This paper presents likelihood methods for measuring statistical evidence as an alternative to traditional frequentist methods in cumulative meta-analyses in ongoing drug safety surveillance. Both methods are compared when both fixed effect and random effect models are used to combine data from multiple studies. Our case study uses data from the recent controversy over safety in two marketed drugs—rosiglitazone for Type 2 diabetes and rofecoxib for pain control. The data are a series of published results for myocardial infarct incidence in 42 rosiglitazone controlled trials and occurrence of cardiovascular events and all cause deaths in 30 rofecoxib controlled trials. The raison d’étre is (1) the assessment and comparison of the statistical evidence for adverse events from rosiglitazone and rofecoxib usage and (2) the determination of the earliest date of a safety signal from accumulating data on completed trials. Strong statistical evidence of increased risk is found for rosiglitazone in fixed effects models (under both likelihood and frequentist interpretations of those models), but not in the random supports a later date of safety signal than that advocated by frequentist methods at the one-sided effects. Likelihood methods, for 1/8 support level using a fixed effects model indicate that the evidence 0.025 level but both methods find the signal about three years earlier than public discussion of this safety issue. For rofecoxib both the fixed effects and random effects models suggest the similar conclusions for frequentist and likelihood methods with the exception of timing. Here 1/8 support level likelihood methods support a safety signal more than one year earlier than one-sided 0.025 frequentist methods and more than two years before the drug was taken off of the market. Recommendations are given for parallel continuous safety surveillance by industry, regulatory agencies and academia and for appropriate methodology.