Does an observed zero-total-event study contain information for inference of odds ratio in meta-analysis?

This note is concerned with the contribution of an observed zero-total-event study, defined to be a study which observes zero events in both treatment and control arms, in meta-analysis. It provides a comparison of two approaches, namely the regular likelihood approach and the classical conditional likelihood approach, from several perspectives. This topic has long been debated, and it has received much renewed interest recently, in part due to the divergent views on the handling of zero-total-event studies in the high profile publication Nissen and Wolski (2007). Following a careful study of both approaches and an illustration of a numerical example, we find that, when we assume the underlying population event rates are not zero, an observed zero-total-event study actually contains information for inference on the parameters such as the common odds ratio in meta-analysis and cannot be left out in our analysis. This is contrary to the belief held by many statisticians that an observed zero-total-event study does not contribute to meta-analysis because it does not contain any information concerning the common odds ratio. The latter belief is mainly formed based on conditional likelihood arguments and/ or that an observed zero-total- event study alone cannot provide a meaningful confidence interval for the odds ratio. Our finding should help clarify a difficult question concerning how to deal with zero-total- event studies in meta-analysis of rare event studies.