RATIO OF PROPORTIONS AND THE USE OF THE D ELTA-METHOD FOR CONFIDENCE-INTERVAL ESTIMATION IN LOGISTIC-REGRESSION

Objective To present an application of logistic regression modelling t o estimate ratios of proportions, such as prevalence ratio or relative risk, and the Delta Method to estimate confidence intervals. Method T he 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 carr ied 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 a djusted prevalence ratio estimated by logistic regression were similar to those estimated by tabular analysis. Also, ranges of the confidenc e intervals of the prevalence ratio according to the Delta Method were nearly equal to those obtained by the Mantel-Haenszel approach. Concl usions The results give support to the use of the Delta Method for the estimation of confidence intervals for ratios of proportions The meth od should be seen as art alternative far situations in which the need to control a large number of potential confounders limits the use of s tratified analysis.