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

Chukiat Viwatwongkasem,Khanokporn Donjdee,Tantanut Poodphraw

doi:10.4236/ojs.2018.86061

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 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).

Highlights

In a clinical trial with binary outcomes, the risk ratio (RR) as an intervention effect is defined by the ratio of probabilities of having an adverse event between a treatment group and a control group [1] [2]
For small center size (k = 4), the simply naive test (SIM) test can capture type I error on some moderate and large sample sizes and the Q test can control type I error on sample size being moderate
For study size is moderate to large ( k ≥ 16 ), two profile likelihood tests (PL1 and PL2) perform well with maintaining type I error rates when sample sizes are moderate to large; in the the Q test can capture type I error on sample size being quite large

Summary

Introduction

In a clinical trial with binary outcomes, the risk ratio (RR) as an intervention effect is defined by the ratio of probabilities (risks) of having an adverse event between a treatment group and a control group [1] [2]. Under the assumption of the fixed effect model, we assume that all studies share a common effect size It means that there is no heterogeneity between the studies; all studies contain only one true effect size over all k independent trials, and the observed effect is determined by the common true effect plus the sampling error (within-study error). The observed effect is determined by the mean of all true effects plus the within-study error and the between-study error In this sense, heterogeneity may refer to various true effect sizes from studies to studies, or the difference of studies gives the difference of the effect sizes so that one can incorporate this heterogeneity into a random effect model. Heterogeneity in the effect sizes from different studies may be explained by a set of covariates, such as characteristics of studies, type of treatment status, some average or aggregate characteristics of patients, even publication bias; a meta-regression approach may be used to account for variation from such covariates among these heterogeneous effects

Results

Discussion

Conclusion