Graduation Date

Fall 12-17-2021

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Programs

Biostatistics

First Advisor

Gleb R. Haynatzki, PhD

Second Advisor

Yeongjin Gwon, PhD

Third Advisor

Hongying (Daisy) Dai, PhD

Fourth Advisor

Xiaoyue (Zoe) Cheng, PhD

Abstract

This dissertation focuses on the development of approximation approaches for the joint modeling (JM) of repeated measures data and time-to-event data in the presence of analytically or numerically intractable likelihoods. Current likelihood-based inferences for JMs show several limitations including (i) intractability of integrals during marginal likelihood derivations due to the complexity in computations, and (ii) the large number of nuisance parameters (unobserved) posing a problem with convergence. The h-likelihood (HL) and synthetic likelihood (SL) are two computationally efficient estimation approaches that overcome these challenges.

In the presence of extremely high censoring rates, the HL can produce bias parameter estimates. We propose a corrected h-likelihood (C-HL) for JM of repeated measures data and time-to-event data that addresses the bias due to censoring. We also apply the synthetic likelihood to infer on the JM parameters. The JMs defined throughout this dissertation use independently and identically Gaussian shared random intercepts in the repeated measures data sub-model, and an unspecified baseline hazard in the event time data sub-model.

Our proposed methods make three contributions. The first shows that C-HL improves efficiency in parameter estimates of the JM in the presence of high censoring (e.g., as high as 80%). The second applies for the first time the SL in the context of JMs of longitudinal data and survival data when the maximizing likelihood function is analytically and numerically non-available. We choose a set of summary statistics that have approximately multivariate Gaussian distribution; and we show that the SL yields credible estimates. Finally, we illustrate our methods with a new MIMIC-IV community acquired pneumonia dataset.

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