A series of two-sample non-parametric tests of quantile residual lifetime

Quantile residual lifetime (QRL) is of significant interest in many clinical studies as an easily interpretable quantity compared to other summary measures of survival distributions. In cancer or other fatal diseases, treatments are often compared based on the distributions or quantiles of the residual lifetime. Thus a common problem of interest is to test the equality of the QRL between two populations. In the first chapter of this dissertation, we propose two classes of tests to compare two QRLs; one class is based on the difference between two estimated QRLs, and the other is based on the estimating function of the QRL, where the estimated QRL from one sample is plugged into the QRL-estimating-function of the other sample. We outline the asymptotic properties of the pro-posed test statistics. Simulation studies demonstrate that the proposed tests produced Type I errors closer to the nominal level and are superior to some existing tests based on both Type I error and power. Our proposed statistics are also computationally less intensive and more straightforward compared to tests based on the confidence intervals. Moreover, for experimental designs, such as for randomized control trials, there is often no interest or need to adjust for the confounding factors due to the nature of the randomization. However, when there is missing data, adding the covariate information can help in improving the efficiency of estimators, e.g., the estimated treatment effect. In the second chapter, we propose an augmented inverse probability weighting estimator (AIPW) for QRL by incorporating the auxiliary covariate information in the presence of right-censoring. Simulation studies shows that our proposed estimator has smaller variance compared to the inverse probability estimator (IPW) and the Kaplan-Meier type estimator for the QRL when the auxiliary covariate is associated with the survival outcome. In contrast, there is minimal efficiency gain over our previously proposed test of equality of two QRLs when using the AIPW estimator compared to the IPW or Kaplan-Meier type estimators. We applied the proposed methods to a randomized multicenter Phase III trial for breast cancer patients with positive lymph nodes. The public health significance of this dissertation is that it provides new methods to estimate and compare the QRLs of the time to event data, that can be used in in epidemiological and clinical studies to estimate and test QRLs more efficiently. This will help make superior inference of the survival outcome in future randomized clinical trials and the observational studies