Fig. 2: DeepNull increases power in the presence of covariate interactions.
From: DeepNull models non-linear covariate effects to improve phenotypic prediction and association power
a Statistical power, and (b) expected χ2 statistics for variants in the causal chromosome (chr22); (c) type I Error, and (d) expected χ2 statistics for variants in the non-causal chromosomes (chr1 and chr2.). In the case of power and expected χ2 statistics for the causal chromosome, higher is better. Methods should maintain a type I error of no more than 0.05, which is shown by the dashed gray horizontal line. For the non-causal chromosomes, the expected χ2 statistics should be 1, which is also shown in dashed gray horizontal line. X-axis values indicate the proportion of phenotypic variance explained by genotypes and covariates, respectively. Error bars are the standard error of the mean for each estimate and each bar plot summarizes results from n = 100 independent simulation replicates. The numerical results are shown in Supplementary Table 5. Indicators for P value (Wilcoxon signed-rank one-sided test) ranges: *P ≤ 0.05, **P ≤ 0.01, ***P ≤ 0.001. Source data are provided as a Source Data file.
