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. Author manuscript; available in PMC: 2017 Apr 1.
Published in final edited form as: Stat Methods Med Res. 2012 Dec 6;25(2):686–705. doi: 10.1177/0962280212465163

Table 3a.

Asymptotic (Asym) and empirical (Emp) powers for 2-visit studies from 2000 simulations under various values for a0 (true value of a), b0 (true value of b), sample size n and drop out rate pd, with joint significance test (Joint Sig) and normal approximation (Norm Appr) methods used for the test of Δ = ab. For normal approximation method, percentage that 95% confidence interval covers the true value (Cover) is also presented. Bias is the simulation bias of Δ̂ = âb̂.

Test of a Test of b Test of Δ = ab
Joint Sig Norm Appr
a b n p pd Bias Δ̂ Asym Emp Asym Emp Asym Emp Cover Asym Emp
0.25 0.10 100 0.25 0 −0.0004 0.242 0.231 0.125 0.125 0.030 0.026 0.951 0.101 0.004
0.10 0.0005 0.242 0.247 0.120 0.136 0.029 0.030 0.945 0.098 0.003
0.30 0.0024 0.242 0.245 0.107 0.139 0.026 0.036 0.961 0.091 0.007
0.75 0 0.0001 0.242 0.234 0.289 0.283 0.070 0.077 0.919 0.153 0.013
0.10 −0.0003 0.242 0.239 0.268 0.279 0.065 0.071 0.915 0.149 0.013
0.30 −0.0007 0.242 0.258 0.223 0.212 0.054 0.050 0.934 0.137 0.007
200 0.25 0 0.0008 0.429 0.426 0.208 0.214 0.089 0.095 0.923 0.160 0.021
0.10 −0.0003 0.429 0.424 0.197 0.193 0.085 0.084 0.919 0.154 0.021
0.30 0.0005 0.429 0.429 0.173 0.178 0.074 0.081 0.928 0.141 0.014
0.75 0 0.0002 0.429 0.442 0.510 0.498 0.219 0.222 0.911 0.263 0.075
0.10 0.0000 0.429 0.432 0.474 0.462 0.203 0.197 0.912 0.254 0.063
0.30 −0.0005 0.429 0.417 0.395 0.381 0.169 0.151 0.901 0.232 0.038
500 0.25 0 0.0002 0.804 0.798 0.441 0.442 0.355 0.351 0.924 0.331 0.164
0.10 −0.0002 0.804 0.800 0.418 0.409 0.336 0.332 0.918 0.318 0.144
0.30 0.0005 0.804 0.794 0.363 0.385 0.292 0.301 0.928 0.287 0.130
1000 0.25 0 −0.0002 0.979 0.979 0.726 0.714 0.711 0.699 0.943 0.577 0.550
0.10 0.0000 0.979 0.982 0.698 0.702 0.683 0.691 0.935 0.557 0.525
0.30 −0.0001 0.979 0.981 0.624 0.613 0.610 0.603 0.935 0.506 0.459
0.30 100 0.25 0 0.0012 0.242 0.250 0.681 0.674 0.165 0.166 0.926 0.200 0.048
0.10 0.0011 0.242 0.245 0.652 0.624 0.158 0.150 0.913 0.198 0.047
0.30 0.0000 0.242 0.240 0.579 0.564 0.140 0.136 0.903 0.192 0.045
200 0.25 0 0.0009 0.429 0.434 0.930 0.920 0.399 0.400 0.934 0.353 0.224
0.10 0.0014 0.429 0.442 0.914 0.911 0.392 0.401 0.940 0.348 0.214
0.30 0.0013 0.429 0.426 0.863 0.838 0.370 0.359 0.924 0.337 0.185
500 0.25 0 0.0005 0.804 0.808 1.000 1.000 0.804 0.807 0.936 0.706 0.759
0.10 0.0007 0.804 0.800 1.000 1.000 0.804 0.800 0.930 0.700 0.748
0.30 0.0004 0.804 0.808 0.998 0.998 0.803 0.806 0.935 0.682 0.728
0.75 0.10 100 0.25 0 −0.0028 0.982 0.983 0.115 0.112 0.112 0.110 0.964 0.112 0.056
0.10 −0.0015 0.982 0.975 0.110 0.117 0.108 0.114 0.961 0.108 0.060
0.30 0.0009 0.982 0.977 0.099 0.106 0.097 0.103 0.965 0.097 0.056
200 0.25 0 −0.0022 1.000 1.000 0.187 0.166 0.187 0.166 0.959 0.182 0.139
0.10 −0.0006 1.000 1.000 0.178 0.170 0.178 0.170 0.947 0.173 0.137
0.30 0.0020 1.000 1.000 0.156 0.162 0.156 0.162 0.964 0.153 0.127
500 0.25 0 0.0001 1.000 1.000 0.395 0.400 0.395 0.400 0.952 0.384 0.381
0.10 −0.0004 1.000 1.000 0.373 0.368 0.373 0.368 0.946 0.363 0.347
0.30 −0.0003 1.000 1.000 0.324 0.321 0.324 0.321 0.951 0.317 0.304
1000 0.25 0 −0.0008 1.000 1.000 0.668 0.665 0.668 0.665 0.952 0.653 0.654
0.10 0.0006 1.000 1.000 0.639 0.633 0.639 0.633 0.958 0.625 0.627
0.30 0.0007 1.000 1.000 0.566 0.572 0.566 0.572 0.953 0.555 0.561
0.30 100 0.25 0 −0.0003 0.982 0.985 0.622 0.617 0.611 0.607 0.937 0.508 0.453
0.10 0.0034 0.982 0.980 0.593 0.597 0.582 0.583 0.937 0.488 0.434
0.30 0.0012 0.982 0.982 0.523 0.517 0.513 0.507 0.948 0.438 0.365
200 0.25 0 −0.0013 1.000 1.000 0.895 0.880 0.895 0.880 0.945 0.800 0.851
0.10 0.0041 1.000 1.000 0.874 0.873 0.874 0.873 0.949 0.779 0.842
0.30 −0.0027 1.000 1.000 0.814 0.792 0.814 0.792 0.934 0.723 0.745