Uncertainty of the time of first significance in random effects cumulative meta-analysis

We propose a process for evaluating quantities of clinical and statistical interest in cumulative meta-analysis. We use Monte Carlo simulation studies to assess the error variance of the time to significance in cumulative meta-analysis. For the specific cumulative meta-analyses that we simulated, the 95% confidence interval of the treatment effect, estimated by the random effects method at the time of earliest significance, appears to be approximately appropriate except when the hypothesized treatment effect is near the null. The Monte Carlo approach that we used can also estimate the power of a cumulative meta-analysis when two treatments differ in efficacy. We illustrate these issues in the context of five cumulative meta-analyses, each comparing two treatments for preventing mortality from myocardial infarction. These simulated meta-analyses demonstrate our main point, which is that the time of first significance, however parameterized, is itself a random variable with error variance.