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Residual Diagnostics and Statistical Inference for Shared Frailty Models

Date

2023-06-19

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Type

Thesis

Degree Level

Doctoral

Abstract

Frailty models are commonly used for analyzing clustered survival data and accounting for unobserved heterogeneity. Shared frailty models are random-effect models in which the frailties are shared among individuals within groups. Several R packages, such as survival, frailtyEM, fraltypack, frailtysurv, and frailtyHL, are available for fitting shared frailty models. However, little research has been conducted to compare their performances, leaving users without clear guidance in selecting an appropriate tool for analyzing clustered survival data. The first study in this thesis aims to address this gap by providing an overview of current R packages for fitting shared frailty models and comparing their performances through simulation studies. After fitting a shared frailty model, model diagnostics are an essential part of the modelling process. The use of residuals in assessing model adequacy is a conventional tool for normal regression. In the second study of this thesis, we propose to use the Z-residual for detecting the non-linearity in the shared frailty model. Through a simulation study, we investigate the power of Z residuals in detecting non-linear effects in covariates and demonstrate their effectiveness in diagnosing models using real data on the survival of acute myeloid leukemia patients. Typically, all residuals in survival analysis are calculated using the full dataset, resulting in a bias problem due to double usage of the dataset. In the third study of this thesis, we propose applying cross-validation methods to compute residuals for diagnosing a semi-parametric shared frailty model and investigate the performance of cross-validatory Z-residual for diagnosing a shared frailty model with non-parametric baseline hazards. We compare Z-residuals calculated through three methods: without cross-validation (No-CV) method which is the basic algorithm, 10-fold cross-validation (10-fold) and leave-one-out cross-validation (LOOCV). Through simulation studies, we investigate their performances in the detection of nonlinear effects in covariates and identification of the outliers in the dataset through graphical visualization and overall GOF test. We also compared No-CV Z-residual and LOOCV Z-residual in a real data application for identifying outliers for a kidney infection dataset. Finally, in the fourth study of this thesis, we extended the Z residual to diagnose the proportional hazards assumption and compare it with existing residual methods.

Description

Keywords

shared frailty models, random effects models, survival analysis, unobserved heterogeneity, random survival probability, functional form of covariates, residual diagnosis, cross-validation, Cox-Snell residual, goodness-of-fit, model checking, Cox PH model, proportional hazard.

Citation

Degree

Doctor of Philosophy (Ph.D.)

Department

School of Public Health

Program

Biostatistics

Advisor

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