Randomized trials of interventions against infectious diseases are often analyzed using data on first or only episodes of disease, even when subsequent episodes have been recorded. It is often said that the Andersen-Gill (AG) model gives a biased estimate of intervention effect if there is event dependency over time. We demonstrate that, in the presence of event dependency, an effective intervention may have an indirect effect on disease risk at time t(j) via its direct effect on disease risk at time t(i), i<j, and that the AG model estimates the total effect instead of the direct effect alone. From a clinical and public health perspective, estimation of the total effect is important. Previous simulation studies showed contradictory results about the performance of the AG model in the presence of unobserved heterogeneity across individuals. We show that some of the previous studies unintentionally created informative censoring in their data generating process by including only a certain maximum number of events per individual. We re-ran some previous simulations with and without altering this maximum. With reference to the situations often seen in pneumococcal vaccine trials, we evaluated the performance of the Cox model for time to first episode and the AG model for multiple episodes. We applied these models to re-analyze data from a pneumococcal conjugate vaccine trial. We maintain that a careful clarification of research purpose is needed before one can choose a statistical model, and that the AG model is useful in the estimation of the total effect of an intervention.