Possible benefits of the "logistic flip" in discerning between two logistic regression models Público

Abstract

Abstract

We investigated the relationship between and properties of odds ratio estimates in two logistic regression models: the model for a dichotomous outcome (Y) and dichotomous predictor (X) including an auxiliary continuous covariate, and the "flipped" model where X and Y are interchanged. The odds ratio is invariant to flipping when no additional covariates are considered. However, its estimates yielded by the two models in the presence of covariates are generally different unless some finer adjustments for covariate effects on the outcome in the flipped model are made (e.g., involving polynomial terms). The reason is appearing in the flipped model a non-linear function of the covariates and the model parameters and a function of the conditional probability of the predictor given the covariates are introduced. We demonstrated that the odds ratio estimates from the two models can be similar without adjustment if the function of the covariate in the flipped model is approximately linear and the predictor and covariate in the initial model are independent or related through a logistic regression. When the model for the predictor and covariate is not logistic, nonparametric approaches (such as LOESS) can be employed to estimate the conditional probability of X given the covariates.

We found that the extent of the equivalence of odds ratio estimates in initial and flipped models can be useful in data sets with covariates when it is not known which outcome is more appropriate, Y or X . We hypothesized that the difference between the odds ratio estimates yielded by the initial and "flipped' models with Y as the outcome in the initial model, and that difference when, instead, X is the outcome, can be used to discern between the correct and incorrect models. It was expected that the estimates based on the initial and reversed correct model would tend be closer to one another than the corresponding estimates based on the incorrect model. The simulation study confirmed this hypothesis in general. This approach can be useful in studies where it is not clear which model is more appropriate.

Table of Contents

Table of Contents

Introduction……………………………………………………………………………...1
Objectives…………………………………………………………………………….…..6
Methodology……………………………………………………………………………..7
I. Invariance of Odds Ratio……………………………………………………...7
II. Logistic flip in discerning between two logistic models……….14
Simulation study……………………………………………………………………….15
Discussion…………………………………………………………………………….... 22
Tables and Figures…………………………………………………………………...28
References……………………………………………………………………………....30
Appendix……………………………………………………………………………….....32
I. The condition for linearity of alpha*……………………………….…...32

II. Example of SAS output…………………………………………………......35
III. SAS partial code…………………………………………………………….....40

About this Master's Thesis

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School	Laney Graduate School
Department	Biostatistics
Degree	MS
Submission	Master's Thesis
Language	English
Research Field	Statistics
Palabra Clave	Logistic regression
Committee Chair / Thesis Advisor	Waller, Lance, Emory University
Committee Members	Lyles, Robert, Emory University Guo, Ying, Emory University

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