Meta-analysis of incidence rate data in the presence of zero events

Matthew J Spittal, Jane Pirkis, Lyle C Gurrin

When summary results from studies of counts of events in time contain zeros, the study-specific incidence rate ratio (IRR) and its standard error cannot be calculated because the log of zero is undefined. This poses problems for the widely used inverse-variance method that weights the study-specific IRRs to generate a pooled estimate. We conducted a simulation study to compare the inverse-variance method of conducting a meta-analysis (with and without the continuity correction) with alternative methods based on either Poisson regression with fixed interventions effects or Poisson regression with random intervention effects. We manipulated the percentage of zeros in the intervention group (from no zeros to approximately 80 percent zeros), the levels of baseline variability and heterogeneity in the intervention effect, and the number of studies that comprise each meta-analysis. We applied these methods to an example from our own work in suicide prevention and to a recent meta-analysis of the effectiveness of condoms in preventing HIV transmission. As the percentage of zeros in the data increased, the inverse-variance method of pooling data shows increased bias and reduced coverage. Estimates from Poisson regression with fixed interventions effects also display evidence of bias and poor coverage, due to their inability to account for heterogeneity. Pooled IRRs from Poisson regression with random intervention effects were unaffected by the percentage of zeros in the data or the amount of heterogeneity. Inverse-variance methods perform poorly when the data contains zeros in either the control or intervention arms. Methods based on Poisson regression with random effect terms for the variance components are very flexible offer substantial improvement.