Meta-analysis of a binary outcome using individual participant data and aggregate data.

In this paper, we develop meta-analysis models that synthesize a binary outcome from health-care studies while accounting for participant-level covariates. In particular, we show how to synthesize the observed event-risk across studies while accounting for the within-study association between participant-level covariates and individual event probability. The models are adapted for situations where studies provide individual participant data (IPD), or a mixture of IPD and aggregate data. We show that the availability of IPD is crucial in at least some studies; this allows one to model potentially complex within-study associations and separate them from across-study associations, so as to account for potential ecological bias and study-level confounding. The models can produce pertinent population-level and individual-level results, such as the pooled event-risk and the covariate-specific event probability for an individual. Application is made to 14 studies of traumatic brain injury, where IPD are available for four studies and the six-month mortality risk is synthesized in relation to individual age. The results show that as individual age increases the probability of six-month mortality also increases; further, the models reveal clear evidence of ecological bias, with the mean age in each study additionally influencing an individual's mortality probability.