Fast stable relative risk regression using an overparameterised EM algorithm

Relative risk regression models can be fitted using a log-link binomial GLM, however standard algorithms can suffer convergence problems. Combinatorial EM (CEM) algorithms that provide stable convergence can be computationally intensive, particularly for large models. We present a new approach using an EM algorithm with an overparameterised model that retains the stability of the CEM algorithm but greatly reduces computing time. This is demonstrated with a small example in which modified Fisher scoring fails to converge to the MLE, and a bootstrap analysis of data from a clinical trial in heart attack patients.