Approximate marginal likelihoods for shrinkage parameter estimation in penalized logistic regression analysis of case-control data

Author: 
Date created: 
2020-04-17
Identifier: 
etd20822
Keywords: 
Case-control study
Penalised likelihood
Log-F priors
Laplace Approximation
Alzheimer’s Disease
Abstract: 

Inference of associations between disease status and rare exposures is complicated by the finite-sample bias of the maximum likelihood estimator for logistic regression. Penalised likelihood methods are useful for reducing such bias. In this project, we studied penalisation by a family of log-F priors indexed by a shrinkage parameter m. We propose a method for estimating m based on an approximate marginal likelihood obtained by Laplace approximation. Derivatives of the approximate marginal likelihood for m are challenging to compute, and so we explore several derivative-free optimization approaches to obtaining the maximum marginal likelihood estimate. We conduct a simulation study to evaluate the performance of our method under a variety of data-generating scenarios, and applied the method to real data from a genetic association study of Alzheimer's disease.

Document type: 
Graduating extended essay / Research project
Rights: 
This thesis may be printed or downloaded for non-commercial research and scholarly purposes. Copyright remains with the author.
File(s): 
Supervisor(s): 
Brad McNeney
Department: 
Science: Department of Statistics and Actuarial Science
Thesis type: 
(Project) M.Sc.
Statistics: