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Table 3 Empirical results for the averages of the relative bias (r.Bias) and standard errors (SEM), standard deviation (SD), and coverage probability (CP) for the regression parameters and variance parameter of the log-normal frailty based on the ‘imputed-by-the-right-endpoint’ and ‘proposed’ methods when the type of regression coefficients is ‘acc’ under three types of LTF proportions (‘low’, ‘moderate’, and ‘high’)

From: Additive-multiplicative hazards regression models for interval-censored semi-competing risks data with missing intermediate events

   Low (LTF(%)=22.3) Moderate (LTF(%)=34.2) High (LTF(%)=47.6)
Parameter True value r.Bias (%) SD (×105) SEM (×105) CP (%) r.Bias (%) SD (×105) SEM (×105) CP (%) r.Bias (%) SD (×105) SEM (×105) CP (%)
   Imputed-by-the-right-endpoint method
α 01 0.01 3.3 14848 14915 95.2 -20.8 16313 15029 92.0 -63.6 15651 15144 95.0
α 02 0.01 140.0 22910 22360 94.0 23.4 24852 24383 95.0 9.0 26169 28020 97.2
α 03 0.01 79.0 25396 26622 96.2 115.9 18132 17194 92.8 -4.9 14262 13148 93.0
α 12 0.0125 -100.2 27253 26397 94.4 10.5 30146 26715 93.0 74.9 25881 25844 95.4
α 32 0.01 479.4 59836 50929 92.0 -108.0 37118 33609 95.2 125.6 26069 25027 94.6
β 01 0.004 -11.6 89 86 89.4 -10.8 92 87 88.6 -11.3 86 87 89.2
β 02 0.004 -1.2 83 92 96.4 -3.9 89 94 95.2 -0.5 102 101 92.8
β 03 0.004 -8.6 83 85 91.4 -10.3 109 103 90.8 -11.6 149 133 89.4
β 12 0.005 3.7 133 130 96.0 2.3 125 126 96.2 3.0 131 129 96.0
β 32 0.004 0.4 197 199 95.8 6.6 172 171 95.2 3.4 139 151 96.2
σ 2 0.01 878.9 8926 8822 92.6 734.8 6989 7754 91.4 775.5 7514 7231 87.6
   Proposed method
α 01 0.01 29.1 15161 15024 95.2 11.9 16449 15111 91.8 -99.5 15704 15169 94.8
α 02 0.01 126.2 22920 22435 93.8 -49.7 25179 24488 95.2 -34.2 26495 28218 97.4
α 03 0.01 9.4 26768 26779 95.8 98.7 17948 17287 93.8 1.1 14013 13191 93.8
α 12 0.0125 21.2 26832 26404 95.2 44.7 29934 26567 92.8 52.4 25781 25861 95.6
α 32 0.01 280.8 60729 51753 91.4 -181.5 36859 33796 95.4 173.3 26819 25056 93.2
β 01 0.004 -7.5 95 90 92.2 -6.8 95 90 90.8 -8.1 89 90 93.0
β 02 0.004 4.1 88 96 97.2 1.8 94 99 96.2 4.6 106 105 93.4
β 03 0.004 -3.9 88 89 93.6 -4.1 116 108 92.8 -6.3 154 138 90.6
β 12 0.005 -0.9 124 124 96.4 -2.0 117 122 97.0 -1.2 123 124 95.4
β 32 0.004 2.3 195 200 95.8 6.9 171 172 95.6 3.8 137 152 97.2
σ 2 0.01 999.2 9282 9124 93.0 936.4 8781 8219 88.6 873.0 8002 7404 85.6