TITLE:
Profile Likelihood Tests for Common Risk Ratios in Meta-Analysis Studies
AUTHORS:
Chukiat Viwatwongkasem, Khanokporn Donjdee, Tantanut Poodphraw
KEYWORDS:
Profile Likelihood Test, Cochran Q Test, Meta-Analysis, Heterogeneity, Risk Ratios
JOURNAL NAME:
Open Journal of Statistics,
Vol.8 No.6,
December
14,
2018
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 (PL1, PL2) 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 (PL1, PL2, and Q)
could control type I error rates in almost all situations. Two proposed tests (PL1, PL2) performed best with
the highest power whenk≥ 16and 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 whenk≥ 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).