Ratio of proportions and the use of the delta method for confidence interval estimation in logistic regression

OBJECTIVE: To present an application of logistic regression modelling to estimate ratios of proportions, such as prevalence ratio or relative risk, and the Delta Method to estimate confidence intervals. METHOD: The Delta Method was used because it is appropriate for the estimation of variance of non-linear functions of random variables. The method is based on Taylor's series expansion and provides a good approximation of variance estimates. A computer program, utilizing the matrix module of SAS, was developed to compute the variance estimates. A practical demonstration is presented with data from a cross-sectional study carried out on a sample of 611 women, to test the hypothesis that the lack of housework sharing is associated with high scores of psychological symptoms as measured by a validated questionnaire. RESULTS: Crude and adjusted prevalence ratio estimated by logistic regression were similar to those estimated by tabular analysis. Also, ranges of the confidence intervals of the prevalence ratio according to the Delta Method were nearly equal to those obtained by the Mantel-Haenszel approach. CONCLUSIONS: The results give support to the use of the Delta Method for the estimation of confidence intervals for ratios of proportions. The method should be seen as an alternative for situations in which the need to control a large number of potential confounders limits the use of stratified analysis.

Logistic regression; Confidence intervals; Relative risk; Delta method

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