To calculate variance explained (R2) by the instrument, first we selected a single SNP to obtain an estimate of the phenotypic variance, var(y). Assuming effect sizes are normally distributed, we used the quantile function of the student t-distribution to transform the p-value of the SNP association into an estimate of t, t ^. The number of degrees of freedom and N were based on the effective sample size (4/(1/cases+1/controls)). The effective sample sizes were estimated at N=130,072 for schizophrenia and N=180,934 for cannabis use. The corresponding value of r was calculated using the formula t=r / (sqrt[(1- R2)/(N-2)] and obtained the R2 that corresponds to t with the online tool http://vassarstats.net/rsig.html. Subsequently, we approximated the variance of the phenotype y using var (y)=(2*MAF*(1-MAF)*β2)/ R2 in which MAF denotes the Minor Allele Frequency and β the effect size of the specific SNP. Finally, we used the estimated value of var (y) to calculate the R2 for the remaining SNPs of interest using R2=(2*MAF*(1-MAF)*β2)/var(y); and summed the R2 of all SNPs of interest included in the instrumental variable to obtain an estimate of the total R2 explained by the instrument.
