Accurate variance estimation for prevalence ratios

The log-binomial model is recommended for calculating the prevalence ratio in cross-sectional studies with binary outcomes. However, convergence problems may occur as this model is numerically unstable. If this happens, the Poisson model should be used, but the Poisson model variance needs to be adjusted. Here, we compare different adjustments.

Using simulation we evaluated the performance of Poisson models with i) a robust variance, ii) the scale parameter adjusted by Pearson's chi-square, and iii) the scale parameter adjusted by the deviance. These models were compared with the log-binomial model with respect to hypothesis testing. Confounding and effect modification are considered.

All adjustment models improved the variance estimation. The Poisson model with a robust variance performed best. When the log-binomial model is numerically stable as well as unstable, this model yields reasonable power and type I error values. But the Poisson model with the scale parameter adjusted by Pearson's chi-square also showed good results.

When estimating prevalence ratios, if the log-binomial fails to converge, we recommend the Poisson model with a robust estimate of variance.