Graduation Date

Fall 12-18-2020

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Programs

Biostatistics

First Advisor

Hongying (Daisy) Dai, PhD

Second Advisor

Gleb Haynatzki, PhD

Third Advisor

Xiaoyue Zoe Cheng, PhD

Fourth Advisor

Yeongjin Gwon, PhD

Abstract

In many clinical trials, time-to-event endpoints are often adopted to demonstrate a clinically convincing effect of treatments appropriately. These variables might be clustered or correlated because of certain common features, such as genetic traits or shared environmental factors or repeated events. Observations from the same cluster are assumed to be correlated because they usually share specific unobserved characteristics. Ignoring the correlations between the survival times may lead to incorrect estimates of parameters of interest and invalid statistical inferences. The scientific interest may lie in the estimation of treatment effect while accounting for the correlated event times. This dissertation proposes a shared frailty model to fit correlated or clustered survival data and investigates the effect on the corresponding estimated regression coefficients. In this work, we propose new methods using hierarchical likelihood (h-likelihood) to fit a wide range of frailty models, in which the latent frailties are treated as “parameters” and estimated jointly with other parameters of interest. The adjusted profile likelihood is adopted to estimate the frailty parameter. In this dissertation, we (1) propose effective bias correction methods for the h-likelihood estimators under the shared gamma frailty models; (2) extend the h-likelihood to log-logistic frailty model, a non-exponential family distribution, and describe the total derivative approach to estimate the model parameters; (3) propose a flexible log-skew normal distribution as the frailty distribution to model the dependency in multivariate survival data. The performance of the proposed models is examined via Monte Carlo simulations. We illustrate our methods using kidney infection and cow mastitis data.

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