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. Author manuscript; available in PMC: 2015 Jan 1.
Published in final edited form as: J Biopharm Stat. 2014;24(3):507–522. doi: 10.1080/10543406.2014.888442

Table 1.

Sample sizes N2(u) and N2(l), corresponding theoretical power φ and empirical power φ̃ for testing intervention group by time interaction effect in a three level mixed-effect fixed slope coefficient linear regression analysis, i.e., when rτ = 0, based on 1000 simulations for each combination.

φ̃(u)
φ̃(l)
ξ ΔT end N3 N1 ρ1 N2 N 2(u) R(u) φ (u) ACAR AAR ANAR N2(l) R(l) φ(l) ACAR AAR ANAR
20% 0.4 10 5 0.4 10 12 1.20 0.822 0.832 0.844 0.832 11 1.10 0.819 0.795 0.795 0.798
0.6 7 8 1.14 0.822 0.804 0.805 0.798 7 1.00 0.802 0.788 0.785 0.790
9 0.4 7 8 1.14 0.833 0.820 0.817 0.817 7 1.00 0.804 0.767 0.777 0.769
0.6 5 5 1.00 0.809 0.822 0.816 0.824 5 1.00 0.831 0.823 0.815 0.818
20 5 0.4 5 6 1.20 0.822 0.835 0.827 0.830 6 1.20 0.851 0.836 0.835 0.842
0.6 4 4 1.00 0.822 0.811 0.816 0.810 4 1.00 0.851 0.821 0.823 0.818
9 0.4 4 4 1.00 0.833 0.840 0.829 0.839 4 1.00 0.854 0.830 0.824 0.827
0.6 3 3 1.00 0.874 0.873 0.879 0.864 3 1.00 0.892 0.890 0.889 0.876
0.5 10 5 0.4 7 8 1.14 0.837 0.828 0.838 0.837 7 1.00 0.817 0.784 0.781 0.774
0.6 5 5 1.00 0.813 0.783 0.792 0.794 5 1.00 0.843 0.841 0.847 0.839
9 0.4 5 5 1.00 0.825 0.832 0.833 0.839 5 1.00 0.845 0.829 0.834 0.829
0.6 3 4 1.33 0.887 0.886 0.902 0.893 3 1.00 0.806 0.805 0.814 0.808
20 5 0.4 4 4 1.00 0.837 0.866 0.847 0.851 4 1.00 0.865 0.857 0.860 0.866
0.6 3 3 1.00 0.877 0.893 0.878 0.888 3 1.00 0.901 0.904 0.889 0.905
9 0.4 3 3 1.00 0.887 0.886 0.889 0.887 3 1.00 0.903 0.884 0.896 0.892
0.6 2 2 1.00 0.887 0.876 0.874 0.872 2 1.00 0.903 0.882 0.890 0.897
Mean 1.07 0.843 0.843 0.843 0.842 1.02 0.849 0.834 0.835 0.834
Min |φ − φ̃| 0.001 0.001 0.000 0.001 0.003 0.001
Max |φ − φ̃| 0.030 0.022 0.024 0.037 0.036 0.043
30% 0.4 10 5 0.4 10 13 1.30 0.810 0.833 0.837 0.825 12 1.20 0.829 0.812 0.803 0.821
0.6 7 9 1.29 0.825 0.838 0.849 0.845 8 1.14 0.829 0.792 0.795 0.795
9 0.4 7 9 1.29 0.843 0.834 0.830 0.836 8 1.14 0.833 0.823 0.815 0.820
0.6 5 6 1.20 0.843 0.858 0.847 0.848 5 1.00 0.809 0.799 0.800 0.798
20 5 0.4 5 7 1.40 0.838 0.852 0.858 0.851 6 1.20 0.829 0.808 0.816 0.811
0.6 4 5 1.25 0.862 0.888 0.881 0.880 4 1.00 0.829 0.801 0.801 0.796
9 0.4 4 5 1.25 0.879 0.869 0.876 0.880 4 1.00 0.833 0.797 0.793 0.801
0.6 3 3 1.00 0.843 0.837 0.832 0.832 3 1.00 0.874 0.860 0.848 0.856
0.5 10 5 0.4 7 9 1.29 0.840 0.865 0.860 0.862 8 1.14 0.844 0.821 0.822 0.827
0.6 5 6 1.20 0.840 0.848 0.846 0.843 5 1.00 0.820 0.812 0.803 0.805
9 0.4 5 6 1.20 0.857 0.848 0.853 0.856 5 1.00 0.825 0.816 0.809 0.814
0.6 3 4 1.33 0.857 0.860 0.857 0.849 4 1.33 0.887 0.859 0.861 0.858
20 5 0.4 4 5 1.25 0.875 0.906 0.889 0.896 4 1.00 0.844 0.844 0.830 0.839
0.6 3 3 1.00 0.840 0.866 0.846 0.849 3 1.00 0.883 0.867 0.869 0.854
9 0.4 3 3 1.00 0.857 0.864 0.854 0.863 3 1.00 0.887 0.862 0.867 0.860
0.6 2 2 1.00 0.857 0.849 0.841 0.840 2 1.00 0.887 0.866 0.864 0.861
Mean 1.20 0.848 0.857 0.854 0.853 1.07 0.846 0.827 0.825 0.826
Min |φ − φ̃| 0.003 0.000 0.001 0.000 0.009 0.005
Max |φ − φ̃| 0.031 0.027 0.022 0.037 0.040 0.034

Note: ACAR = Attrition Completely At Random; AAR = Attrition At Random; ANAR = Attrition Not At Random