Evaluating the performance of maximum likelihood estimation in a discriminant function framework to account for non-detectable exposure measurements in matched case-control studies Open Access

Abstract

For matched case-control studies, conditional logistic regression is the typical approach to be applied. With multivariate normality unnecessary, it is possible to investigate the discriminant function approach as an alternative to conditional logistic regression in matched case-control studies. Particularly when few or small matched sets were involved, the approach was found to give a more precise and unbiased estimator of the log odds ratio associated with a continuous predictor of primary interest. The most common method in environmental chemistry to deal with non-detects is simply substituting the detection limit or some fraction of it in place of the unknown exposure, which very likely give an estimator that far from the true value. This thesis specifically focuses on evaluating the performance of maximum likelihood estimation in a discriminant function framework to account for non-detectable exposure measurements in matched case-control studies. Compared with the expedient approach of plugging in the detection limit for non-detects and using regular or conditional logistic regression, the adjusted maximum likelihood estimation based on the discriminant function analysis shows less bias and the mean standard errors for ln(OR) are also noticeably reduced. Potential improvements could be sought to better adjust the MLE of the residual variance when using maximum likelihood accounting for nondetectable exposures in matched case-control studies.

Table of Contents

Introduction 1

Motivating Study 2

Methods 3

---Standard logistic regression 4

---Conditional logistic regression 4

---Discriminant function approach 5

---Handling non-detects 5

---Adjustment of the MLE of residual variance 6

---Delta Method 7

Simulation Studies and Results 8

Real Data Example 19

Discussion 22

References 24

About this Master's Thesis

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School	Rollins School of Public Health
Department	Biostatistics
Subfield / Discipline	Biostatistics - MPH & MSPH
Degree	M.S.P.H.
Submission	Master's Thesis
Language	English
Research Field	Statistics
Keyword	Maximum likelihood estimation Logistic regression Bias Discriminant function approach Non-detects
Committee Chair / Thesis Advisor	Lyles, Robert H., Emory University
Committee Members	Hanfelt, John, Emory University

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