The Shortest Width Confidence Interval for Odds Ratio in Logistic Regression

Affiliation(s)

Section of Biostatistics and Epidemiology Geisel School of Medicine at Dartmouth, Hanover, NH, USA.

Section of Biostatistics and Epidemiology Geisel School of Medicine at Dartmouth, Hanover, NH, USA.

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.

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.

Cite this paper

E. Demidenko, "The Shortest Width Confidence Interval for Odds Ratio in Logistic Regression,"*Open Journal of Statistics*, Vol. 2 No. 3, 2012, pp. 305-308. doi: 10.4236/ojs.2012.23037.

E. Demidenko, "The Shortest Width Confidence Interval for Odds Ratio in Logistic Regression,"

References

[1] A. Agresti, “Categorical Data Analysis,” 3d Edition, Wiley, New York, 2002.

[2] B. Rosner, “Fundamentals of Biostatistics,” 7th Edition, Pacific Grove, Duxbury, 2010.

[3] R. C. Dahiya and I. Guttman, “Shortest Confidence and Prediction Intervals for the Log-Normal,” Canadian Journal of Statistics, Vol. 10, No. 4, 1982, pp. 277-291. doi:10.2307/3556194

[4] P. D. Wilson and P. Langenberg, “Usual and Shortest Confidence Intervals on Odds Ratios from Logistic Regression,” The American Statistician, Vol. 53, No. 4, 1999, pp. 332-335.

[5] K. Dietrich, E. Demidenko, A. Schned, M. S. Zens, J. Heaney and M. R. Karagas, “Parity, Early Menopause and the Incidence of Bladder Cancer in Women: A Case— Control Study and Meta-Analysis,” European Journal of Cancer, Vol. 47, No. 4, 2011, pp. 592-599. doi:10.1016/j.ejca.2010.10.007

[1] A. Agresti, “Categorical Data Analysis,” 3d Edition, Wiley, New York, 2002.

[2] B. Rosner, “Fundamentals of Biostatistics,” 7th Edition, Pacific Grove, Duxbury, 2010.

[3] R. C. Dahiya and I. Guttman, “Shortest Confidence and Prediction Intervals for the Log-Normal,” Canadian Journal of Statistics, Vol. 10, No. 4, 1982, pp. 277-291. doi:10.2307/3556194

[4] P. D. Wilson and P. Langenberg, “Usual and Shortest Confidence Intervals on Odds Ratios from Logistic Regression,” The American Statistician, Vol. 53, No. 4, 1999, pp. 332-335.

[5] K. Dietrich, E. Demidenko, A. Schned, M. S. Zens, J. Heaney and M. R. Karagas, “Parity, Early Menopause and the Incidence of Bladder Cancer in Women: A Case— Control Study and Meta-Analysis,” European Journal of Cancer, Vol. 47, No. 4, 2011, pp. 592-599. doi:10.1016/j.ejca.2010.10.007