The basic principle of meta-analysis is to combine the evidence for association from individual studies, using appropriate weights. METAL implements two approaches. The first approach converts the direction of effect and P-value observed in each study into a signed Z-score such that very negative Z-scores indicate a small P-value and an allele associated with lower disease risk or quantitative trait levels, whereas large positive Z-scores indicate a small P-value and an allele associated with higher disease risk or quantitative trait levels. Z-scores for each allele are combined across samples in a weighted sum, with weights proportional to the square-root of the sample size for each study (Stouffer et al., 1949). In a study with unequal numbers of cases and controls, we recommend that the effective sample size be provided in the input file, where Neff = 4/(1/Ncases+1/Nctrls). This approach is very flexible and allows results to be combined even when effect size estimates are not available or the β-coefficients and standard errors from individual studies are in different units. The second approach implemented in METAL weights the effect size estimates,
