Statistical Inference for the Treatment Effect in Cancer Clinical Trials
Randomized clinical trials provide the best evidence on the effect of treatment studied. There are different types of measures on the treatment effect, depending on the endpoints of the trials. For a given measure, based on the data from clinical trials, various statistical procedures are available for the inference of the treatment effect in terms of this measure. In a cancer clinical trial with a time to an event as the endpoint, hazard ratio is a popular measure for the relative difference between treatment groups. Most current statistical inference procedures for hazard ratio rely on the proportional hazard assumption, which may not be applicable to practice when it does not hold. Nonparametric confidence intervals for the hazard ratio have been proposed based on the asymptotic normality of the kernel estimate for the hazard ratio, but they were found not very satisfactory in the simulation studies. In the first part of this thesis, the empirical likelihood method is used to construct the confidence interval for the time-dependent hazard ratio. The asymptotic distribution of the empirical likelihood ratio is derived and simulation studies are conducted to evaluate the proposed method. It was also argued that the measure of the relative treatment effect based on the hazard ratio may be difficult to understand by clinicians. An alternative measure called probabilistic index was suggested and the C-index was proposed to estimate this index. However, it was pointed out recently that the expected value of the estimate based on the C-index may be far removed from the true index. In the second part of this thesis, assuming a semi-parametric density ratio model, two new estimates based on respectively the conditional likelihood and weighted empirical likelihood are proposed. Associated confidence intervals are also derived based on the bootstrap re-sampling method. The proposed inference procedures are evaluated by Monte-Carlo simulations and applied to the analysis of data from a clinical trial on early breast cancer. After primary analysis including all patients is completed in clinical trials, analysis by subgroups defined based on covariates of patients is often of interest to assess the homogeneity of treatment effects over these subgroups. The treatment-covariate interaction is usually used for this assessment. In the last part of this thesis, a non-parametric measure is used to quantify the interaction between treatments and binary covariates in the presence of censoring. Asymptotic distribution of the interaction estimates are derived and the bootstrap method is applied to construct the confidence intervals. The proposed approaches are also evaluated and compared by Monte-Carlo simulations and applied to a real data set from clinical trial.
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