Likelihood Ratio Meta-Analysis
Background: A CI in an updated meta-analysis may not have the expected coverage if the investigator does not account for whether the earlier meta-analysis failed to reject the null hypothesis.
Objectives: To discuss the method of likelihood ratio meta-analysis (LRMA) in relation to Cochrane’s usual method of meta-analysis.
Methods: A likelihood ratio–based approach is used in a meta-analysis to pool data from separate studies to quantitatively assess where the total evidence points. A log-likelihood ratio function is used for the measure of association in each study. Those functions are summed to obtain a combined function from which a total effect estimate, and ‘intrinsic’ confidence interval, can be retrieved. Results can be presented in a familiar forest plot format. An LRMA is demonstrated using an example of the influence of a concomitant conventional synthetic disease-modifying antirheumatic drug (csDMARD) on adherence to biologic DMARDs (bDMARD) in rheumatoid arthritis. The example includes population-based cohort studies of adult patients with rheumatoid arthritis between January 2007 and March 2014 in five Canadian provinces, and the US IBM MarketScan database. The outcome of discontinuation of bDMARD therapy is compared between patients who are concomitant versus non-concomitant users of csDMARDs.
Results: The study population comprises 20 221 new users of bDMARDs: those using adalimumab (7609), etanercept (9809), abatacept (1024) or infliximab (1779). Overall, concomitant use of csDMARD therapy is not statistically significantly associated with reduced discontinuation of bDMARD treatment in a random effects LRMA in these patients (hazard ratio=0.90, 95% intrinsic CI=0.79-1.02). The association is statistically significant when using usual random effects meta-analysis (95% CI=0.81-0.99). In the hypothetical scenario where the IBM MarketScan data were added after the original analysis, the 95% intrinsic CI remains unchanged at 0.79-1.02, but the 95% CI becomes uninterpretable.
Conclusions: LRMA yields the same point estimate as a usual meta-analysis but with a 95% intrinsic CI that is wider than the traditional 95% CI. The intrinsic CI is more readily interpretable. Further, with LRMA, there is no need to account for previous statistical significance in an updated analysis.
Patient, public and/or healthcare consumer involvement: None.