming the inverse Gaussian distribution for an omitted exponentiated covariate that induces a nonproportionality under the proportional hazards model. We perform a simulation study to compare the new procedure with ones using other popular weight functions including members of the Harrington-Fleming's G-rho family. The nonproportional hazards data are generated by changing the hazard ratios over time under the proportional hazards model. The results indicate that the inverse Gaussian-based test tends to have higher power than some of the members that belong to the G-rho family in detecting a difference between two survival distributions when populations become homogeneous as time progresses. The second part of the research includes development of a parametric method in detecting the validity of the proportional odds model assumption between two groups of survival data. The research is based on the premise that the test procedure developed would take advantage of knowledge of the distributional information about the data, which will improve the sensitivity of a nonparametric test method. We evaluate type I error and power probabilities of the new parametric test by using the simulated survival data following the log-logistic distribution. The error probabilities are compared with ones in the literature. The results indicate that the extended test performs with a higher sensitivity than the existing nonparametric method.The results from the proposed study provide statistical test methods that are more sensitive than existing ones under certain situations which can be used in public health relevance applications such as clinical trials