Meta-analyses triggered by previous (false-)significant findings: problems and solutions

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Abstract
Meta-analyses are typically triggered by a (potentially false-significant) finding in one of the preceding primary studies. We studied consequences of meta-analysis investigating effects when primary studies that triggered such meta-analysis are also included. We analytically determined the bias of the treatment effect estimates obtained by meta-analysis, conditional on the number of included primary and false-significant studies. The type I error rate and power of the meta-analysis were assessed using simulations. We applied a method for bias-correction, by subtracting an analytically derived bias from the treatment effect estimated in meta-analysis. Bias in meta-analytical effects and type I error rates increased when increasing numbers of primary studies with false-significant effects were included. When 20% of the primary studies showed false-significant effects, the bias was 0.33 (z-score) instead of 0, and the type I error rate was 23% instead of 5%. After applying a bias-correction, the type I error rate became indeed 5%. Inclusion of primary studies with false-significant effects leads to biased effect estimates and inflated type I error rates in the meta-analysis, depending on the number of false-significant studies. This bias can be adjusted for.

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