Winner's curse in rare variants analysis: effect size estimation bias depends on effect directions and the association methods used

David Soave^1,2*Melisa Hayalioglu²Lei Sun^3,4

• ¹ontario institute for cancer research, Toronto, Ontario, Canada
• ²Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada
• ³Department of Statistical Sciences, University of Toronto, Toronto, Ontario, Canada
• ⁴Division of Biostatistics, Dalla Lana School of Public Health, University of Toronto, Toronto, Ontario, Canada

For complex human traits, a large portion of genetic heritability remains unaccounted for beyond common genetic variants; interest, therefore, exists in estimating the contribution of rare variants (RVs) to the etiology of complex traits. Research in this domain has primarily focused on genebased RV testing methods, wherein information from multiple variants is combined to maximize statistical power in detecting genes associated with the trait of interest. However, after discovering an association, estimating individual effects becomes challenging due to sample size limitations.Hence, the focus may be on estimating the average genetic effect (AGE) for the group of RVs analyzed. This study demonstrates that both AGEs and individual variant effects can be influenced by competing upward and downward biases, resulting from the winner's curse and the heterogeneity of individual variant effects, respectively. Various bias-correction techniques, including Bootstrap resampling and likelihood-based methods, have been proposed to address the winner's curse bias. We conduct a simulation study to illustrate the ramifications of these competing biases on variant effect size estimation and how they complicate the precision of pooled estimates obtained from the different bias-correction techniques. We then examine the individual effect estimates of the causal variants over the simulation replicates to show how they may contribute to the observed upward and downward biases when RVs are pooled.