Parametric inference for epidemic models

The likelihood function corresponding to epidemic data is often very complicated. We illustrate that the EM algorithm can sometimes help to simplify likelihood inferences. Difficulties with likelihood inferences about parameters of epidemic models have established a role for martingale methods. These are methods of statistical inference based on estimating equations derived from the rich theory of martingales, and they have produced simple methods of inference in a number of important applications to epidemic data. We contrast likelihood methods with martingale methods and determine which specific assumptions cause changes in inferences about the infection potential of a disease. It is found that the martingale-based estimate of the infection potential remains unaltered under a variety of commonly used model specifications but that the precision of this estimate changes as model assumptions are altered.