Table 2 Description, parameter estimates and confidence intervals for the competing risks models with/without frailty

Variable

No frailty terms

Frailty for revision only

Independent frailty terms

Correlated frailty terms

Sample size

113,772

113,772

113,772

113,772

Number of revisions

1336

1336

1336

1336

Number of deaths

9586

9586

9586

9586

Number of censored

102,850

102,850

102,850

102,850

Loglik

-114132.6

-114081.9

-114081.9

-114081.9

AIC

228305.2

228205.9

228207.9

228209.9

BIC

228498.0

228408.3

228419.9

228431.6

Revisions

Estimate

CI

Estimate

CI

Estimate

CI

Estimate

CI

λ_r (year)

15.46

8.923 - 26.79

11.58

7.298 - 18.39

11.52

7.262 - 18.27

11.59

7.298 - 18.4

k_r

1.66

1.171 - 2.355

1.63

1.149 - 2.312

1.642

1.158 - 2.329

1.63

1.149 - 2.311

k_r Females

1.096

1.018 - 1.179

1.137

1.049 - 1.233

1.134

1.046 - 1.23

1.137

1.049 - 1.233

k_r Age

0.9936

0.9884 - 0.9988

0.9936

0.9884 - 0.9987

0.9934

0.9883 - 0.9986

0.9936

0.9884 - 0.9987

k_r Cup/Head Resurf/Metal

1.515

1.126 - 2.039

1.569

1.167 - 2.11

1.576

1.172 - 2.119

1.57

1.167 - 2.11

Operation Date from 2007

1.26

1.112 - 1.427

1.288

1.132 - 1.464

1.286

1.131 - 1.463

1.288

1.132 - 1.464

Age

0.9692

0.9621 - 0.9765

0.9695

0.963 - 0.976

0.9694

0.9629 - 0.9758

0.9695

0.963 - 0.976

Uncemented

1.732

1.522 - 1.97

1.595

1.376 - 1.85

1.595

1.376 - 1.85

1.595

1.376 - 1.85

Head size

0.9677

0.9506 - 0.985

0.9563

0.94 - 0.9728

0.9563

0.9401 - 0.9728

0.9563

0.94 - 0.9728

Cup/Head Poly/Ceram

0.6017

0.4859 - 0.745

0.6592

0.5275 - 0.8238

0.6592

0.5274 - 0.8238

0.6593

0.5276 - 0.824

Cup/Head Resurf/Metal

9.37

4.556 - 19.27

10.88

5.796 - 20.43

10.8

5.75 - 20.28

10.89

5.797 - 20.45

Cup/Head Resurf/Resurf

4.558

3.113 - 6.673

5.595

3.804 - 8.227

5.593

3.803 - 8.224

5.594

3.804 - 8.226

\(\sigma ^{2}_{r}\)

-

-

0.1829

0.1205 - 0.2778

0.1829

0.1205 - 0.2777

0.1837

0.121 - 0.2787

Deaths

Estimate

CI

Estimate

CI

Estimate

CI

Estimate

CI

10⁵ λ_d (1/year)

1.286

0.9214 - 1.795

1.286

0.9214 - 1.795

1.288

0.9223 - 1.8

1.284

0.9204 - 1.792

10k_d (1/year)

0.9873

0.9404 - 1.037

0.9873

0.9404 - 1.037

0.987

0.9398 - 1.037

0.9875

0.9406 - 1.037

k_d Operation Date from 2007

0.9624

0.9561 - 0.9687

0.9624

0.9561 - 0.9687

0.9624

0.9562 - 0.9688

0.9624

0.9561 - 0.9687

k_d ASA P3-P5

0.6133

0.5639 - 0.6671

0.6133

0.5639 - 0.6671

0.6135

0.5641 - 0.6672

0.6132

0.5638 - 0.6669

k_d Cup/Head Poly/Metal

0.9458

0.9073 - 0.9859

0.9458

0.9073 - 0.9859

0.9459

0.9073 - 0.9861

0.9456

0.9072 - 0.9857

ASA P3-P5

36.53

23.83 - 56.01

36.54

23.83 - 56.01

36.46

23.79 - 55.86

36.58

23.86 - 56.08

Cup/Head Poly/Metal

1.563

1.193 - 2.047

1.563

1.193 - 2.047

1.562

1.192 - 2.045

1.564

1.194 - 2.049

4-5 quintiles of the IMD

1.084

1.04 - 1.13

1.084

1.04 - 1.13

1.084

1.04 - 1.13

1.084

1.04 - 1.13

\(\sigma ^{2}_{d} \)

-

-

-

-

2.031e-07

2e-07 - 2e-07

5e-07

5e-07 - 5e-07

ρ

-

-

-

-

-

-

0.00166

0.0013 - 0.0020