The Shortest Width Confidence Interval for Odds Ratio in Logistic Regression

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.