Estimating the Odds Ratio for a Continuous Predictor Using Parametric, Semi-parametric, and Non-parametric Methods: a Comparison Study Open Access

Abstract

The odds ratio (OR) is a common metric for quantifying the association between a continuous predictor (X) and a binary response (Y). Logistic regression is the predominant parametric method for estimating ORs, although variants of an alternative procedure termed the discriminant function approach offer desirable properties in certain situations. Extending beyond strictly parametric methods, this thesis investigates two additional OR estimators. The first one is based on semi-parametric restricted cubic spline (RCS) regression, while the second uses kernel density estimation (KDE) to construct a non-parametric alternative grounded in a formulation of the OR that arises in the discriminant function framework. We evaluate the RCS and KDE approaches against the discriminant function–based estimators under correctly and incorrectly specified models using simulation experiments. Our findings suggest that the non-parametric KDE-based estimator can exhibit a noteworthy degree of bias and comparatively high variance when estimating the ln(OR) specific to a given value of X. On the other hand, the semi-parametric estimator based on RCS regression attains a level of accuracy more comparable to that of the parametric methods, while capturing variation in the ln(OR) with X and demonstrating enhanced numerical stability and consistency relative to the KDE approach. In addition, when the true OR varies with X, we compute and assess a population-average estimate as a summary statistic to characterize the overall association. The OR estimators formulated in this work may be particularly advantageous when the assumptions underlying conventional logistic regression or the discriminant function approach are violated or difficult to validate empirically. The RCS approach, in particular, can naturally be extended to scenarios where more covariates are present.

Table of Contents

Introduction

Methods

Simulation Studies & Results

Discussion

References

About this Master's Thesis

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School	Laney Graduate School
Department	Biostatistics
Degree	M.S.
Submission	Master's Thesis
Language	English
Research Field	Statistics
Keyword	Restricted cubic splines Odds ratio Kernel density estimation Discriminant function approach
Committee Chair / Thesis Advisor	Robert H. Lyles, Emory University
Committee Members	Lance A. Waller, Emory University

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