Profile Likelihood Tests for Common Risk Ratios in Meta-Analysis Studies

Abstract

It is well-known that the power of Cochran’s Q test to assess the presence of heterogeneity among treatment effects in a clinical meta-analysis is low due to the small number of studies combined. Two modified tests ( PL 1 , PL 2) were proposed by replacing the profile maximum likelihood estimator (PMLE) into the variance formula of logarithm of risk ratio in the standard chi-square test statistic for testing the null common risk ratios across all k studies ( i = 1, L, k ). The simply naive test ( SIM ) as another comparative candidate has considerably arisen. The performance of tests in terms of type I error rate under the null hypothesis and power of test under the random effects hypothesis was done via a simulation plan with various combinations of significance levels, numbers of studies, sample sizes in treatment and control arms, and true risk ratios as effect sizes of interest. The results indicated that for moderate to large study sizes ( k ≥ 16 ) in combination with moderate to large sample sizes ( ≥ 50 ) , three tests ( PL 1 , PL 2 , and Q ) could control type I error rates in almost all situations. Two proposed tests ( PL 1 , PL 2) performed best with the highest power when k ≥ 16 and moderate sample sizes ( = 50,100 ); this finding was very useful to make a recommendation to use them in practical situations. Meanwhile, the standard Q test performed best when k ≥ 16 and large sample sizes ( ≥ 500 ). Moreover, no tests were reasonable for small sample sizes ( ≤ 10 ), regardless of study size k. The simply naive test ( SIM ) is recommended to be adopted with high performance when k = 4 in combination with ( ≥ 500 ).