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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 2.

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 random slope coefficient linear regression analysis, i.e., when rτ >0, based on 1000 simulations for each combination.

φ̃(u)
φ̃(l)
ξ rτ ΔT end N3 ρ1 N2 N2(u) R(u) φ (u) ACAR AAR ANAR N2(l) R(l) φ(l) ACAR AAR ANAR
20% 0.1 0.4 10 0.4 26 28 1.08 0.814 0.792 0.796 0.799 27 1.04 0.812 0.780 0.764 0.774
0.6 22 24 1.09 0.812 0.789 0.785 0.782 23 1.05 0.806 0.785 0.779 0.784
20 0.4 13 14 1.08 0.814 0.802 0.784 0.799 14 1.08 0.826 0.800 0.808 0.803
0.6 11 12 1.09 0.812 0.794 0.788 0.790 12 1.09 0.822 0.786 0.787 0.783
0.5 10 0.4 17 18 1.06 0.815 0.798 0.799 0.802 17 1.00 0.806 0.780 0.780 0.785
0.6 15 15 1.00 0.803 0.787 0.778 0.790 15 1.00 0.813 0.785 0.785 0.786
20 0.4 9 9 1.00 0.815 0.776 0.785 0.777 9 1.00 0.828 0.764 0.766 0.772
0.6 8 8 1.00 0.828 0.799 0.815 0.806 8 1.00 0.837 0.836 0.824 0.813
0.2 0.4 10 0.4 41 43 1.05 0.802 0.779 0.777 0.764 42 1.02 0.801 0.781 0.759 0.773
0.6 38 39 1.03 0.800 0.771 0.771 0.763 39 1.03 0.806 0.789 0.797 0.776
20 0.4 21 22 1.05 0.811 0.790 0.785 0.787 21 1.00 0.801 0.772 0.775 0.765
0.6 19 20 1.05 0.810 0.766 0.769 0.774 20 1.05 0.816 0.788 0.794 0.793
0.5 10 0.4 27 28 1.04 0.809 0.785 0.781 0.785 27 1.00 0.803 0.757 0.764 0.767
0.6 25 25 1.00 0.801 0.754 0.751 0.752 25 1.00 0.807 0.809 0.815 0.817
20 0.4 14 14 1.00 0.809 0.759 0.757 0.762 14 1.00 0.817 0.783 0.788 0.776
0.6 13 13 1.00 0.816 0.786 0.789 0.787 13 1.00 0.822 0.789 0.798 0.794
Mean 1.04 0.811 0.783 0.782 0.782 1.02 0.814 0.787 0.786 0.785
Min |φ− φ̃| 0.012 0.013 0.013 0.001 0.008 0.010
Max |φ− φ̃| 0.050 0.052 0.049 0.064 0.062 0.056
30% 0.1 0.4 10 0.4 26 29 1.12 0.809 0.777 0.775 0.778 27 1.04 0.802 0.752 0.738 0.739
0.6 22 25 1.14 0.814 0.745 0.745 0.750 24 1.09 0.814 0.772 0.777 0.771
20 0.4 13 15 1.15 0.822 0.783 0.786 0.788 14 1.08 0.817 0.766 0.768 0.754
0.6 11 13 1.18 0.828 0.771 0.788 0.769 12 1.09 0.814 0.738 0.756 0.742
0.5 10 0.4 17 19 1.12 0.818 0.778 0.781 0.799 18 1.06 0.818 0.742 0.756 0.774
0.6 15 16 1.07 0.814 0.769 0.763 0.756 15 1.00 0.805 0.741 0.744 0.730
20 0.4 9 10 1.11 0.837 0.796 0.806 0.794 9 1.00 0.818 0.773 0.765 0.763
0.6 8 8 1.00 0.814 0.782 0.776 0.770 8 1.00 0.830 0.770 0.770 0.776
0.2 0.4 10 0.4 41 45 1.10 0.808 0.763 0.746 0.766 43 1.05 0.804 0.759 0.762 0.764
0.6 38 40 1.05 0.802 0.740 0.742 0.739 39 1.03 0.802 0.751 0.757 0.756
20 0.4 21 23 1.10 0.817 0.774 0.766 0.759 22 1.05 0.813 0.779 0.775 0.779
0.6 19 20 1.05 0.802 0.749 0.769 0.748 20 1.05 0.812 0.760 0.760 0.765
0.5 10 0.4 27 29 1.07 0.811 0.745 0.749 0.751 28 1.04 0.811 0.757 0.757 0.742
0.6 25 26 1.04 0.808 0.746 0.730 0.741 25 1.00 0.802 0.744 0.742 0.736
20 0.4 14 15 1.07 0.824 0.779 0.771 0.772 14 1.00 0.811 0.762 0.767 0.759
0.6 13 13 1.00 0.808 0.758 0.766 0.753 13 1.00 0.818 0.763 0.765 0.774
Mean 1.09 0.815 0.766 0.766 0.765 1.04 0.812 0.758 0.760 0.758
Min |φ − φ̃| 0.032 0.031 0.019 0.034 0.037 0.034
Max |φ− φ̃| 0.069 0.078 0.067 0.076 0.064 0.075

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