TABLE A1.

Estimation results and computational performance of the five methods used in modeling interval-censored single-event data. The accuracy of the estimation is evaluated by measuring the biases and RMSE of the estimated regression coefficients, with the corresponding standard errors in parentheses. The computational performance is evaluated by the median CPU times in seconds and median number of iterations required to converge, along with the corresponding inter-quartile ranges in brackets.

Method	$\mathrm{B}\mathrm{i}\mathrm{a}\mathrm{s}({\widehat{\beta }}_1)$	$\mathrm{B}\mathrm{i}\mathrm{a}\mathrm{s}({\widehat{\beta }}_2)$	$\mathrm{B}\mathrm{i}\mathrm{a}\mathrm{s}({\widehat{\beta }}_3)$	$\mathrm{B}\mathrm{i}\mathrm{a}\mathrm{s}({\widehat{\beta }}_4)$	$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}(\widehat{\mathit{\beta }})$	CPU Time (Seconds)	Iterations
Case (I)
0th Order Approx	−0.038 (0.002)	−0.031 (0.002)	−0.021 (0.002)	−0.006 (0.002)	0.110 (0.002)	0.21 [0.20,0.21]	5 [5,5]
1st Order Approx	−0.034 (0.002)	−0.028 (0.002)	−0.019 (0.002)	−0.005 (0.002)	0.109 (0.002)	0.22 [0.21,0.22]	5 [5,5]
No Approx	0.009 (0.003)	0.004 (0.002)	0.002 (0.002)	0.005 (0.002)	0.109 (0.002)	46.41 [39.64,54.79]	940 [832,1046]
Cox PH	−0.043 (0.003)	−0.034 (0.002)	−0.024 (0.002)	−0.007 (0.002)	0.120 (0.002)	0.01 [0.01,0.01]	3 [3,3]
Package icenReg	0.009 (0.003)	0.005 (0.002)	0.002 (0.002)	0.006 (0.002)	0.110 (0.002)	0.09 [0.08,0.09]	10 [9,11]
Case (II)
0th Order Approx	−0.045 (0.002)	−0.033 (0.002)	−0.020 (0.001)	−0.012 (0.002)	0.091 (0.001)	0.49 [0.48,0.49]	5 [5,5]
1st Order Approx	−0.041 (0.002)	−0.030 (0.002)	−0.018 (0.002)	−0.011 (0.002)	0.088 (0.001)	0.51 [0.50,0.52]	5 [5,5]
No Approx	0.002 (0.002)	0.002 (0.002)	0.003 (0.002)	0.000 (0.002)	0.076 (0.001)	100.52 [69.91,115.81]	957 [885,1034]
Cox PH	−0.051 (0.002)	−0.037 (0.002)	−0.024 (0.002)	−0.014 (0.002)	0.100 (0.001)	0.02 [0.02,0.02]	3 [3,3]
Package icenReg	0.002 (0.002)	0.002 (0.002)	0.003 (0.002)	0.000 (0.002)	0.077 (0.001)	0.75 [0.73,0.78]	8 [8,8]
Case (III)
0th Order Approx	−0.043 (0.001)	−0.035 (0.001)	−0.024 (0.001)	−0.009 (0.001)	0.077 (0.001)	0.76 [0.75,0.77]	5 [5,5]
1st Order Approx	−0.039 (0.001)	−0.032 (0.001)	−0.022 (0.001)	−0.008 (0.001)	0.074 (0.001)	0.79 [0.78,0.80]	5 [5,5]
No Approx	0.002 (0.001)	−0.001 (0.001)	−0.002 (0.001)	0.002 (0.001)	0.054 (0.001)	137.35 [124.93,146.15]	970 [921,1024]
Cox PH	−0.049 (0.001)	−0.039 (0.001)	−0.027 (0.001)	−0.011 (0.001)	0.086 (0.001)	0.02 [0.02,0.02]	3 [3,3]
Package icenReg	0.002 (0.001)	−0.001 (0.001)	−0.002 (0.001)	0.002 (0.001)	0.054 (0.001)	0.43 [0.38,0.48]	12 [11,14]
Case (IV)
0th Order Approx	−0.033 (0.002)	−0.023 (0.002)	−0.014 (0.001)	−0.008 (0.002)	0.081 (0.001)	0.69 [0.62,0.71]	5 [5,5]
1st Order Approx	−0.028 (0.002)	−0.020 (0.002)	−0.011 (0.001)	−0.007 (0.002)	0.079 (0.001)	0.76 [0.66,0.78]	5 [5,5]
No Approx	0.002 (0.002)	0.002 (0.002)	0.004 (0.002)	0.000 (0.002)	0.075 (0.001)	118.86 [99.55,129.15]	918 [849,987]
Cox PH	−0.036 (0.002)	−0.025 (0.002)	−0.015 (0.002)	−0.010 (0.002)	0.086 (0.001)	0.01 [0.01,0.01]	3 [3,3]
Package icenReg	0.002 (0.002)	0.003 (0.002)	0.004 (0.002)	0.000 (0.002)	0.075 (0.001)	0.76 [0.74,0.79]	8 [8,8]
Case (V)
0th Order Approx	−0.054 (0.001)	−0.040 (0.001)	−0.025 (0.001)	−0.014 (0.002)	0.099 (0.001)	0.41 [0.41,0.42]	5 [5,5]
1st Order Approx	−0.051 (0.001)	−0.038 (0.002)	−0.023 (0.001)	−0.013 (0.002)	0.096 (0.001)	0.43 [0.42,0.43]	5 [5,5]
No Approx	0.003 (0.002)	0.003 (0.002)	0.004 (0.002)	0.001 (0.002)	0.078 (0.001)	144.31 [118.43,157.38]	1015 [937,1080]
Cox PH	−0.062 (0.002)	−0.046 (0.002)	−0.029 (0.002)	−0.017 (0.002)	0.111 (0.001)	0.01 [0.01,0.01]	3 [3,3]
Package icenReg	0.003 (0.002)	0.002 (0.002)	0.004 (0.002)	0.001 (0.002)	0.078 (0.001)	0.16 [0.15,0.17]	9 [9,10]