Log-mean linear regression models for assessing the effect of HIV-infection on multimorbidity in a case-control study

We propose a multivariate regression approach for binary variables based on the log-mean linear link function for the response variables. This approach has shown to provide useful insights for assessing the effect of HIV-infection on multimorbidity, defined as the occurrence of co-existing noninfectious diseases for a sample of patients deriving from a case-control study. The coefficients of these regression models are log-linear combinations of relative risks and we show that submodels identified by zero regression coefficients encode relevant hypotheses for the considered application.