Measures of single arm outcome in meta-analyses of rare events in the presence of competing risks

When performing single arm meta-analyses of rare events in small populations, if the outcome of interest is incidence, it is not uncommon to have at least one study with zero events, especially in the presence of competing risks. In this paper, we address the problem of how to include studies with zero events in inverse variance meta-analyses when individual patient data are not available, going beyond the naive approach of not including the study or the use of a continuity correction. The proposed solution is the arcsine transformation of the crude cumulative incidence as its approximate variance, which is inversely proportional to the sample size, can be calculated also for studies with a zero estimate. As an alternative, generalized linear mixed models (GLMM) can be used. Simulations were performed to compare the results from inverse variance method meta-analyses of the arcsine transformed cumulative incidence to those obtained from meta-analyses of the cumulative incidence itself and of the logit transformation of the cumulative incidence. The comparisons have been carried out for different scenarios of heterogeneity, incidence, and censoring and for competing and not competing risks. The arcsine transformation showed the smallest bias and the highest coverage among models assuming within study normality. At the same time, the GLMM model had the best performance at very low incidences. The proposed method was applied to the clinical context that motivated this work, i.e. a meta-analysis of 5-year crude cumulative incidence of central nervous system recurrences in children treated for acute lymphoblastic leukemia.