Be wary of using Poisson regression to estimate risk and relative risk

Fitting a log binomial model to binary outcome data makes it possible to estimate risk and relative risk for follow-up data, and prevalence and prevalence ratios for cross-sectional data. However, the fitting algorithm may fail to converge when the maximum likelihood solution is on the boundary of the allowable parameter space. Some authorities recommend switching to Poisson regression with robust standard errors to approximate the coefficients of the log binomial model in those circumstances. This solves the problem of non-convergence, but results in errors in the coefficient estimates that may be substantial particularly when the maximum fitted value is large. The paradox is that the circumstances in which the modified Poisson approach is needed to overcome estimation problems are the same circumstances when the error in using it is greatest. We recommend that practitioners should be wary of using modified Poisson regression to approximate risk and relative risk.