Estimating risk and rate ratio in rare events meta-analysis with the Mantel–Haenszel estimator and assessing heterogeneity

Böhning Dankmar (), Sangnawakij Patarawan () and Holling Heinz ()
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Böhning Dankmar: Mathematical Sciences and Southampton Statistical Sciences Research Institute, University of Southampton, Southampton SO17 1BJ, UK
Sangnawakij Patarawan: Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand
Holling Heinz: Statistics and Quantitative Methods, Faculty of Psychology and Sports Science, University of Münster, Münster 48149, Germany

The International Journal of Biostatistics, 2023, vol. 19, issue 1, 21-38

Abstract: Meta-analysis of binary outcome data faces often a situation where studies with a rare event are part of the set of studies to be considered. These studies have low occurrence of event counts to the extreme that no events occur in one or both groups to be compared. This raises issues how to estimate validly the summary risk or rate ratio across studies. A preferred choice is the Mantel–Haenszel estimator, which is still defined in the situation of zero studies unless all studies have zeros in one of the groups to be compared. For this situation, a modified Mantel–Haenszel estimator is suggested and shown to perform well by means of simulation work. Also, confidence interval estimation is discussed and evaluated in a simulation study. In a second part, heterogeneity of relative risk across studies is investigated with a new chi-square type statistic which is based on a conditional binomial distribution where the conditioning is on the event margin for each study. This is necessary as the conventional Q-statistic is undefined in the occurrence of zero studies. The null-distribution of the proposed Q-statistic is obtained by means of a parametric bootstrap as a chi-square approximation is not valid for rare events meta-analysis, as bootstrapping of the null-distribution shows. In addition, for the effect heterogeneity situation, confidence interval estimation is considered using a nonparametric bootstrap procedure. The proposed techniques are illustrated at hand of three meta-analytic data sets.

Keywords: heterogeneity; Mantel–Haenszel estimator; parametric bootstrap; Q-statistic; rare events; single- and double-zero studies (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1515/ijb-2021-0087

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