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For the calculation of relative measures such as risk ratio (RR) and odds ratio (OR) in a single study, additional approaches are required for the case of zero events. In the case of zero events in one treatment arm, the Peto odds ratio (POR) can be calculated without continuity correction, and is currently the relative effect estimation method of choice for binary data with rare events. The aim of this simulation study is a variegated comparison of the estimated OR and estimated POR with the true OR in a single study with two parallel groups without confounders in data situations where the POR is currently recommended. This comparison was performed by means of several performance measures, that is the coverage, confidence interval (CI) width, mean squared error (MSE), and mean percentage error (MPE). We demonstrated that the estimator for the POR does not outperform the estimator for the OR for all the performance measures investigated. In the case of rare events, small treatment effects and similar group sizes, we demonstrated that the estimator for the POR performed better than the estimator for the OR only regarding the coverage and MPE, but not the CI width and MSE. For larger effects and unbalanced group size ratios, the coverage and MPE of the estimator for the POR were inappropriate. As in practice the true effect is unknown, the POR method should be applied only with the utmost caution.

Meta-analysis has generally been accepted as a fundamental tool for combining effect estimates from several studies. For binary studies with rare events, the Peto odds ratio (POR) method has become the relative effect estimator of choice. However, the POR leads to biased estimates for the OR when treatment effects are large or the group size ratio is not balanced. The aim of this work is to derive the limit of the POR estimator for increasing sample size, to investigate whether the POR limit is equal to the true OR and, if this is not the case, in which situations the POR limit is sufficiently close to the OR. It was found that the derived limit of the expected POR is not equivalent to the OR, because it depends on the group size ratio. Thus, the POR represents a different effect measure. We investigated in which situations the POR is reasonably close to the OR and found that this depends only slightly on the baseline risk within the range (0.001; 0.1) yet substantially on the group size ratio and the effect size itself. We derived the maximum effect size of the POR for different group size ratios and tolerated amounts of bias, for which the POR method results in an acceptable estimator of the OR. We conclude that the limit of the expected POR can be regarded as a new effect measure, which can be used in the presented situations as a valid estimate of the true OR.

For the calculation of relative measures such as risk ratio (RR) and odds ratio (OR) in a single study, additional approaches are required for the case of zero events. In the case of zero events in one treatment arm, the Peto odds ratio (POR) can be calculated without continuity correction, and is currently the relative effect estimation method of choice for binary data with rare events. The aim of this simulation study is a variegated comparison of the estimated OR and estimated POR with the true OR in a single study with two parallel groups without confounders in data situations where the POR is currently recommended. This comparison was performed by means of several performance measures, that is the coverage, confidence interval (CI) width, mean squared error (MSE), and mean percentage error (MPE). We demonstrated that the estimator for the POR does not outperform the estimator for the OR for all the performance measures investigated. In the case of rare events, small treatment effects and similar group sizes, we demonstrated that the estimator for the POR performed better than the estimator for the OR only regarding the coverage and MPE, but not the CI width and MSE. For larger effects and unbalanced group size ratios, the coverage and MPE of the estimator for the POR were inappropriate. As in practice the true effect is unknown, the POR method should be applied only with the utmost caution.

Meta-analysis has generally been accepted as a fundamental tool for combining effect estimates from several studies. For binary studies with rare events, the Peto odds ratio (POR) method has become the relative effect estimator of choice. However, the POR leads to biased estimates for the OR when treatment effects are large or the group size ratio is not balanced. The aim of this work is to derive the limit of the POR estimator for increasing sample size, to investigate whether the POR limit is equal to the true OR and, if this is not the case, in which situations the POR limit is sufficiently close to the OR. It was found that the derived limit of the expected POR is not equivalent to the OR, because it depends on the group size ratio. Thus, the POR represents a different effect measure. We investigated in which situations the POR is reasonably close to the OR and found that this depends only slightly on the baseline risk within the range (0.001; 0.1) yet substantially on the group size ratio and the effect size itself. We derived the maximum effect size of the POR for different group size ratios and tolerated amounts of bias, for which the POR method results in an acceptable estimator of the OR. We conclude that the limit of the expected POR can be regarded as a new effect measure, which can be used in the presented situations as a valid estimate of the true OR.

Background The early repolarization pattern (ERP) is common and associated with risk of sudden cardiac death. ERP is heritable, and mutations have been described in syndromatic cases. Objective To conduct a meta-analysis of genome-wide association studies to identify common genetic variants influencing ERP. Methods We ascertained ERP on the basis of electrocardiograms in 3 large community-based cohorts from Europe and the United States: the Framingham Heart Study, the Health 2000 Study, and the KORA F4 Study. We analyzed genome-wide association studies in participants with and without ERP by logistic regression assuming an additive genetic model and meta-analyzed individual cohort results. We then sought to strengthen support for findings that reached P ≤ 1 × 10 −5 in independent individuals by direct genotyping or in-silico analysis of genome-wide data. We meta-analyzed the results from both stages. Results Of 7482 individuals in the discovery stage, 452 showed ERP (ERP positive: mean age 46.9 ± 8.9 years, 30.3% women; ERP negative: 47.5 ± 9.4 years, 54.2% women). After meta-analysis, 8 single nucleotide polymorphisms reached P ≤ 1 × 10 −5 : The most significant finding was intergenic rs11653989 (odds ratio 0.47; 95% confidence interval 0.36–0.61; P = 6.9 × 10 −9 ). The most biologically relevant finding was intronic to KCND3: rs17029069 (odds ratio 1.46; 95% confidence interval 1.25–1.69; P = 8.5 × 10 −7 ). In the replication step (7151 individuals), none of the 8 variants replicated, and combined meta-analysis results failed to reach genome-wide significance. Conclusions In a genome-wide association study, we were not able to reliably identify genetic variants predisposing to ERP, presumably due to insufficient statistical power and phenotype heterogeneity. The reported heritability of ERP warrants continued investigation in larger well-phenotyped populations.