Software for attributable risk and confidence interval estimation in case-control studies

Abstract

The increasing interest in obtaining model-based estimates of attributable risk (AR) and corresponding confidence intervals, in particular when more than one risk factor and/or several confounding factors are jointly considered, led us to develop a program based on the procedure described by Benichou and Gail for case-control data. This program is structured as an SAS-macro. It is suited to analysis of the relationship between risk factors and disease in case-control studies with simple random sampling of controls, in terms of relative risks and ARs, by means of unconditional logistic regression analysis. The variance of the AR is obtained by the delta method and is based on three components, namely, (i) the variance-covariance matrix of the vector of the estimated probabilities of belonging to joint levels of the exposure and confounding factors conditional on being a case, (ii) the variance-covariance matrix of the odds ratio parameter estimates from the logistic model, and (iii) the covariances between these probability and parameter estimates. Only a limited number of commands is requested from the user (i.e., the name of the work file and the names of the variables considered). The estimated relative risks for all the factors included in the model, the attributable risk for the exposure factor under consideration, and the corresponding 95% confidence intervals are given as outputs by the macro. Computational problems, if any, may arise for large numbers of covariates because of the resulting large size of vectors and matrices. The macro was tested for reliability and consistency on published data sets of case-control studies.