The Shortest Width Confidence Interval for Odds Ratio in Logistic Regression

Eugene Demidenko

doi:10.4236/ojs.2012.23037

Abstract

The shortest width confidence interval (CI) for odds ratio (OR) in logistic regression is developed based on a theorem proved by Dahiya and Guttman (1982). When the variance of the logistic regression coefficient estimate is small, the shortest width CI is close to the regular Wald CI obtained by exponentiating the CI for the regression coefficient estimate. However, when the variance increases, the optimal CI may be up to 25% narrower. It is demonstrated that the shortest width CI is favorable because it has a smaller probability of covering the wrong OR value compared with the standard CI. The closed-form iterations based on the Newton's algorithm are provided, and the R function is supplied. A simulation study confirms the superior properties of the new CI for OR in small sample. Our method is illustrated with eight studies on parity as a preventive factor against bladder cancer in women.

Highlights

Odds ratio, as the exponentiated logistic regression coefficient, is a popular measure of association in medicine, epidemiology and biostatistics
The shortest width confidence interval (CI) for odds ratio (OR) in logistic regression is developed based on a theorem proved by Dahiya and Guttman (1982)
When the variance of the logistic regression coefficient estimate is small, the shortest width CI is close to the regular Wald CI obtained by exponentiating the CI for the regression coefficient estimate

Summary

Introduction

As the exponentiated logistic regression coefficient, is a popular measure of association in medicine, epidemiology and biostatistics. The confidence interval (CI) for odds ratio (OR) in logistic regression is computed by exponentiating the CI for the beta-coefficient (log OR, hereafter denoted as ), [1,2]. While it is true that if a CI for has coverage probability 1 the exponentiated CI for OR has the same coverage probability, such CI does not have the shortest width and can be improved. [4] suggested to find the shortest confidence interval for OR using the same approach but their procedure of minimization of the interval’s width was just an approximate solution. We find the exact minimum via Newton’s iterations

The Method

Why Shortest Confidence Interval?

Simulations

Example

Findings

The R Function