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. Author manuscript; available in PMC: 2017 Feb 1.
Published in final edited form as: Genet Epidemiol. 2016 Jan 18;40(2):133–143. doi: 10.1002/gepi.21947

Table 1. Empirical Type I Error Rates of the Cox FR LRT Statistics and Cox SKAT LRT, When All Variants in 6 kb Regions Were Used to Generate Genotype Data.

The order of B-spline basis was 4, and the number of B-spline basis functions was K = Kβ = 10; the number of Fourier basis functions was K = Kβ = 11. The results of Cox SKAT LRT were from R SeqMeta package by Chen et al. (2014).

Sample
Size
n 		The
Censoring
Scheme		 Number
of
Simulations		 Nominal
Level
α		 Cox FR LRT Statistics Cox
SKAT
LRT
Basis of both GVF and β (u) Basis of beta-Smooth Only
B-sp Basis Fourier Basis B-sp Basis Fourier Basis
1,000 ∞ 2,600,000 0.05 0.05608 0.05576 0.05608 0.05576 0.06944
10−3 0.00123 0.00120 0.00123 0.00120 0.00184
10−4 0.00014 0.00013 0.00014 0.00013 0.00021
10−5 1.42 × 10−5 1.19 × 10−5 1.42 × 10−5 1.19 × 10−5 2.38 × 10−5
U(0, 10) 2,100,000 0.05 0.05634 0.05604 0.0564 0.05604 0.07244
10−3 0.00127 0.00123 0.00127 0.00123 0.00188
10−4 0.00012 0.00013 0.00012 0.00013 0.00020
10−5 1.19 × 10−5 1.29 × 10−5 1.19 × 10−5 1.29 × 10−5 1.67 × 10−5
U(0, 5) 1,600,000 0.05 0.05805 0.057089 0.05810 0.05709 0.07739
10−3 0.00134 0.00129 0.00134 0.00129 0.00203
10−4 0.00015 0.00013 0.00015 0.00013 0.00021
10−5 1.31 × 10−5 9.38 × 10−6 1.31 × 10−5 9.38 × 10−6 1.63 × 10−5
U(0, 3) 1,400,000 0.05 0.06139 0.05963 0.06156 0.05963 0.08189
10−3 0.00145 0.00138 0.00146 0.00138 0.00198
10−4 0.00017 0.00017 0.00018 0.00017 0.00021
10−5 1.43 × 10−5 1.57 × 10−5 1.50 × 10−5 1.57 × 10−5 2.00 × 10−5
2,000 ∞ 3,500,000 0.05 0.05318 0.05288 0.05318 0.05288 0.06207
10−3 0.00115 0.00111 0.00115 0.00111 0.00145
10−4 0.00012 0.00012 0.00012 0.00012 0.00016
10−5 1.51 × 10−5 1.37 × 10−5 1.51 × 10−5 1.37 × 10−5 1.97 × 10−5
U(0, 10) 3,400,000 0.05 0.05331 0.05318 0.05331 0.05318 0.06411
10−3 0.00116 0.00113 0.00116 0.00113 0.00155
10−4 0.00011 0.00011 0.00011 0.00011 0.00017
10−5 1.29 × 10−5 1.35 × 10−5 1.29 × 10−5 1.35 × 10−5 1.91 × 10−5
U(0, 5) 2,900,000 0.05 0.05418 0.05354 0.05418 0.05354 0.06782
10−3 0.00118 0.00111 0.00118 0.00111 0.00162
10−4 0.00013 0.00011 0.00013 0.00011 0.00018
10−5 1.66 × 10−5 1.00 × 10−5 1.66 × 10−5 1.00 × 10−5 2.76 × 10−5
U(0, 3) 1,400,000 0.05 0.05605 0.05438 0.05610 0.05438 0.07248
10−3 0.00127 0.00116 0.00128 0.00116 0.00166
10−4 0.00014 0.00012 0.00014 0.00012 0.00017
10−5 1.43 × 10−5 1.50 × 10−5 1.43 × 10−5 1.50 × 10−5 1.57 × 10−5
3,000 ∞ 3,400,000 0.05 0.05200 0.05176 0.05200 0.05176 0.05927
10−3 0.00109 0.00106 0.00109 0.00106 0.00137
10−4 0.00012 0.00010 0.00012 0.00010 0.00014
10−5 1.29 × 10−5 1.18 × 10−5 1.29 × 10−5 1.18 × 10−5 1.71 × 10−5
U(0, 10) 3,500,000 0.05 0.05207 0.05196 0.05207 0.05196 0.06041
10−3 0.00109 0.00110 0.00109 0.00110 0.00136
10−4 0.00012 0.00011 0.00012 0.00011 0.00014
10−5 9.14 × 10−6 1.20 × 10−5 9.14 × 10−6 1.20 × 10−5 1.69 × 10−5
U(0, 5) 3,400,000 0.05 0.05275 0.05232 0.05276 0.05232 0.06303
10−3 0.00109 0.00108 0.00109 0.00108 0.00144
10−4 0.00012 0.00012 0.00012 0.00012 0.00015
10−5 1.18 × 10−5 1.44 × 10−5 1.18 × 10−5 1.44 × 10−5 1.23 × 10−5
U(0, 3) 2,500,000 0.05 0.05422 0.05295 0.05422 0.05295 0.06736
10−3 0.00114 0.00114 0.00114 0.00114 0.00147
10−4 0.00012 0.00011 0.00012 0.00011 0.00015
10−5 1.36 × 10−5 6.80 × 10−6 1.40 × 10−5 6.80 × 10−6 1.44 × 10−5
4,000 ∞ 3,500,000 0.05 0.05131 0.05125 0.05131 0.05125 0.05750
10−3 0.00107 0.00104 0.00107 0.00104 0.00127
10−4 0.00011 0.00012 0.00011 0.00012 0.00015
10−5 1.14 × 10−5 1.40 × 10−5 1.14 × 10−5 1.40 × 10−5 1.34 × 10−5
U(0, 10) 3,400,000 0.05 0.05153 0.05142 0.05153 0.05142 0.05855
10−3 0.00110 0.00108 0.00110 0.00108 0.00129
10−4 0.00011 0.00011 0.00011 0.00011 0.00014
10−5 1.09 × 10−5 1.00 × 10−5 1.09 × 10−5 1.00 × 10−5 1.56 × 10−5
U(0, 5) 3,300,000 0.05 0.05201 0.05166 0.05201 0.05166 0.06081
10−3 0.00105 0.00107 0.00105 0.00107 0.00134
10−4 0.00011 0.00011 0.00011 0.00011 0.00014
10−5 7.58 × 10−6 1.03 × 10−5 7.58 × 10−6 1.03 × 10−5 1.48 × 10−5
0.05 0.05304 0.05220 0.05305 0.05220 0.06466
103 0.00112 0.00108 0.00112 0.00108 0.00137