## Doctoral Dissertations

Dissertations that have an embargo placed on them will not be available to anyone until the embargo expires.

N/A

#### Document Type

Campus-Only Access for Five (5) Years

#### Degree Name

Doctor of Philosophy (PhD)

Mathematics

2018

September

Jing Qian

#### Subject Categories

Biostatistics | Statistical Models | Survival Analysis

#### Abstract

Delayed entry arises frequently in follow-up studies for survival outcomes, where additional study subjects enter during the study period. We propose a quantile regression model to analyze survival data subject to delayed entry and right-censoring. Such a model offers flexibility in assessing covariate effects on survival outcome and the regression coefficients are interpretable as direct effects on the event time. Under the conditional independent censoring assumption, we proposed a weighted martingale-based estimating equation, and formulated the solution finding as a $\ell_1$-type convex optimization problem, which was solved through a linear programming algorithm. We established uniform consistency and weak convergence of the resultant estimators. We developed and justified a resampling inference procedure for variance and covariance estimation. The finite-sample performance of the proposed method was demonstrated via simulation studies. The proposed method was illustrated through an application to an atomic bomb survivors study.