Table 1 Type I error rates of SimReg tests with vs. without low-rank approximation in rare-variant (RV) simulations
% variance retained in Embedded Image (denoted by p)Case–control samplingRandom sampling
Joint test Embedded Image
 p = 100%0.052 (0.0070)a0.025 (0.0049)
p = 99%0.052 (0.0070)0.052 (0.0070)
G×E test Embedded Image
p = 100%0.036 (0.0059)0.024 (0.0048)
p = 99%0.047 (0.0067)0.043 (0.0064)
G×E test Embedded Image
 p = 99% with 20 causal G SNPs0.064 (0.0077)0.046 (0.0066)
 p = 99% with 40 causal G SNPs0.049 (0.0068)0.046 (0.0066)
 p = 99% with 60 causal G SNPs0.045 (0.0066)0.043 (0.0064)
 p = 99% with 80 causal G SNPs0.050 (0.0069)0.042 (0.0063)
 p = 99% with 100 causal G SNPs0.041 (0.0063)0.045 (0.0066)
  • The corresponding standard errors (SEs) are shown in parentheses. The values in italics are those whose 95% confidence intervals (i.e., rate Embedded Image) fall below the nominal level. The results are based on 1000 replications. Embedded Image and Embedded Image are the group PARs of the genetic main effect and the G×E effect, respectively.

  • a Standard errors of the type I error rates.