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The GWAS meta-analysis was performed using the METAL program [ 18], which tests the combined effects and standard errors of effects of each common SNP across the tested populations by taking sample size and direction of genotype effects into account.
Note: Standard errors of effects are in parentheses; the % changes in hospitalizations relative to the unaffected control group due to the cleft effects are listed in brackets (the 95% confidence intervals of these % changes are included in curly brackets); ** = p < 0.05; **** = p < 0.001; the effects are estimated from (Equation 1), adjusting for the covariates in that model.
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An alternative approach to select models is a direct utilization of bootstrap samples: first using bootstrap samples to improve the estimates of standard errors of effect estimates, and then identifying models based on improved test statistics [ 24].
Publication bias was assessed by plotting the inverse of the standard errors of effect estimates with funnel plots to explore symmetry, which were assessed visually, as well as with use of Egger's regression test using the "metabias" macros in STATA 13.
This does not influence the estimated direct effects but decreases the standard errors of these effects and thereby enhances the significance of the estimated effects.
As expected, trimming decreased the standard error of effect estimates across all estimation methods and scenarios in a monotonic fashion (Figure 2).
We evaluate the performance of weight trimming by examining the bias (the absolute percentage difference from the true treatment effect), 95% confidence interval (CI) coverage, and standard error of effect estimates.
The Begg and Mazumdar rank correlation test reports the rank correlation (Kendall's tau) between the standardized effect size and the standard errors of these effects.
Standard errors of marginal effects clustered at the household level are calculated with the delta method.
When the nonlinearity increased, linearisation correctly predicted standard errors of fixed effects, but over-predicted, with sparse designs, standard errors of some variability terms.
Standard errors of indirect effects were estimated using Sobel's (1982) method [ 19].
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