On Logit Confidence Intervals for the Odds Ratio with Small Samples

Unless the true association is very strong, simple large-sample confidence intervals for the odds ratio based on the delta method perform well even for small samples. Such intervals include the Woolf logit interval and the related Gart interval based on adding .5 before computing the log odds ratio estimate and its standard error. The Gart interval smooths the observed counts toward the model of equiprobability, but one obtains better coverage probabilities by smoothing toward the independence model and by extending the interval in the appropriate direction when a cell count is zero.

[1]  E. Bedrick.  Estimating the Variance of Empirical Logits and Contrasts in Empirical Log Probabilities , 1984 .

[2]  A. Agresti,et al.  Categorical Data Analysis , 1991, International Encyclopedia of Statistical Science.

[3]  A F R S Sir Ronald Fisher,et al.  CONFIDENCE LIMITS FOR A CROSS‐PRODUCT RATIO , 1962 .

[4]  J. Fleiss.  Statistical methods for rates and proportions , 1974 .

[5]  Cyrus R. Mehta,et al.  Comparison of Exact, Mid-p, and Mantel–Haenszel Confidence Intervals for the Common Odds Ratio Across Several 2 × 2 Contingency Tables , 1992 .

[6]  J. Gart.  Alternative Analyses of Contingency Tables , 1966 .

[7]  Jerome Cornfield,et al.  A Statistical Problem Arising from Retrospective Studies , 1956 .

[8]  F. J. Anscombe,et al.  On estimating binomial response relations , 1956 .

[9]  Alan Agresti,et al.  Categorical Data Analysis , 1991, International Encyclopedia of Statistical Science.

[10]  B. Haldane.  THE ESTIMATION AND SIGNIFICANCE OF THE LOGARITHM OF A RATIO OF FREQUENCIES , 1956, Annals of human genetics.

[11]  A. Agresti,et al.  Approximate is Better than “Exact” for Interval Estimation of Binomial Proportions , 1998 .

[12]  N. E. Breslow.  Statistical Methods in Cancer Research , 1986 .

[13]  J. Neyman,et al.  On the Problem of Confidence Intervals , 1935 .

[14]  B. Woolf.  ON ESTIMATING THE RELATION BETWEEN BLOOD GROUP AND DISEASE , 1955, Annals of human genetics.

[15]  J. Gart,et al.  Numerical Results on Approximate Confidence Limits for the Odds Ratio , 1972 .

[16]  P. Holland,et al.  Discrete Multivariate Analysis. , 1976 .

[17]  John J. Gart,et al.  THE COMPARISON OF PROPORTIONS: A REVIEW OF SIGNIFICANCE TESTS, CONFIDENCE INTERVALS AND ADJUSTMENTS FOR STRATIFICATION' , 1971 .

[18]  John Hinde,et al.  Statistical Modelling in GLIM. , 1989 .