hybrid omnibus tests are also possible39. Recent studies have shown that both burden tests and overdispersion tests can be performed using only summary association statistics from each rare variant, together with summary LD information40–42 (see Box 2). Roughly, burden tests are computed as weighted sums of single-variant z-scores and overdispersion tests are computed as weighted sums of squared single-variant z-scores (analogous to previous work on common variant overdispersion tests using summary statistics19,20), with summary LD information used to specify appropriate null distributions in each case. However, a key limitation is that these studies require the use of in-sample summary LD information in preference to reference LD information to ensure appropriate null distributions and avoid false-positive associations. Thus, in contrast to summary statistic based methods for common variants (see above), both summary association statistics and in-sample summary LD information are required in order for these methods to be useful (see Discussion). An additional limitation is that, for case-control traits, asymptotic null distributions may not be valid when variant counts or case or control sample sizes are small, necessitating careful scrutiny of quantile-quantile plots.
