Researchers often combine the results from multiple clinical trials in a meta-analysis (“analysis of analyses”) in order to answer medical questions on the occurrence of medical events. For example, side effects of drugs are often so rare that for a meaningful analysis, data from many trials must be investigated simultaneously.

Ideally, analyses of medical event occurrence should use information from individual patients. For example, the information about which patient experienced an event and after what length of observation this happened, or for how long the patient was in the trial without having the event. However, such individual patient data are often not available. In this case, researchers often compare the percentage of patients with an event between treatment groups. In most trials some patients (“drop-outs”) are not observed for the full planned trial duration. When there are differences in the distribution of dropout times between the treatment groups in a trial, a comparison of the percentages of patients with an event between groups is biased. This is because the probability of a patient having a medical event typically increases the longer the patient is followed. However, it is still possible to obtain a valid comparison of the treatment groups by assuming specific distributions for the event and drop-out times. This requires the aggregate data on the number of patients that were in each treatment group, the number which had an event, that died due to an event, and that dropped out as well as the planned length of the trial.

By using a statistical model that borrows information about the hazard rates (probability of an event in a small time interval for a patient that has not had an event, yet, divided by the length of the time interval) for events and for dropouts across trials (a “hierarchical model”) it is possible to let all trials contribute to treatment comparisons even when there are no events in some or all treatment groups of some trials. This requires the assumption that, without seeing the data, it is unknown whether these hazard rates are higher or lower in any trial compared to any of the other trials. A hierarchical model that makes this assumption about the expected percentage of patients with an event is problematic, because a higher percentage of patients is expected to have an event in a longer trial.

It is difficult to estimate the hazard rate for events and dropouts from aggregate data, if we do not assume that both are constant over time, because the observed aggregate data of a particular single trial could equally likely have arisen under a number of different scenarios. For example, the same number of patients may have events based on a close to constant hazard rate throughout a trial or based on an initially higher hazard rate that decreased over time. In such a scenario, it helps to have prior information on these hazard rates and to assume that they are similar across trials.

When using prior information, it is important to allow for the possibility that the selected prior information is not fully supported by the new data under analysis. If this happens, researchers typically wish to partially discount the prior information or to even almost entirely ignore it in an appropriate manner. This can be achieved by using a robust prior distribution that also assigns some probability to the possibility that the prior information is not as relevant as was originally believed.