On pooling data summaries in the absence of interactions “response-by-study”

The standard hypothesis testing procedure in meta-analysis (or multi-center clinical trials) in the absence of treatment-by-center interaction relies on approximating the null distribution of the standard test statistic by a standard normal distribution. For relatively small sample sizes, the standard procedure has been shown by various authors to have poor control of the type I error probability, leading to too many liberal decisions. In this article, two test procedures are proposed, which rely on thet—distribution as the reference distribution. A simulation study indicates that the proposed procedures attain significance levels closer to the nominal level compared with the standard procedure.     

A note on testing the nullity of the between group variance in the one-way random effects model under variance heterogeneity

In an unbalanced and heteroscedastic one-way random effects model, we compare, by way of simulation, several test statistics for testing the null hypothesis that the variance of the random effects, also named the between group variance, is zero. These tests are the classical F-test, the test proposed by Jeyaratnam & Othman, the Welch test, and a modified version of Welch's test.     

Supplementary test procedures for overall treatment effect

Two tests are proposed for the nullity of the overall mean parameter. Simulation results are used to compare the empirical type I error rates of the tests and two other well-known tests from the literature. An example is given to demonstrate the application of the procedures.     

Extended tests for non-zero between-study variance

The ANOVA F-test, James tests and generalized F-test are extended to test hypotheses on the between-study variance for values greater than zero. Using simulations, we compare the performance of extended test procedures with respect to the actual attained type I error rate. Examples are provided to demonstrate the application of the procedures in ANOVA models and meta-analysis.     

Small sample properties of tests on homogeneity in one—way Anova and Meta—analysis

Received: January 12, 2000; revised version: July 26, 2000     

Weighted inverse chi-square method for correlated significance tests

Fisher's inverse chi-square method for combining independent significance tests is extended to cover cases of dependence among the individual tests. A weighted version of the method and its approximate null distribution are presented. To illustrate the use of the proposed method, two tests for the overall treatment efficacy are combined, with the resulting test procedure exhibiting good control of the type I error probability. Two examples from clinical trials are given to illustrate the applicability of the procedures to real-life situations.