Required sample size and nonreplicability thresholds for heterogeneous genetic associations

Many gene–disease associations proposed to date have not been consistently replicated across different populations. Nonreplication often reflects false positives in the original claims. However, occasionally, nonreplication may be due to heterogeneity due to biases or even genuine diversity of the genetic effects in different populations. Here, we propose methods for estimating the required sample size to replicate an association across many studies with different amounts of between-study heterogeneity, when data are summarized through metaanalysis. We demonstrate thresholds of between-study heterogeneity (τ 0 2 ) above which one cannot reach adequate power to replicate a proposed association at a specified level of statistical significance when k studies are performed (regardless of how large these studies are). Based on empirical evidence from 91 proposed gene–disease associations (50 on candidate genes and 41 from genome-wide association efforts), the observed between-study heterogeneity is often close to or even surpasses nonreplicability thresholds. With more modest between-study heterogeneity, the required sample size increases considerably compared with when no between-study heterogeneity exists. Increases are steep as τ 0 2 is approached. Therefore, some true associations may not be practically possible to replicate with consistency, no matter how large studies are conducted. Efforts should be made to minimize between-study heterogeneity in targeted genetic effects.