Abstract
BackgroundThe use of meta-analysis to aggregate the results of multiple studies has increased dramatically over the last 40 years. For homogeneous meta-analysis, the Mantel–Haenszel technique has typically been utilized. In such meta-analyses, the effect size across the contributing studies of the meta-analysis differs only by statistical error. If homogeneity cannot be assumed or established, the most popular technique developed to date is the inverse-variance DerSimonian and Laird (DL) technique (DerSimonian and Laird, in Control Clin Trials 7(3):177–88, 1986). However, both of these techniques are based on large sample, asymptotic assumptions. At best, they are approximations especially when the number of cases observed in any cell of the corresponding contingency tables is small.ResultsThis research develops an exact, non-parametric test for evaluating statistical significance and a related method for estimating effect size in the meta-analysis of k 2 × 2 tables for any level of heterogeneity as an alternative to the asymptotic techniques. Monte Carlo simulations show that even for large values of heterogeneity, the Enhanced Bernoulli Technique (EBT) is far superior at maintaining the pre-specified level of Type I Error than the DL technique. A fully tested implementation in the R statistical language is freely available from the author. In addition, a second related exact test for estimating the Effect Size was developed and is also freely available.ConclusionsThis research has developed two exact tests for the meta-analysis of dichotomous, categorical data. The EBT technique was strongly superior to the DL technique in maintaining a pre-specified level of Type I Error even at extremely high levels of heterogeneity. As shown, the DL technique demonstrated many large violations of this level. Given the various biases towards finding statistical significance prevalent in epidemiology today, a strong focus on maintaining a pre-specified level of Type I Error would seem critical. In addition, a related exact method for estimating the Effect Size was developed.
Highlights
The use of meta-analysis to aggregate the results of multiple studies has increased dramatically over the last 40 years
A non‐parametric exact test of overall statistical significance for dichotomous categorical meta‐analysis Jakob Bernoulli’s notion of what is called a Bernoulli Trial offers the basis for a non-parametric approach to aggregating multiple epidemiological studies based on dichotomous categorical data
The enhancements to the Bernoulli method developed in this paper offer a practical exact method for assessing the overall statistical significance
Summary
A non‐parametric exact test of overall statistical significance for dichotomous categorical meta‐analysis Jakob Bernoulli’s notion of what is called a Bernoulli Trial offers the basis for a non-parametric approach to aggregating multiple epidemiological studies based on dichotomous categorical data. Even for equal sample size, each of the k contributing studies could have a different Bernoulli probability, p, requiring a full convolution to determine the null distribution of the total number of times there were more cases in the exposure group relative to the control group across the k contributing studies. The ties problem The problem in adapting the standard Bernoulli Trials technique to practical meta-analysis is a procedure to deal with the situation where there are an identical number of cases in both the exposure and control arms of a study contributing to the meta-analysis. Unlike a simple Sign Test, the EBT method is based on a reasonable approach to the ties problem and combines the individual PEi values by doing the equivalent of a formal convolution of the frequency distributions of the individual contributing studies. Even for the relative risk of 1.0 depicted in the figure, the exposure distribution will have positive excursions that are
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