Fig. 2

Statistical power in hypothesis testing to detect a true association between a genetic variant and COVID-19 disease severity at the genome-wide significance level (5e−8). A 1:1 case-control study design was used for all parameter settings. Only one red curve is shown since the study design uses confirmed infected individuals with mild or no symptoms as controls (test-positive controls), which is unaffected by population-level infection rates and the corresponding case-control misclassification. Effect sizes are reported on the odds ratio (OR) scale for each additional risk allele (log-additive scale). Perfect test accuracy is assumed in all plots. a Assumes a common variant with large effect size (OR = 1.7, MAF = 0.2). Using test-positive controls (red) yields higher power than using population-based (untested) controls (blue). High population infection rates reduce the gap between the two study designs but remains unlikely in the current phase of the pandemic. b Detecting a common variant with moderate effect size (OR = 1.3, MAF = 0.2) is challenging without drastically increasing the number of participants included for either design. c Detecting a rare variant even with a large effect size (OR = 5, MAF = 0.01) is more difficult with currently available sample sizes. Using test-positive controls without misclassification once again demonstrates higher power compared to population-based untested controls with misclassification. d Assumes OR = 1.7 and MAF = 0.2. Relative reduction in sample size, \( 1-\frac{n_{\mathrm{test}\_\mathrm{positive}\_\mathrm{controls}}}{n_{\mathrm{population}\_\mathrm{controls}}} \), from using test-positive controls compared to population-based controls. n_{test _ positive _ controls} and n_{population _ controls} refer to the number of cases (1:1 case-control ratio) needed to achieve 80% power at the genome-wide significance level (5e–8) [18]. Relative reduction in sample size for other settings show similar trend and can be found in Additional file 2: Table S1