Table 2 Type I error rates of the G×E test and the joint test for rare-variant (RV) simulations
Nominal levelSimRegaBurden-basedGESAT
Joint test Embedded Image
 0.050.0504 (0.0022)b0.0511 (0.0022)NA
 0.010.0093 (0.0010)0.0110 (0.0010)NA
 0.0050.0047 (0.0007)0.0056 (0.0007)NA
 0.0010.0010 (0.0003)0.0011 (0.0003)NA
G×E test Embedded Image
 0.050.0496 (0.0022)0.0523 (0.0022)0.05090 (0.0024)
 0.010.0085 (0.0009)0.0104 (0.0010)0.0119 (0.0011)
 0.0050.0038 (0.0006)0.0044 (0.0007)0.0050 (0.0007)
 0.0010.0007 (0.0026)0.0008 (0.0003)0.0007 (0.0003)
G×E test Embedded Imagec
 0.050.0473 (0.0021)0.0482 (0.0021)0.0602 (0.0024)
 0.010.0099 (0.0010)0.0112 (0.0011)0.0119 (0.0011)
 0.0050.0052 (0.0007)0.0055 (0.0007)0.0062 (0.0008)
 0.0010.0014 (0.0004)0.0010 (0.0003)0.0009 (0.0003)
  • Data were generated using a case–control design. The corresponding standard errors (SEs) are shown in parentheses. The values in italics/boldface type are those whose 95% confidence intervals (i.e., rate ± 1.96 × SE) fall below/above the nominal level. Embedded Image and Embedded Image are the group PARs of the genetic main effect and the G×E effect, respectively. The results were obtained based on 10,000 replications.

  • a Using p (the proportion of variation explained by the leading eigenvalues in Embedded Image) = 0.99.

  • b Standard errors of the type I error rates.

  • c Assuming 40 SNPs with causal main (G) effect.