Fig. 4: Reporting-error-adjusted participation weights.

a, Truncated density curves of the normalized UKBB weights (w), estimated for n = 63,898 participants. The effective sample size was estimated as n × {1/[Var(w) + 1]}. b, R² = variance explained by standard (ordinary least squares) regression models regressing P_T2 onto P_T1, while controlling for follow-up time (time_{T2 − T1}). R²_w = variance explained by weighted (weighted least squares regression) models, incorporating UKBB weights to adjust for selective participation (top: unadjusted participation weights), reporting error (middle: reporting error weights) or both (bottom: reporting-error-adjusted participation weights). Positive values in R²_diff (R² − R²_w) index reduced measurement repeatability following weighting. c, Change in means as a function of weighting, obtained for two continuous phenotypes known to link to UKBB participation (age and education). Change in means was expressed as a standardized mean difference, that is, the difference between the unweighted mean (m) and the weighted mean (m_w), divided by the unweighted standard deviation (m_w − m/s.d.).