Quality control of the C3 and C4 protein concentrations

The C3 and C4 protein concentrations were measured in 78,268 iPSYCH2012 participants of multiple ancestries. We focused on 68,768 individuals of European ancestry with measures of C3 and C4 protein concentrations. The protein assay plates captured a substantial amount of variance (C3 = 49.4%, C4 = 45.3%). Therefore, we used a linear mixed model (LMM)⁹⁸ approach to adjust protein concentrations, y = Z_plateu_plate + e, where y represents the C3/4 protein concentration; Z_plate represents protein assay plate, a random variable; u_plate represents the random effect of protein assay plate; and e represents residual. The mixed model regression was conducted by the R package of lme4.⁹⁹ The rank-based inverse normal transformation (RINT)¹⁰⁰ was applied to the residuals to have mean 0 and variance 1. The standard deviations (SDs) adjusted for variance captured by protein assay plate were used for the interpretation of results of C3 and C4 protein concentrations, for C3 protein concentration, 1 SD unit = 2.56 mg/L (3.60 mg/L × √(1 - 0.49)), and for C4 protein concentration, 1 SD unit = 2.46 mg/L (3.33 mg/L × √(1 - 0.45)). We then performed quality control analysis in 150 individuals of African ancestry and 94 individuals of South Asian ancestry. These individuals of non-European ancestries had the measures of both C3 and C4 protein concentrations. Due to the small sample sizes, nearly all these neonatal blood samples were separately measured on different protein assay plates. We were unable to use the LMM approach to adjust protein concentration for protein assay plate. Therefore, we used a linear regression model where the protein assay plate was a fixed variable. After adjustment, we applied RINT to standardize the residuals with mean 0 and variance 1.