Table 2 Bias and mean square error (MSE) for log hazard ratio estimates, estimated at 3 months, across shared frailty models in the presence of both unobserved heterogeneity and non-proportional hazards

1

500

0.25

0.03

−0.0284 (0.0021), 0.0050 (0.0002)

− 0.0033 (0.0023), 0.0051 (0.0002)

0.0021 (0.0023), 0.0052 (0.0002)

−17.4231 (2.1208)

− 18.7145 (2.0875)

2

500

0.50

0.03

− 0.0285 (0.0024), 0.0068 (0.0003)

− 0.0023 (0.0026), 0.0067 (0.0003)

0.0031 (0.0026), 0.0068 (0.0003)

−11.1578 (1.9985)

−12.3537 (1.9639)

3

500

0.75

0.03

−0.0233 (0.0027), 0.0076 (0.0004)

0.0035 (0.0029), 0.0081 (0.0004)

0.0093 (0.0029), 0.0083 (0.0004)

−12.7599 (1.9452)

−14.1747 (1.8756)

4

300

0.25

0.03

− 0.0259 (0.0028), 0.0085 (0.0004)

− 0.0015 (0.0030), 0.0093 (0.0004)

0.0041 (0.0031), 0.0096 (0.0004)

− 15.4391 (2.0856)

− 18.0137 (2.0061)

5

300

0.50

0.03

− 0.0215 (0.0032), 0.0105 (0.0005)

0.0047 (0.0033), 0.0111 (0.0005)

0.0103 (0.0034), 0.0114 (0.0005)

−9.4606 (2.1449)

−11.4682 (2.0577)

6

300

0.75

0.03

−0.0252 (0.0035), 0.0126 (0.0006)

0.0019 (0.0037) 0.0134 (0.0006)

0.0069 (0.0037), 0.0137 (0.0006)

− 10.3721 (1.9615)

− 12.1647 (1.8949)

7

500

0.25

−0.03

0.0287 (0.0021), 0.0051 (0.0002)

− 0.0075 (0.0023), 0.0053 (0.0002)

0.0018 (0.0023), 0.0053 (0.0002)

−18.3401 (2.1438)

−19.5151 (2.1016)

8

500

0.50

−0.03

0.0289 (0.0024), 0.0068 (0.0003),

− 0.0072 (0.0026), 0.0069 (0.0003)

0.0021 (0.0026), 0.0069 (0.0003)

−12.1807 (2.0392)

− 13.6435 (1.9931)

9

500

0.75

−0.03

0.0341 (0.0027), 0.0083 (0.0004)

−0.0011 (0.0029), 0.0083 (0.0004)

0.0086 (0.0029), 0.0085 (0.0004)

−14.1771 (1.9844)

−15.7796 (1.9005)

10

300

0.25

−0.03

0.0311 (0.0028), 0.0088 (0.0004)

− 0.0059 (0.0031), 0.0095 (0.0004)

0.0035 (0.0031), 0.0098(0.0004)

−16.7676 (2.1182)

−19.2818 (2.0272)

11

300

0.50

−0.03

0.0361 (0.0032), 0.0114 (0.0005)

0.0004 (0.0033), 0.0112 (0.0005)

0.0096 (0.0034), 0.0116 (0.0005)

−10.0998 (2.1977)

−12.4175 (2.0889)

12

300

0.75

−0.03

0.0316 (0.0035), 0.0130 (0.0006)

− 0.0032 (0.0037), 0.0136 (0.0006)

0.0052 (0.0037), 0.0139 (0.0007)

−11.6808 (2.0013)

− 13.7017 (1.9235)

13

500

0.25

0

−0.0009 (0.0021), 0.0042 (0.0002)

− 0.0051 (0.0023), 0.0052(0.0002)

0.0020 (0.0023), 0.0053 (0.0002)

−17.8005 (2.1303)

−19.0529 (2.0932)

14

500

0.50

0

−0.0009 (0.0024), 0.0059 (0.0003)

− 0.0044 (0.0026), 0.0067 (0.0003)

0.0027(0.0026), 0.0068 (0.0003)

−11.4262 (2.0238)

−12.6627 (1.9860)

15

500

0.75

0

0.0044 (0.0027), 0.0071 (0.0003)

0.0016 (0.0029), 0.0082 (0.0004)

0.0091 (0.0029), 0.0084 (0.0004)

−13.4164 (1.9621)

−14.9156 (1.8853)

16

300

0.25

0

0.0017 (0.0028), 0.0079 (0.0004)

−0.0032 (0.0031), 0.0094 (0.0004)

0.0041 (0.0031), 0.0097 (0.0004)

−15.8830 (2.0985)

−18.3944 (2.0120)

17

300

0.50

0

0.0061 (0.0032), 0.0101 (0.0005)

0.0027 (0.0033), 0.0112 (0.0005)

0.0097 (0.0034), 0.0115 (0.0005)

−9.7878 (2.1647)

−11.9642 (2.0672)

18

300

0.75

0

0.0021 (0.0035), 0.0120 (0.0006)

−0.0004 (0.0037), 0.0134 (0.0006)

0.0062 (0.0037), 0.0138 (0.0006)

−11.0009 (1.9807)

−12.9017 (1.9108)