A Tables

Table A.1: Bias, comparison with analytical formulae, scenario with a small frailty variance and a negative regression coefficient.

Sample size	Method	Lambda	P	Beta	Theta
1000c. of 2i.	AF	0.002 (0.002)	0.001 (0.001)	-0.003 (0.002)	-0.017 (0.008)
1000c. of 2i.	IN	0.000 (0.002)	0.000 (0.001)	-0.003 (0.002)	-0.032 (0.008)
1000c. of 2i.	GQ15	0.011 (0.002)	0.005 (0.001)	-0.007 (0.002)	0.086 (0.003)
1000c. of 2i.	GQ35	0.002 (0.002)	0.001 (0.001)	-0.003 (0.002)	-0.011 (0.008)
1000c. of 2i.	GQ75	0.002 (0.002)	0.001 (0.001)	-0.003 (0.002)	-0.017 (0.008)
1000c. of 2i.	GQ105	0.002 (0.002)	0.001 (0.001)	-0.003 (0.002)	-0.017 (0.008)
15c. of 100i.	AF	-0.008 (0.004)	0.002 (0.001)	-0.001 (0.002)	-0.146 (0.013)
15c. of 100i.	IN	-0.007 (0.004)	0.002 (0.001)	-0.001 (0.002)	-0.146 (0.013)
15c. of 100i.	GQ15	-0.165 (0.008)	0.003 (0.001)	-0.002 (0.002)	0.223 (0.013)
15c. of 100i.	GQ35	-0.086 (0.006)	0.002 (0.001)	-0.001 (0.002)	-0.028 (0.013)
15c. of 100i.	GQ75	-0.040 (0.005)	0.001 (0.001)	-0.001 (0.002)	-0.114 (0.013)
15c. of 100i.	GQ105	-0.008 (0.005)	0.002 (0.001)	-0.001 (0.002)	-0.130 (0.013)
15c. of 30i.	AF	-0.010 (0.005)	0.002 (0.002)	-0.007 (0.004)	-0.215 (0.017)
15c. of 30i.	IN	-0.008 (0.005)	0.002 (0.002)	-0.008 (0.004)	-0.215 (0.017)
15c. of 30i.	GQ15	-0.053 (0.007)	0.003 (0.002)	-0.007 (0.004)	-0.025 (0.014)
15c. of 30i.	GQ35	-0.003 (0.005)	0.002 (0.002)	-0.008 (0.004)	-0.194 (0.021)
15c. of 30i.	GQ75	-0.010 (0.005)	0.002 (0.002)	-0.007 (0.004)	-0.216 (0.017)
15c. of 30i.	GQ105	-0.010 (0.005)	0.002 (0.002)	-0.007 (0.004)	-0.216 (0.017)
15c. of 500i.	AF	-0.011 (0.004)	0.000 (0.000)	0.001 (0.001)	-0.142 (0.012)
15c. of 500i.	IN	-0.049 (0.005)	0.000 (0.000)	0.001 (0.001)	-0.067 (0.013)
15c. of 500i.	GQ15	-0.225 (0.009)	0.001 (0.000)	0.001 (0.001)	0.317 (0.015)
15c. of 500i.	GQ35	-0.145 (0.006)	0.001 (0.000)	0.001 (0.001)	0.073 (0.013)
15c. of 500i.	GQ75	-0.109 (0.005)	0.000 (0.000)	0.001 (0.001)	-0.033 (0.012)
15c. of 500i.	GQ105	-0.101 (0.005)	0.000 (0.000)	0.001 (0.001)	-0.057 (0.012)
50c. of 100i.	AF	0.000 (0.002)	0.000 (0.001)	-0.002 (0.001)	-0.044 (0.007)
50c. of 100i.	IN	0.001 (0.002)	0.000 (0.001)	-0.002 (0.001)	-0.045 (0.007)
50c. of 100i.	GQ15	-0.207 (0.006)	0.001 (0.001)	-0.003 (0.001)	0.316 (0.009)
50c. of 100i.	GQ35	-0.088 (0.004)	0.000 (0.001)	-0.002 (0.001)	0.062 (0.007)
50c. of 100i.	GQ75	-0.020 (0.003)	0.000 (0.001)	-0.002 (0.001)	-0.025 (0.007)
50c. of 100i.	GQ105	-0.002 (0.003)	0.000 (0.001)	-0.002 (0.001)	-0.036 (0.007)
50c. of 30i.	AF	-0.002 (0.003)	0.000 (0.001)	-0.002 (0.002)	-0.046 (0.008)
50c. of 30i.	IN	-0.002 (0.003)	0.000 (0.001)	-0.004 (0.002)	-0.043 (0.008)
50c. of 30i.	GQ15	-0.045 (0.004)	0.001 (0.001)	-0.003 (0.002)	0.082 (0.007)
50c. of 30i.	GQ35	-0.002 (0.003)	0.000 (0.001)	-0.002 (0.002)	-0.038 (0.008)
50c. of 30i.	GQ75	-0.002 (0.003)	0.000 (0.001)	-0.002 (0.002)	-0.046 (0.008)
50c. of 30i.	GQ105	-0.002 (0.003)	0.000 (0.001)	-0.002 (0.002)	-0.046 (0.008)

Table A.2: Coverage, comparison with analytical formulae, scenario with a small frailty variance and a negative regression coefficient.

Sample size	Method	Lambda	P	Beta	Theta
1000c. of 2i.	AF	94.20 (0.74)	95.50 (0.66)	95.00 (0.69)	96.50 (0.58)
1000c. of 2i.	IN	93.42 (0.78)	95.70 (0.64)	93.02 (0.81)	77.45 (1.32)
1000c. of 2i.	GQ15	93.60 (0.77)	95.40 (0.66)	95.10 (0.68)	98.70 (0.36)
1000c. of 2i.	GQ35	94.29 (0.73)	95.10 (0.68)	95.30 (0.67)	95.90 (0.63)
1000c. of 2i.	GQ75	94.20 (0.74)	95.50 (0.66)	95.00 (0.69)	96.50 (0.58)
1000c. of 2i.	GQ105	94.20 (0.74)	95.50 (0.66)	95.00 (0.69)	96.50 (0.58)
15c. of 100i.	AF	92.40 (0.84)	95.50 (0.66)	94.70 (0.71)	92.60 (0.83)
15c. of 100i.	IN	90.65 (0.92)	95.48 (0.66)	94.45 (0.72)	92.39 (0.84)
15c. of 100i.	GQ15	27.80 (1.42)	94.60 (0.71)	94.90 (0.70)	86.70 (1.07)
15c. of 100i.	GQ35	44.04 (1.57)	94.79 (0.70)	94.89 (0.70)	93.99 (0.75)
15c. of 100i.	GQ75	66.00 (1.50)	95.10 (0.68)	95.10 (0.68)	93.00 (0.81)
15c. of 100i.	GQ105	76.20 (1.35)	95.50 (0.66)	94.80 (0.70)	92.50 (0.83)
15c. of 30i.	AF	92.70 (0.82)	95.00 (0.69)	94.70 (0.71)	94.50 (0.72)
15c. of 30i.	IN	92.21 (0.85)	94.91 (0.69)	94.08 (0.75)	93.15 (0.80)
15c. of 30i.	GQ15	68.10 (1.47)	94.70 (0.71)	94.70 (0.71)	93.10 (0.80)
15c. of 30i.	GQ35	88.91 (0.99)	94.61 (0.71)	94.20 (0.74)	95.23 (0.67)
15c. of 30i.	GQ75	92.50 (0.83)	95.00 (0.69)	94.70 (0.71)	94.10 (0.75)
15c. of 30i.	GQ105	92.70 (0.82)	95.00 (0.69)	94.60 (0.71)	94.60 (0.71)
15c. of 500i.	AF	92.50 (0.83)	95.40 (0.66)	95.70 (0.64)	91.60 (0.88)
15c. of 500i.	IN	31.74 (1.47)	95.02 (0.69)	95.63 (0.65)	91.25 (0.89)
15c. of 500i.	GQ15	11.00 (0.99)	92.50 (0.83)	94.90 (0.70)	80.40 (1.26)
15c. of 500i.	GQ35	14.20 (1.10)	93.80 (0.76)	95.70 (0.64)	91.50 (0.88)
15c. of 500i.	GQ75	18.40 (1.23)	94.80 (0.70)	95.90 (0.63)	93.40 (0.79)
15c. of 500i.	GQ105	22.00 (1.31)	95.20 (0.68)	95.40 (0.66)	93.20 (0.80)
50c. of 100i.	AF	95.40 (0.66)	94.90 (0.70)	94.30 (0.73)	93.30 (0.79)
50c. of 100i.	IN	93.07 (0.80)	94.56 (0.72)	93.82 (0.76)	91.68 (0.87)
50c. of 100i.	GQ15	17.20 (1.19)	94.30 (0.73)	94.70 (0.71)	60.60 (1.55)
50c. of 100i.	GQ35	37.80 (1.53)	94.60 (0.71)	94.30 (0.73)	91.50 (0.88)
50c. of 100i.	GQ75	69.80 (1.45)	94.80 (0.70)	94.50 (0.72)	93.70 (0.77)
50c. of 100i.	GQ105	82.90 (1.19)	94.90 (0.70)	94.20 (0.74)	93.60 (0.77)
50c. of 30i.	AF	93.80 (0.76)	95.30 (0.67)	95.30 (0.67)	95.40 (0.66)
50c. of 30i.	IN	92.65 (0.83)	95.28 (0.67)	94.73 (0.71)	93.30 (0.79)
50c. of 30i.	GQ15	71.90 (1.42)	95.00 (0.69)	95.10 (0.68)	92.60 (0.83)
50c. of 30i.	GQ35	92.00 (0.86)	95.10 (0.68)	95.10 (0.68)	93.90 (0.76)
50c. of 30i.	GQ75	93.80 (0.76)	95.40 (0.66)	95.20 (0.68)	95.40 (0.66)
50c. of 30i.	GQ105	93.70 (0.77)	95.30 (0.67)	95.30 (0.67)	95.40 (0.66)

Table A.3: Mean squared error, comparison with analytical formulae, scenario with a small frailty variance and a negative regression coefficient.

Sample size	Method	Lambda	P	Beta	Theta
1000c. of 2i.	AF	0.0026	0.0008	0.0042	0.0670
1000c. of 2i.	IN	0.0024	0.0008	0.0041	0.0635
1000c. of 2i.	GQ15	0.0024	0.0007	0.0042	0.0159
1000c. of 2i.	GQ35	0.0025	0.0008	0.0042	0.0571
1000c. of 2i.	GQ75	0.0026	0.0008	0.0042	0.0668
1000c. of 2i.	GQ105	0.0026	0.0008	0.0042	0.0669
15c. of 100i.	AF	0.0190	0.0009	0.0045	0.1886
15c. of 100i.	IN	0.0193	0.0009	0.0046	0.1880
15c. of 100i.	GQ15	0.0867	0.0009	0.0046	0.2116
15c. of 100i.	GQ35	0.0432	0.0009	0.0046	0.1621
15c. of 100i.	GQ75	0.0274	0.0009	0.0045	0.1816
15c. of 100i.	GQ105	0.0242	0.0009	0.0045	0.1877
15c. of 30i.	AF	0.0262	0.0029	0.0157	0.3341
15c. of 30i.	IN	0.0259	0.0029	0.0158	0.3353
15c. of 30i.	GQ15	0.0517	0.0029	0.0161	0.2038
15c. of 30i.	GQ35	0.0283	0.0029	0.0159	0.4801
15c. of 30i.	GQ75	0.0263	0.0029	0.0157	0.3365
15c. of 30i.	GQ105	0.0262	0.0029	0.0157	0.3414
15c. of 500i.	AF	0.0169	0.0002	0.0009	0.1691
15c. of 500i.	IN	0.0284	0.0002	0.0009	0.1835
15c. of 500i.	GQ15	0.1315	0.0002	0.0009	0.3364
15c. of 500i.	GQ35	0.0599	0.0002	0.0009	0.1638
15c. of 500i.	GQ75	0.0394	0.0002	0.0009	0.1486
15c. of 500i.	GQ105	0.0345	0.0002	0.0009	0.1477
50c. of 100i.	AF	0.0053	0.0003	0.0014	0.0487
50c. of 100i.	IN	0.0054	0.0003	0.0014	0.0488
50c. of 100i.	GQ15	0.0816	0.0003	0.0014	0.1827
50c. of 100i.	GQ35	0.0242	0.0003	0.0014	0.0555
50c. of 100i.	GQ75	0.0095	0.0003	0.0014	0.0480
50c. of 100i.	GQ105	0.0076	0.0003	0.0014	0.0491
50c. of 30i.	AF	0.0073	0.0009	0.0047	0.0628
50c. of 30i.	IN	0.0074	0.0009	0.0047	0.0629
50c. of 30i.	GQ15	0.0180	0.0009	0.0048	0.0560
50c. of 30i.	GQ35	0.0082	0.0009	0.0047	0.0647
50c. of 30i.	GQ75	0.0073	0.0009	0.0047	0.0627
50c. of 30i.	GQ105	0.0073	0.0009	0.0047	0.0628

Table A.4: Bias, comparison without analytical formulae, scenario with a small frailty variance and a negative regression coefficient.

Sample size	Method	Lambda	P	Beta	Sigma
1000c. of 2i.	GQ15	0.0187 (0.0012)	-0.0415 (0.0008)	0.0149 (0.0019)	-0.3010 (0.0250)
1000c. of 2i.	GQ35	0.0188 (0.0012)	-0.0415 (0.0008)	0.0144 (0.0019)	-0.2842 (0.0232)
1000c. of 2i.	GQ75	0.0188 (0.0012)	-0.0415 (0.0008)	0.0146 (0.0019)	-0.3057 (0.0254)
1000c. of 2i.	GQ105	0.0187 (0.0012)	-0.0415 (0.0008)	0.0147 (0.0019)	-0.2946 (0.0243)
15c. of 100i.	GQ15	0.0102 (0.0040)	-0.0332 (0.0010)	0.0552 (0.0040)	0.0282 (0.0113)
15c. of 100i.	GQ35	0.0102 (0.0040)	-0.0333 (0.0010)	0.0173 (0.0024)	-0.0854 (0.0085)
15c. of 100i.	GQ75	0.0102 (0.0040)	-0.0333 (0.0010)	0.0088 (0.0022)	-0.1015 (0.0075)
15c. of 100i.	GQ105	0.0102 (0.0040)	-0.0333 (0.0010)	0.0088 (0.0022)	-0.1015 (0.0075)
15c. of 30i.	GQ15	0.0193 (0.0045)	-0.0348 (0.0017)	0.0047 (0.0039)	-0.2510 (0.0272)
15c. of 30i.	GQ35	0.0192 (0.0045)	-0.0348 (0.0017)	0.0041 (0.0039)	-0.2455 (0.0256)
15c. of 30i.	GQ75	0.0191 (0.0045)	-0.0348 (0.0017)	0.0041 (0.0039)	-0.2593 (0.0275)
15c. of 30i.	GQ105	0.0195 (0.0045)	-0.0347 (0.0017)	0.0040 (0.0039)	-0.2522 (0.0265)
15c. of 500i.	GQ15	0.0113 (0.0037)	-0.0411 (0.0006)	0.0867 (0.0050)	0.2427 (0.0104)
15c. of 500i.	GQ35	0.0157 (0.0038)	-0.0423 (0.0006)	0.0860 (0.0040)	0.4011 (0.0091)
15c. of 500i.	GQ75	0.0078 (0.0036)	-0.0405 (0.0005)	0.0707 (0.0033)	0.4020 (0.0112)
15c. of 500i.	GQ105	0.0059 (0.0036)	-0.0410 (0.0006)	0.0600 (0.0028)	0.3119 (0.0125)
50c. of 100i.	GQ15	0.0135 (0.0022)	-0.0365 (0.0005)	0.0244 (0.0020)	-0.0095 (0.0049)
50c. of 100i.	GQ35	0.0135 (0.0022)	-0.0365 (0.0005)	0.0102 (0.0012)	-0.0350 (0.0038)
50c. of 100i.	GQ75	0.0135 (0.0022)	-0.0365 (0.0005)	0.0105 (0.0012)	-0.0350 (0.0037)
50c. of 100i.	GQ105	0.0135 (0.0022)	-0.0365 (0.0005)	0.0105 (0.0012)	-0.0350 (0.0037)
50c. of 30i.	GQ15	0.0154 (0.0025)	-0.0367 (0.0009)	0.0079 (0.0021)	-0.0535 (0.0052)
50c. of 30i.	GQ35	0.0154 (0.0025)	-0.0367 (0.0009)	0.0079 (0.0021)	-0.0536 (0.0052)
50c. of 30i.	GQ75	0.0154 (0.0025)	-0.0367 (0.0009)	0.0079 (0.0021)	-0.0536 (0.0052)
50c. of 30i.	GQ105	0.0154 (0.0025)	-0.0367 (0.0009)	0.0079 (0.0021)	-0.0536 (0.0052)

Table A.5: Coverage, comparison without analytical formulae, scenario with a small frailty variance and a negative regression coefficient.

Sample size	Method	Lambda	P	Beta	Sigma
1000c. of 2i.	GQ15	92.5662 (0.8295)	64.8676 (1.5096)	94.5010 (0.7209)	99.0835 (0.3013)
1000c. of 2i.	GQ35	92.4413 (0.8359)	64.7600 (1.5107)	94.6885 (0.7092)	99.0807 (0.3018)
1000c. of 2i.	GQ75	92.4720 (0.8343)	64.6999 (1.5113)	94.6083 (0.7142)	99.0844 (0.3012)
1000c. of 2i.	GQ105	92.5586 (0.8299)	64.8318 (1.5100)	94.5973 (0.7149)	99.0826 (0.3015)
15c. of 100i.	GQ15	52.1000 (1.5797)	76.4000 (1.3428)	86.0000 (1.0973)	70.2000 (1.4464)
15c. of 100i.	GQ35	52.1000 (1.5797)	76.5000 (1.3408)	98.8000 (0.3443)	88.9000 (0.9934)
15c. of 100i.	GQ75	52.1000 (1.5797)	76.4000 (1.3428)	99.9000 (0.0999)	94.0000 (0.7510)
15c. of 100i.	GQ105	52.1000 (1.5797)	76.4000 (1.3428)	99.9000 (0.0999)	94.1000 (0.7451)
15c. of 30i.	GQ15	75.4016 (1.3619)	90.0602 (0.9461)	99.0964 (0.2992)	98.3936 (0.3976)
15c. of 30i.	GQ35	75.3769 (1.3624)	90.2513 (0.9380)	99.0955 (0.2994)	99.1960 (0.2824)
15c. of 30i.	GQ75	75.4263 (1.3614)	90.0702 (0.9457)	99.0973 (0.2991)	99.2979 (0.2640)
15c. of 30i.	GQ105	75.5020 (1.3600)	90.0602 (0.9461)	99.0964 (0.2992)	99.2972 (0.2642)
15c. of 500i.	GQ15	30.0813 (1.4503)	21.3415 (1.2956)	27.6423 (1.4143)	23.1707 (1.3342)
15c. of 500i.	GQ35	27.8826 (1.4180)	17.8197 (1.2101)	37.1069 (1.5277)	15.7233 (1.1511)
15c. of 500i.	GQ75	30.1053 (1.4506)	18.9474 (1.2392)	55.5789 (1.5713)	16.6316 (1.1775)
15c. of 500i.	GQ105	29.1028 (1.4364)	18.3807 (1.2248)	67.8337 (1.4771)	32.1663 (1.4771)
50c. of 100i.	GQ15	51.9000 (1.5800)	37.8000 (1.5333)	94.8000 (0.7021)	85.6000 (1.1102)
50c. of 100i.	GQ35	51.9000 (1.5800)	37.5000 (1.5309)	100.0000 (0.0000)	95.0000 (0.6892)
50c. of 100i.	GQ75	51.9000 (1.5800)	37.5000 (1.5309)	100.0000 (0.0000)	94.9000 (0.6957)
50c. of 100i.	GQ105	51.9000 (1.5800)	37.5000 (1.5309)	100.0000 (0.0000)	94.9000 (0.6957)
50c. of 30i.	GQ15	73.9000 (1.3888)	74.1000 (1.3853)	99.4000 (0.2442)	97.2000 (0.5217)
50c. of 30i.	GQ35	73.9000 (1.3888)	74.1000 (1.3853)	99.4000 (0.2442)	97.2000 (0.5217)
50c. of 30i.	GQ75	73.9000 (1.3888)	74.1000 (1.3853)	99.4000 (0.2442)	97.2000 (0.5217)
50c. of 30i.	GQ105	73.9000 (1.3888)	74.1000 (1.3853)	99.4000 (0.2442)	97.2000 (0.5217)

Table A.6: Mean squared error, comparison without analytical formulae, scenario with a small frailty variance and a negative regression coefficient.

Sample size	Method	Lambda	P	Beta	Sigma
1000c. of 2i.	GQ15	0.0019	0.0024	0.0040	0.7180
1000c. of 2i.	GQ35	0.0019	0.0024	0.0039	0.6198
1000c. of 2i.	GQ75	0.0019	0.0024	0.0039	0.7394
1000c. of 2i.	GQ105	0.0019	0.0024	0.0039	0.6752
15c. of 100i.	GQ15	0.0164	0.0021	0.0189	0.1285
15c. of 100i.	GQ35	0.0164	0.0021	0.0063	0.0790
15c. of 100i.	GQ75	0.0164	0.0022	0.0048	0.0665
15c. of 100i.	GQ105	0.0164	0.0022	0.0048	0.0665
15c. of 30i.	GQ15	0.0208	0.0041	0.0152	0.8029
15c. of 30i.	GQ35	0.0208	0.0040	0.0149	0.7164
15c. of 30i.	GQ75	0.0208	0.0041	0.0149	0.8228
15c. of 30i.	GQ105	0.0207	0.0041	0.0149	0.7636
15c. of 500i.	GQ15	0.0141	0.0020	0.0326	0.1666
15c. of 500i.	GQ35	0.0146	0.0021	0.0234	0.2438
15c. of 500i.	GQ75	0.0131	0.0019	0.0160	0.2881
15c. of 500i.	GQ105	0.0129	0.0020	0.0113	0.2542
50c. of 100i.	GQ15	0.0048	0.0016	0.0046	0.0237
50c. of 100i.	GQ35	0.0048	0.0016	0.0015	0.0153
50c. of 100i.	GQ75	0.0048	0.0016	0.0015	0.0153
50c. of 100i.	GQ105	0.0048	0.0016	0.0015	0.0153
50c. of 30i.	GQ15	0.0066	0.0022	0.0043	0.0301
50c. of 30i.	GQ35	0.0066	0.0022	0.0043	0.0300
50c. of 30i.	GQ75	0.0066	0.0022	0.0043	0.0300
50c. of 30i.	GQ105	0.0066	0.0022	0.0043	0.0300

Table A.7: Bias with Monte Carlo standard error of estimated regression coefficient, simulation study on model misspecification in survival models with shared frailty terms, scenario with 15 clusters of 100 individuals each and a small frailty variance.

True frailty	Model frailty	Model baseline	Exponential	Weibull	Gompertz	Weibull-Weibull (1)	Weibull-Weibull (2)
Gamma	Gamma	Cox	0.001 (0.002)	0.007 (0.002)	0.009 (0.002)	0.013 (0.002)	-0.007 (0.002)
Gamma	Gamma	Exp	-0.002 (0.002)	-0.083 (0.003)	0.133 (0.002)	0.102 (0.002)	-0.116 (0.002)
Gamma	Gamma	Wei	-0.002 (0.002)	0.002 (0.002)	0.034 (0.002)	-0.067 (0.002)	0.000 (0.002)
Gamma	Gamma	Gom	-0.006 (0.002)	-0.086 (0.003)	-0.002 (0.002)	0.028 (0.002)	-0.114 (0.002)
Gamma	Gamma	RP(5)	-0.002 (0.002)	-0.001 (0.002)	-0.002 (0.002)	-0.002 (0.002)	-0.001 (0.002)
Gamma	Gamma	RP(9)	-0.002 (0.002)	-0.001 (0.002)	-0.002 (0.002)	-0.001 (0.002)	-0.002 (0.002)
Gamma	Gamma	RP(P)	-0.002 (0.002)	-0.001 (0.002)	0.003 (0.002)	0.000 (0.002)	-0.000 (0.002)
Log-Normal	Gamma	Cox	0.004 (0.002)	-0.002 (0.002)	0.000 (0.002)	-0.006 (0.002)	0.002 (0.002)
Log-Normal	Gamma	Exp	0.001 (0.002)	-0.085 (0.002)	0.136 (0.001)	0.100 (0.002)	-0.115 (0.002)
Log-Normal	Gamma	Wei	0.001 (0.002)	-0.002 (0.002)	0.038 (0.002)	-0.066 (0.002)	0.001 (0.002)
Log-Normal	Gamma	Gom	0.001 (0.002)	-0.085 (0.002)	0.003 (0.002)	0.022 (0.002)	-0.115 (0.002)
Log-Normal	Gamma	RP(5)	0.002 (0.002)	-0.002 (0.002)	0.003 (0.002)	0.001 (0.002)	0.008 (0.002)
Log-Normal	Gamma	RP(9)	0.002 (0.002)	-0.002 (0.002)	0.003 (0.002)	0.002 (0.002)	0.007 (0.002)
Log-Normal	Gamma	RP(P)	0.002 (0.002)	-0.002 (0.002)	0.008 (0.002)	0.003 (0.002)	0.009 (0.002)
Gamma	Log-Normal	Cox	-0.002 (0.002)	0.001 (0.002)	-0.002 (0.002)	-0.001 (0.002)	0.001 (0.002)
Gamma	Log-Normal	Exp	-0.002 (0.002)	-0.083 (0.003)	0.133 (0.002)	0.102 (0.002)	-0.116 (0.002)
Gamma	Log-Normal	Wei	-0.002 (0.002)	0.001 (0.002)	0.034 (0.002)	-0.067 (0.002)	0.000 (0.002)
Gamma	Log-Normal	Gom	-0.005 (0.002)	-0.084 (0.003)	-0.002 (0.002)	0.027 (0.002)	-0.115 (0.002)
Gamma	Log-Normal	RP(5)	-0.002 (0.002)	-0.001 (0.002)	-0.002 (0.002)	-0.002 (0.002)	-0.001 (0.002)
Gamma	Log-Normal	RP(9)	-0.002 (0.002)	-0.001 (0.002)	-0.002 (0.002)	-0.001 (0.002)	-0.002 (0.002)
Gamma	Log-Normal	RP(P)	-0.002 (0.002)	-0.001 (0.002)	0.003 (0.002)	0.000 (0.002)	-0.000 (0.002)
Log-Normal	Log-Normal	Cox	0.001 (0.002)	-0.002 (0.002)	0.003 (0.002)	0.002 (0.002)	0.002 (0.002)
Log-Normal	Log-Normal	Exp	0.001 (0.002)	-0.086 (0.002)	0.136 (0.001)	0.100 (0.002)	-0.115 (0.002)
Log-Normal	Log-Normal	Wei	0.001 (0.002)	-0.002 (0.002)	0.038 (0.002)	-0.066 (0.002)	0.001 (0.002)
Log-Normal	Log-Normal	Gom	0.001 (0.002)	-0.084 (0.002)	0.003 (0.002)	0.022 (0.002)	-0.114 (0.002)
Log-Normal	Log-Normal	RP(5)	0.001 (0.002)	-0.002 (0.002)	0.003 (0.002)	0.001 (0.002)	0.008 (0.002)
Log-Normal	Log-Normal	RP(9)	0.001 (0.002)	-0.002 (0.002)	0.003 (0.002)	0.002 (0.002)	0.007 (0.002)
Log-Normal	Log-Normal	RP(P)	0.001 (0.002)	-0.002 (0.002)	0.007 (0.002)	0.003 (0.002)	0.009 (0.002)

Table A.8: Coverage with Monte Carlo standard error of estimated regression coefficient, simulation study on model misspecification in survival models with shared frailty terms, scenario with 15 clusters of 100 individuals each and a small frailty variance.

True frailty	Model frailty	Model baseline	Exponential	Weibull	Gompertz	Weibull-Weibull (1)	Weibull-Weibull (2)
Gamma	Gamma	Cox	93.68 (0.77)	96.17 (0.61)	93.33 (0.79)	93.33 (0.79)	93.33 (0.79)
Gamma	Gamma	Exp	95.20 (0.68)	72.60 (1.41)	35.30 (1.51)	53.80 (1.58)	49.20 (1.58)
Gamma	Gamma	Wei	95.20 (0.68)	95.50 (0.66)	91.70 (0.87)	72.80 (1.41)	94.59 (0.72)
Gamma	Gamma	Gom	95.67 (0.64)	70.21 (1.45)	94.80 (0.70)	89.98 (0.95)	49.87 (1.58)
Gamma	Gamma	RP(5)	95.09 (0.68)	95.27 (0.67)	94.89 (0.70)	94.27 (0.73)	93.64 (0.77)
Gamma	Gamma	RP(9)	95.09 (0.68)	95.27 (0.67)	95.00 (0.69)	94.35 (0.73)	93.64 (0.77)
Gamma	Gamma	RP(P)	95.17 (0.68)	95.42 (0.66)	94.59 (0.72)	94.36 (0.73)	93.64 (0.77)
Log-Normal	Gamma	Cox	95.55 (0.65)	94.79 (0.70)	97.18 (0.52)	92.68 (0.82)	92.59 (0.83)
Log-Normal	Gamma	Exp	95.30 (0.67)	74.80 (1.37)	35.40 (1.51)	53.30 (1.58)	47.50 (1.58)
Log-Normal	Gamma	Wei	95.50 (0.66)	95.00 (0.69)	91.50 (0.88)	74.10 (1.39)	94.68 (0.71)
Log-Normal	Gamma	Gom	95.28 (0.67)	76.13 (1.35)	95.40 (0.66)	93.17 (0.80)	49.22 (1.58)
Log-Normal	Gamma	RP(5)	95.30 (0.67)	96.20 (0.60)	95.49 (0.66)	95.38 (0.66)	95.73 (0.64)
Log-Normal	Gamma	RP(9)	95.30 (0.67)	96.35 (0.59)	95.39 (0.66)	95.05 (0.69)	95.73 (0.64)
Log-Normal	Gamma	RP(P)	95.60 (0.65)	96.20 (0.60)	95.60 (0.65)	94.92 (0.69)	95.30 (0.67)
Gamma	Log-Normal	Cox	95.20 (0.68)	95.30 (0.67)	95.00 (0.69)	94.30 (0.73)	94.70 (0.71)
Gamma	Log-Normal	Exp	95.19 (0.68)	72.37 (1.41)	35.30 (1.51)	53.80 (1.58)	48.95 (1.58)
Gamma	Log-Normal	Wei	95.19 (0.68)	95.50 (0.66)	91.69 (0.87)	73.22 (1.40)	94.68 (0.71)
Gamma	Log-Normal	Gom	95.94 (0.62)	71.47 (1.43)	94.99 (0.69)	90.42 (0.93)	49.48 (1.58)
Gamma	Log-Normal	RP(5)	95.09 (0.68)	95.27 (0.67)	94.90 (0.70)	94.20 (0.74)	93.64 (0.77)
Gamma	Log-Normal	RP(9)	95.09 (0.68)	95.27 (0.67)	94.90 (0.70)	94.30 (0.73)	93.64 (0.77)
Gamma	Log-Normal	RP(P)	95.09 (0.68)	95.42 (0.66)	94.60 (0.71)	94.50 (0.72)	93.64 (0.77)
Log-Normal	Log-Normal	Cox	95.20 (0.68)	95.40 (0.66)	95.30 (0.67)	95.10 (0.68)	94.80 (0.70)
Log-Normal	Log-Normal	Exp	95.30 (0.67)	74.87 (1.37)	35.40 (1.51)	53.20 (1.58)	47.59 (1.58)
Log-Normal	Log-Normal	Wei	95.49 (0.66)	95.10 (0.68)	91.59 (0.88)	73.92 (1.39)	94.78 (0.70)
Log-Normal	Log-Normal	Gom	94.75 (0.71)	76.04 (1.35)	95.39 (0.66)	93.17 (0.80)	48.99 (1.58)
Log-Normal	Log-Normal	RP(5)	95.20 (0.68)	96.50 (0.58)	95.49 (0.66)	95.40 (0.66)	95.73 (0.64)
Log-Normal	Log-Normal	RP(9)	95.30 (0.67)	96.35 (0.59)	95.39 (0.66)	95.10 (0.68)	95.73 (0.64)
Log-Normal	Log-Normal	RP(P)	95.40 (0.66)	96.05 (0.62)	95.70 (0.64)	94.90 (0.70)	95.73 (0.64)

Table A.9: Mean squared error of estimated regression coefficient, simulation study on model misspecification in survival models with shared frailty terms, scenario with 15 clusters of 100 individuals each and a small frailty variance.

True frailty	Model frailty	Model baseline	Exponential	Weibull	Gompertz	Weibull-Weibull (1)	Weibull-Weibull (2)
Gamma	Gamma	Cox	0.005	0.005	0.004	0.005	0.004
Gamma	Gamma	Exp	0.004	0.013	0.020	0.013	0.019
Gamma	Gamma	Wei	0.004	0.005	0.005	0.009	0.003
Gamma	Gamma	Gom	0.004	0.014	0.004	0.004	0.018
Gamma	Gamma	RP(5)	0.004	0.004	0.004	0.003	0.004
Gamma	Gamma	RP(9)	0.004	0.004	0.004	0.003	0.004
Gamma	Gamma	RP(P)	0.004	0.004	0.004	0.003	0.004
Log-Normal	Gamma	Cox	0.004	0.005	0.004	0.003	0.003
Log-Normal	Gamma	Exp	0.004	0.013	0.020	0.012	0.018
Log-Normal	Gamma	Wei	0.004	0.005	0.005	0.009	0.003
Log-Normal	Gamma	Gom	0.004	0.013	0.004	0.004	0.019
Log-Normal	Gamma	RP(5)	0.004	0.004	0.004	0.003	0.003
Log-Normal	Gamma	RP(9)	0.004	0.004	0.004	0.003	0.003
Log-Normal	Gamma	RP(P)	0.004	0.004	0.004	0.003	0.003
Gamma	Log-Normal	Cox	0.004	0.005	0.004	0.003	0.003
Gamma	Log-Normal	Exp	0.004	0.014	0.020	0.013	0.019
Gamma	Log-Normal	Wei	0.004	0.005	0.005	0.009	0.003
Gamma	Log-Normal	Gom	0.004	0.013	0.004	0.004	0.018
Gamma	Log-Normal	RP(5)	0.004	0.004	0.004	0.003	0.004
Gamma	Log-Normal	RP(9)	0.004	0.004	0.004	0.003	0.004
Gamma	Log-Normal	RP(P)	0.004	0.004	0.004	0.003	0.004
Log-Normal	Log-Normal	Cox	0.004	0.005	0.004	0.003	0.003
Log-Normal	Log-Normal	Exp	0.004	0.014	0.020	0.012	0.018
Log-Normal	Log-Normal	Wei	0.004	0.005	0.005	0.009	0.003
Log-Normal	Log-Normal	Gom	0.004	0.013	0.004	0.004	0.018
Log-Normal	Log-Normal	RP(5)	0.004	0.004	0.004	0.003	0.003
Log-Normal	Log-Normal	RP(9)	0.004	0.004	0.004	0.003	0.003
Log-Normal	Log-Normal	RP(P)	0.004	0.004	0.004	0.003	0.003

Table A.10: Bias with Monte Carlo standard error of estimated frailty variance, simulation study on model misspecification in survival models with shared frailty terms, scenario with 15 clusters of 100 individuals each and a small frailty variance.

True frailty	Model frailty	Model baseline	Exponential	Weibull	Gompertz	Weibull-Weibull (1)	Weibull-Weibull (2)
Gamma	Gamma	Cox	-0.096 (0.002)	-0.087 (0.002)	-0.144 (0.001)	-0.177 (0.001)	-0.164 (0.001)
Gamma	Gamma	Exp	-0.014 (0.003)	0.056 (0.004)	-0.116 (0.002)	-0.090 (0.002)	0.091 (0.004)
Gamma	Gamma	Wei	-0.014 (0.003)	-0.020 (0.003)	-0.043 (0.003)	0.049 (0.003)	-0.015 (0.003)
Gamma	Gamma	Gom	-0.018 (0.003)	0.063 (0.004)	-0.013 (0.003)	-0.042 (0.002)	0.089 (0.004)
Gamma	Gamma	RP(5)	-0.014 (0.003)	-0.020 (0.003)	-0.013 (0.003)	-0.011 (0.003)	-0.024 (0.003)
Gamma	Gamma	RP(9)	-0.014 (0.003)	-0.020 (0.003)	-0.013 (0.003)	-0.012 (0.003)	-0.023 (0.003)
Gamma	Gamma	RP(P)	-0.015 (0.003)	-0.020 (0.003)	-0.018 (0.003)	-0.016 (0.003)	-0.024 (0.003)
Log-Normal	Gamma	Cox	-0.113 (0.001)	-0.102 (0.001)	-0.148 (0.001)	-0.182 (0.001)	-0.168 (0.001)
Log-Normal	Gamma	Exp	-0.048 (0.003)	0.016 (0.004)	-0.147 (0.001)	-0.130 (0.001)	0.047 (0.004)
Log-Normal	Gamma	Wei	-0.048 (0.003)	-0.057 (0.003)	-0.081 (0.002)	-0.009 (0.003)	-0.056 (0.002)
Log-Normal	Gamma	Gom	-0.054 (0.003)	0.022 (0.004)	-0.053 (0.003)	-0.080 (0.002)	0.040 (0.004)
Log-Normal	Gamma	RP(5)	-0.048 (0.003)	-0.058 (0.003)	-0.053 (0.003)	-0.057 (0.002)	-0.065 (0.002)
Log-Normal	Gamma	RP(9)	-0.048 (0.003)	-0.058 (0.003)	-0.053 (0.003)	-0.057 (0.002)	-0.065 (0.002)
Log-Normal	Gamma	RP(P)	-0.048 (0.003)	-0.058 (0.003)	-0.057 (0.002)	-0.059 (0.002)	-0.066 (0.002)
Gamma	Log-Normal	Cox	0.037 (0.004)	0.027 (0.004)	0.038 (0.004)	0.039 (0.004)	0.033 (0.004)
Gamma	Log-Normal	Exp	0.016 (0.004)	0.091 (0.005)	-0.101 (0.003)	-0.067 (0.003)	0.144 (0.005)
Gamma	Log-Normal	Wei	0.016 (0.004)	0.006 (0.004)	-0.018 (0.003)	0.104 (0.005)	0.019 (0.004)
Gamma	Log-Normal	Gom	0.014 (0.004)	0.089 (0.005)	0.017 (0.004)	-0.009 (0.003)	0.138 (0.005)
Gamma	Log-Normal	RP(5)	0.016 (0.004)	0.007 (0.004)	0.017 (0.004)	0.019 (0.004)	0.007 (0.004)
Gamma	Log-Normal	RP(9)	0.016 (0.004)	0.007 (0.004)	0.017 (0.004)	0.018 (0.004)	0.007 (0.004)
Gamma	Log-Normal	RP(P)	0.016 (0.004)	0.007 (0.004)	0.012 (0.004)	0.017 (0.004)	0.006 (0.004)
Log-Normal	Log-Normal	Cox	-0.023 (0.003)	-0.032 (0.003)	-0.028 (0.003)	-0.032 (0.003)	-0.029 (0.003)
Log-Normal	Log-Normal	Exp	-0.039 (0.003)	0.027 (0.004)	-0.142 (0.002)	-0.121 (0.002)	0.066 (0.004)
Log-Normal	Log-Normal	Wei	-0.039 (0.003)	-0.048 (0.003)	-0.073 (0.002)	0.014 (0.003)	-0.043 (0.003)
Log-Normal	Log-Normal	Gom	-0.049 (0.003)	0.031 (0.004)	-0.043 (0.003)	-0.064 (0.002)	0.066 (0.004)
Log-Normal	Log-Normal	RP(5)	-0.039 (0.003)	-0.049 (0.003)	-0.043 (0.003)	-0.047 (0.002)	-0.056 (0.002)
Log-Normal	Log-Normal	RP(9)	-0.039 (0.003)	-0.049 (0.003)	-0.043 (0.003)	-0.047 (0.002)	-0.056 (0.002)
Log-Normal	Log-Normal	RP(P)	-0.039 (0.003)	-0.048 (0.003)	-0.047 (0.003)	-0.048 (0.002)	-0.057 (0.002)

Table A.11: Coverage with Monte Carlo standard error of estimated frailty variance, simulation study on model misspecification in survival models with shared frailty terms, scenario with 15 clusters of 100 individuals each and a small frailty variance.

True frailty	Model frailty	Model baseline	Exponential	Weibull	Gompertz	Weibull-Weibull (1)	Weibull-Weibull (2)
Gamma	Gamma	Cox	59.48 (1.55)	64.26 (1.52)	5.71 (0.73)	0.00 (0.00)	2.22 (0.47)
Gamma	Gamma	Exp	85.70 (1.11)	94.50 (0.72)	38.10 (1.54)	54.90 (1.57)	96.80 (0.56)
Gamma	Gamma	Wei	86.10 (1.09)	83.30 (1.18)	77.20 (1.33)	95.80 (0.63)	85.60 (1.11)
Gamma	Gamma	Gom	82.35 (1.21)	96.28 (0.60)	85.70 (1.11)	83.06 (1.19)	96.42 (0.59)
Gamma	Gamma	RP(5)	85.97 (1.10)	83.36 (1.18)	85.77 (1.10)	86.83 (1.07)	80.45 (1.25)
Gamma	Gamma	RP(9)	85.87 (1.10)	83.36 (1.18)	85.80 (1.10)	86.90 (1.07)	81.36 (1.23)
Gamma	Gamma	RP(P)	86.02 (1.10)	83.36 (1.18)	85.09 (1.13)	86.37 (1.08)	80.45 (1.25)
Log-Normal	Gamma	Cox	47.66 (1.58)	55.37 (1.57)	6.78 (0.79)	0.00 (0.00)	0.00 (0.00)
Log-Normal	Gamma	Exp	76.80 (1.33)	89.00 (0.99)	17.80 (1.21)	28.30 (1.42)	93.50 (0.78)
Log-Normal	Gamma	Wei	77.10 (1.33)	72.60 (1.41)	61.70 (1.54)	90.20 (0.94)	73.62 (1.39)
Log-Normal	Gamma	Gom	74.20 (1.38)	90.98 (0.91)	74.70 (1.37)	66.47 (1.49)	91.41 (0.89)
Log-Normal	Gamma	RP(5)	76.48 (1.34)	72.04 (1.42)	75.05 (1.37)	73.69 (1.39)	71.37 (1.43)
Log-Normal	Gamma	RP(9)	76.78 (1.34)	72.04 (1.42)	74.92 (1.37)	73.54 (1.40)	71.37 (1.43)
Log-Normal	Gamma	RP(P)	76.98 (1.33)	72.04 (1.42)	73.17 (1.40)	72.36 (1.41)	71.37 (1.43)
Gamma	Log-Normal	Cox	84.50 (1.14)	82.20 (1.21)	83.30 (1.18)	84.40 (1.15)	82.50 (1.20)
Gamma	Log-Normal	Exp	87.78 (1.04)	96.00 (0.62)	45.70 (1.58)	63.30 (1.52)	96.80 (0.56)
Gamma	Log-Normal	Wei	87.88 (1.03)	85.89 (1.10)	80.88 (1.24)	96.99 (0.54)	88.23 (1.02)
Gamma	Log-Normal	Gom	86.29 (1.09)	96.60 (0.57)	88.08 (1.02)	86.84 (1.07)	97.38 (0.50)
Gamma	Log-Normal	RP(5)	87.68 (1.04)	85.95 (1.10)	88.10 (1.02)	89.60 (0.97)	85.91 (1.10)
Gamma	Log-Normal	RP(9)	87.68 (1.04)	85.95 (1.10)	88.20 (1.02)	89.50 (0.97)	85.91 (1.10)
Gamma	Log-Normal	RP(P)	87.78 (1.04)	85.95 (1.10)	87.50 (1.05)	89.20 (0.98)	85.91 (1.10)
Log-Normal	Log-Normal	Cox	76.70 (1.34)	73.80 (1.39)	76.00 (1.35)	74.00 (1.39)	72.60 (1.41)
Log-Normal	Log-Normal	Exp	80.18 (1.26)	91.09 (0.90)	21.70 (1.30)	36.50 (1.52)	94.38 (0.73)
Log-Normal	Log-Normal	Wei	79.84 (1.27)	77.48 (1.32)	66.87 (1.49)	92.08 (0.85)	77.89 (1.31)
Log-Normal	Log-Normal	Gom	77.34 (1.32)	92.97 (0.81)	77.56 (1.32)	71.36 (1.43)	92.42 (0.84)
Log-Normal	Log-Normal	RP(5)	80.08 (1.26)	76.44 (1.34)	77.66 (1.32)	77.58 (1.32)	77.35 (1.32)
Log-Normal	Log-Normal	RP(9)	79.98 (1.27)	76.44 (1.34)	77.66 (1.32)	77.38 (1.32)	77.35 (1.32)
Log-Normal	Log-Normal	RP(P)	79.88 (1.27)	76.60 (1.34)	76.78 (1.34)	77.20 (1.33)	77.35 (1.32)

Table A.12: Mean squared error of estimated frailty variance, simulation study on model misspecification in survival models with shared frailty terms, scenario with 15 clusters of 100 individuals each and a small frailty variance.

True frailty	Model frailty	Model baseline	Exponential	Weibull	Gompertz	Weibull-Weibull (1)	Weibull-Weibull (2)
Gamma	Gamma	Cox	0.012	0.010	0.021	0.032	0.027
Gamma	Gamma	Exp	0.009	0.017	0.017	0.013	0.023
Gamma	Gamma	Wei	0.009	0.009	0.009	0.013	0.008
Gamma	Gamma	Gom	0.009	0.017	0.009	0.006	0.022
Gamma	Gamma	RP(5)	0.009	0.009	0.009	0.008	0.008
Gamma	Gamma	RP(9)	0.009	0.009	0.009	0.008	0.008
Gamma	Gamma	RP(P)	0.009	0.009	0.009	0.008	0.008
Log-Normal	Gamma	Cox	0.014	0.012	0.023	0.033	0.028
Log-Normal	Gamma	Exp	0.009	0.014	0.024	0.019	0.015
Log-Normal	Gamma	Wei	0.009	0.010	0.011	0.007	0.009
Log-Normal	Gamma	Gom	0.009	0.015	0.009	0.010	0.015
Log-Normal	Gamma	RP(5)	0.009	0.010	0.009	0.009	0.009
Log-Normal	Gamma	RP(9)	0.009	0.010	0.009	0.009	0.009
Log-Normal	Gamma	RP(P)	0.009	0.010	0.009	0.009	0.009
Gamma	Log-Normal	Cox	0.018	0.017	0.019	0.016	0.017
Gamma	Log-Normal	Exp	0.014	0.030	0.017	0.012	0.048
Gamma	Log-Normal	Wei	0.014	0.014	0.012	0.032	0.015
Gamma	Log-Normal	Gom	0.014	0.030	0.015	0.009	0.045
Gamma	Log-Normal	RP(5)	0.014	0.014	0.015	0.013	0.012
Gamma	Log-Normal	RP(9)	0.014	0.014	0.015	0.013	0.012
Gamma	Log-Normal	RP(P)	0.014	0.014	0.015	0.013	0.012
Log-Normal	Log-Normal	Cox	0.009	0.009	0.009	0.008	0.009
Log-Normal	Log-Normal	Exp	0.009	0.015	0.023	0.017	0.020
Log-Normal	Log-Normal	Wei	0.009	0.009	0.011	0.010	0.009
Log-Normal	Log-Normal	Gom	0.009	0.015	0.009	0.009	0.022
Log-Normal	Log-Normal	RP(5)	0.009	0.010	0.009	0.008	0.009
Log-Normal	Log-Normal	RP(9)	0.009	0.010	0.009	0.008	0.009
Log-Normal	Log-Normal	RP(P)	0.009	0.010	0.009	0.008	0.009

Table A.13: Bias with Monte Carlo standard error of difference in 5-years life expectancy, simulation study on model misspecification in survival models with shared frailty terms, scenario with 15 clusters of 100 individuals each and a small frailty variance.

True frailty	Model frailty	Model baseline	Exponential	Weibull	Gompertz	Weibull-Weibull (1)	Weibull-Weibull (2)
Gamma	Gamma	Cox	0.008 (0.003)	-0.000 (0.003)	0.003 (0.002)	0.009 (0.003)	0.053 (0.003)
Gamma	Gamma	Exp	0.001 (0.003)	0.024 (0.003)	-0.038 (0.002)	-0.008 (0.002)	0.072 (0.003)
Gamma	Gamma	Wei	0.001 (0.003)	-0.001 (0.003)	-0.023 (0.002)	0.061 (0.002)	0.019 (0.003)
Gamma	Gamma	Gom	0.005 (0.003)	0.030 (0.003)	0.001 (0.002)	0.037 (0.002)	0.069 (0.003)
Gamma	Gamma	RP(5)	0.001 (0.003)	0.000 (0.003)	0.000 (0.002)	-0.005 (0.002)	0.013 (0.003)
Gamma	Gamma	RP(9)	0.001 (0.003)	0.000 (0.003)	0.001 (0.002)	-0.002 (0.002)	0.012 (0.003)
Gamma	Gamma	RP(P)	0.001 (0.003)	0.001 (0.003)	-0.003 (0.002)	-0.001 (0.002)	0.014 (0.003)
Log-Normal	Gamma	Cox	0.001 (0.003)	0.008 (0.003)	0.006 (0.002)	0.032 (0.002)	0.033 (0.003)
Log-Normal	Gamma	Exp	-0.000 (0.003)	0.028 (0.003)	-0.040 (0.002)	-0.009 (0.002)	0.064 (0.003)
Log-Normal	Gamma	Wei	-0.000 (0.003)	0.006 (0.003)	-0.025 (0.002)	0.060 (0.002)	0.013 (0.003)
Log-Normal	Gamma	Gom	-0.000 (0.003)	0.027 (0.003)	-0.002 (0.002)	0.040 (0.002)	0.066 (0.003)
Log-Normal	Gamma	RP(5)	-0.000 (0.003)	0.005 (0.003)	-0.002 (0.002)	-0.011 (0.002)	-0.009 (0.002)
Log-Normal	Gamma	RP(9)	-0.000 (0.003)	0.005 (0.003)	-0.002 (0.002)	-0.009 (0.002)	-0.010 (0.002)
Log-Normal	Gamma	RP(P)	-0.000 (0.003)	0.005 (0.003)	-0.006 (0.002)	-0.007 (0.002)	-0.008 (0.002)
Gamma	Log-Normal	Cox	-0.012 (0.003)	-0.016 (0.003)	-0.004 (0.002)	0.066 (0.002)	0.045 (0.003)
Gamma	Log-Normal	Exp	-0.022 (0.003)	-0.004 (0.003)	-0.048 (0.002)	0.003 (0.002)	0.118 (0.003)
Gamma	Log-Normal	Wei	-0.022 (0.003)	-0.025 (0.003)	-0.035 (0.002)	0.094 (0.002)	0.042 (0.003)
Gamma	Log-Normal	Gom	-0.020 (0.003)	-0.000 (0.004)	-0.016 (0.002)	0.056 (0.002)	0.116 (0.003)
Gamma	Log-Normal	RP(5)	0.014 (0.003)	0.016 (0.003)	0.011 (0.002)	0.017 (0.002)	0.045 (0.003)
Gamma	Log-Normal	RP(9)	0.014 (0.003)	0.016 (0.003)	0.011 (0.002)	0.020 (0.002)	0.044 (0.003)
Gamma	Log-Normal	RP(P)	0.014 (0.003)	0.016 (0.003)	0.007 (0.002)	0.021 (0.002)	0.046 (0.003)
Log-Normal	Log-Normal	Cox	-0.009 (0.003)	-0.006 (0.003)	-0.005 (0.002)	0.053 (0.002)	0.036 (0.003)
Log-Normal	Log-Normal	Exp	-0.017 (0.003)	0.008 (0.003)	-0.047 (0.002)	0.001 (0.002)	0.109 (0.003)
Log-Normal	Log-Normal	Wei	-0.017 (0.003)	-0.012 (0.003)	-0.034 (0.002)	0.088 (0.002)	0.035 (0.003)
Log-Normal	Log-Normal	Gom	-0.016 (0.003)	0.005 (0.003)	-0.015 (0.002)	0.056 (0.002)	0.106 (0.003)
Log-Normal	Log-Normal	RP(5)	0.013 (0.003)	0.020 (0.003)	0.007 (0.002)	0.006 (0.002)	0.019 (0.003)
Log-Normal	Log-Normal	RP(9)	0.013 (0.003)	0.020 (0.003)	0.007 (0.002)	0.009 (0.002)	0.018 (0.003)
Log-Normal	Log-Normal	RP(P)	0.013 (0.003)	0.020 (0.003)	0.004 (0.002)	0.010 (0.002)	0.020 (0.003)

Table A.14: Mean squared error of difference in 5-years life expectancy, simulation study on model misspecification in survival models with shared frailty terms, scenario with 15 clusters of 100 individuals each and a small frailty variance.

True frailty	Model frailty	Model baseline	Exponential	Weibull	Gompertz	Weibull-Weibull (1)	Weibull-Weibull (2)
Gamma	Gamma	Cox	0.008	0.010	0.005	0.009	0.010
Gamma	Gamma	Exp	0.007	0.012	0.005	0.005	0.014
Gamma	Gamma	Wei	0.007	0.010	0.004	0.010	0.008
Gamma	Gamma	Gom	0.007	0.013	0.004	0.007	0.014
Gamma	Gamma	RP(5)	0.007	0.009	0.005	0.005	0.009
Gamma	Gamma	RP(9)	0.007	0.009	0.004	0.005	0.009
Gamma	Gamma	RP(P)	0.007	0.009	0.004	0.005	0.009
Log-Normal	Gamma	Cox	0.008	0.010	0.004	0.006	0.008
Log-Normal	Gamma	Exp	0.007	0.011	0.005	0.005	0.014
Log-Normal	Gamma	Wei	0.007	0.009	0.005	0.010	0.008
Log-Normal	Gamma	Gom	0.007	0.011	0.004	0.007	0.014
Log-Normal	Gamma	RP(5)	0.007	0.009	0.004	0.005	0.006
Log-Normal	Gamma	RP(9)	0.007	0.009	0.004	0.005	0.006
Log-Normal	Gamma	RP(P)	0.007	0.009	0.004	0.005	0.006
Gamma	Log-Normal	Cox	0.007	0.010	0.004	0.009	0.009
Gamma	Log-Normal	Exp	0.008	0.012	0.006	0.005	0.023
Gamma	Log-Normal	Wei	0.008	0.011	0.005	0.015	0.009
Gamma	Log-Normal	Gom	0.008	0.013	0.005	0.009	0.022
Gamma	Log-Normal	RP(5)	0.008	0.010	0.005	0.006	0.011
Gamma	Log-Normal	RP(9)	0.008	0.010	0.005	0.006	0.011
Gamma	Log-Normal	RP(P)	0.008	0.010	0.005	0.006	0.011
Log-Normal	Log-Normal	Cox	0.007	0.009	0.004	0.008	0.008
Log-Normal	Log-Normal	Exp	0.007	0.011	0.006	0.005	0.021
Log-Normal	Log-Normal	Wei	0.007	0.010	0.005	0.014	0.009
Log-Normal	Log-Normal	Gom	0.008	0.010	0.005	0.009	0.020
Log-Normal	Log-Normal	RP(5)	0.008	0.009	0.005	0.005	0.007
Log-Normal	Log-Normal	RP(9)	0.008	0.009	0.005	0.005	0.007
Log-Normal	Log-Normal	RP(P)	0.008	0.009	0.004	0.005	0.007