Objective: To empirically compare the Cox, log-binomial, Poisson and logistic regressions to obtain estimates of prevalence ratios (PR) in cross-sectional studies.
Methods: Data from a population-based cross-sectional epidemiological study (n = 2072) on elderly people in Sao Paulo (Southeastern Brazil), conducted between May 2003 and April 2005, were used. Diagnoses of dementia, possible cases of common mental disorders and self-rated poor health were chosen as outcomes with low, intermediate and high prevalence, respectively. Confounding variables with two or more categories or continuous values were used. Reference values for point and interval estimates of prevalence ratio (PR) were obtained by means of the Mantel-Haenszel stratification method. Adjusted PR estimates were calculated using Cox and Poisson regressions with robust variance, and using log-binomial regression. Crude and adjusted odds ratios (ORs) were obtained using logistic regression.
Results: The point and interval estimates obtained using Cox and Poisson regressions were very similar to those obtained using Mantel-Haenszel stratification, independent of the outcome prevalence and the covariates in the model. The log-binomial model presented convergence difficulties when the outcome had high prevalence and there was a continuous covariate in the model. Logistic regression produced point and interval estimates that were higher than those obtained using the other methods, particularly when for outcomes with high initial prevalence. If interpreted as PR estimates, the ORs would overestimate the associations for outcomes with low, intermediate and high prevalence by 13%, almost by 100% and fourfold, respectively.
Conclusions: In analyses of data from cross-sectional studies, the Cox and Poisson models with robust variance are better alternatives than logistic regression is. The log-binomial regression model produces unbiased PR estimates, but may present convergence difficulties when the outcome is very prevalent and the confounding variable is continuous.