For TKAs, the revision rate was 4.1% at eight years and the hazard function was non-monotonic; revision risk was high initially after surgery, decreased, then spiked approximately one year after surgery before decreasing again (Fig. 1a and 1b). For THAs, the revision rate was 3.9% at eight years and the hazard function monotonically decreased over time, with the risk of revision highest immediately after surgery (Fig. 1c and 1d).
For both TKA and THA, the discrimination of the four modelling approaches was virtually identical (c-index 0.64 for all four approaches for TKA revision and 0.59 for all four approaches for THA revision). (Table 3, Table 4).
For TKAs the random survival forest had worse calibration than the Cox, Weibull or flexible parametric models. The ICI showed that on average, predicted risks from the Cox model differed from actual risk by 0.16% (95% CI [0.15, 0.18]), but this difference was 0.27% (95% CI [0.25,0.29]) for the random survival forest (Table 3). The Cox, Weibull, and flexible parametric models were well calibrated across the range of possible risks, whereas the random survival forest overestimated the risk for lower risk patients and underestimated the risk for higher risk patients (Fig. 2a).
For THA, all modelling approaches had similar overall calibration according to the ICI (Table 4). The Cox, Weibull and flexible parametric models were well calibrated for low-risk patients but overestimated the revision risk for higher risk patients. Conversely, the random survival forests were well calibrated in those with high risk but underestimated the risk for lower risk patients (Fig. 2b).
When predicting TKA revision, the Cox and flexible parametric models returned the highest integrated IPA, each with a value of 0.056 (95% CI [0.054, 0.057]) while the Weibull model had the lowest IPA of 0.054 (95% CI [0.053, 0.056]) (Table 3). All models performed similarly in the later follow-up period, with the Weibull and random survival forest slightly worse (Fig. 3a). Within the first year of TKA, the random survival forest was the best performing approach for prediction of revision. In this earlier time period, the Weibull model had negative IPA, implying it performed worse than the null model.
When predicting THA revision, the Cox and flexible parametric models had the highest integrated IPA (0.029 95% CI [0.027, 0.030] compared to 0.027 (95% CI [0.025, 0.028]) for the random survival forest) (Table 4). The random survival forest had the highest IPA for revisions within the first two years but showed poorer performance than the other modelling approaches for later time periods. The Weibull model had slightly worse performance than the Cox and flexible parametric models over the entire eight-year period (Fig. 3b).
Table 3
Performance metrics for predicting revision of TKA using Cox, Weibull parametric, flexible parametric, and random survival forest models
TKA
|
Modelling Approach
|
c-index
|
Integrated Index of Prediction Accuracy
|
Integrated calibration index (×100)
|
Cox
|
0.643 (0.641, 0.645)
|
0.056 (0.054, 0.057)
|
0.16 (0.15, 0.18)
|
Weibull
|
0.642 (0.641, 0.644)
|
0.054 (0.053, 0.056)
|
0.17 (0.16, 0.19)
|
Flexible parametric
|
0.643 (0.641, 0.645)
|
0.056 (0.054, 0.057)
|
0.17 (0.15, 0.18)
|
Random survival forest
|
0.643 (0.642, 0.645)
|
0.055 (0.054, 0.056)
|
0.27 (0.25, 0.29)
|
Table 4
Performance metrics for predicting revision of THA using Cox, Weibull parametric, flexible parametric, and random survival forest models
THA
|
|
c-index
|
Index of Prediction Accuracy
|
Integrated calibration index (×100)
|
Cox
|
0.591 (0.589, 0.594)
|
0.029 (0.027, 0.03)
|
0.27 (0.25, 0.3)
|
Weibull
|
0.591 (0.588, 0.594)
|
0.028 (0.026, 0.029)
|
0.29 (0.26, 0.31)
|
Flexible parametric
|
0.591 (0.588, 0.594)
|
0.029 (0.027, 0.030)
|
0.28 (0.25, 0.3)
|
Random survival forest
|
0.59 (0.587, 0.592)
|
0.027 (0.025, 0.028)
|
0.28 (0.25, 0.3)
|
For TKA, rankings of variable importance from backwards elimination and random survival forest minimal depth identified the same three most important predictors of revision (age, use of pain medication (opioids), and use of patella resurfacing). Both selection methods ranked prosthesis stability, prosthesis bearing surface and patient depression as the three next most important predictors, with the order differing between methods (Table 5).
For THA, rankings of variable importance from backwards elimination and random survival forest minimal depth identified the same five most important predictors of revision in the same order: femoral cement, patient depression, use of pain medication (opioids), gastro-oesophageal reflux disease, and sex. Patient age and steroid responsive diseases were the next most important predictors, with the ordering swapped between methods (Table 6).
Table 5
Ranked importance of variables from backward elimination in Cox model compared to minimal depth from random survival forest, for prediction of TKA revision. Variables are displayed in decreasing order of importance.
Bootstrap backwards elimination in Cox model (95% CI)
|
Minimal depth from random survival forest (95% CI)
|
Age
|
1 (1,1)
|
Age
|
1.54 (1.45,1.64)
|
Pain
|
2.26 (2.21,2.3)
|
Pain
|
1.91 (1.8,2.02)
|
Patella usage
|
2.92 (2.86,2.97)
|
Patella usage
|
2.04 (1.93,2.15)
|
Stability
|
4.39 (4.34,4.44)
|
Depression
|
2.2 (2.08,2.32)
|
Bearing surface
|
4.51 (4.43,4.59)
|
Bearing surface
|
2.46 (2.34,2.58)
|
Depression
|
6.22 (6.17,6.28)
|
Stability
|
2.79 (2.68,2.9)
|
Sex
|
7.39 (7.32,7.46)
|
Mobility
|
3.05 (2.91,3.18)
|
Tibial cement
|
8.8 (8.62,8.98)
|
Anxiety
|
3.05 (2.91,3.19)
|
Anxiety
|
10.6 (10.44,10.77)
|
Sex
|
3.24 (3.13,3.35)
|
Ischaemic heart disease angina
|
10.68 (10.48,10.87)
|
Tibial cement
|
3.49 (3.36,3.62)
|
Mobility
|
10.77 (10.6,10.95)
|
Inflammation pain
|
4.2 (4.07,4.33)
|
Gastro-oesophageal reflux disease
|
11.02 (10.81,11.23)
|
Ischaemic heart disease angina
|
4.2 (4.09,4.32)
|
Steroid responsive diseases
|
12.48 (12.27,12.7)
|
Steroid responsive diseases
|
4.23 (4.11,4.35)
|
Computer navigation
|
16.48 (16.22,16.74)
|
Gastro-oesophageal reflux disease
|
4.28 (4.15,4.41)
|
congestive heart failure
|
16.89 (16.5,17.28)
|
Hypertension
|
4.47 (4.35,4.6)
|
Arrhythmia
|
17.1 (16.74,17.46)
|
Ischaemic heart disease hypertension
|
4.68 (4.56,4.8)
|
Ischaemic heart disease hypertension
|
18.62 (18.29,18.95)
|
Computer navigation
|
4.73 (4.62,4.83)
|
Hypothyroidism
|
19.16 (18.82,19.5)
|
congestive heart failure
|
4.74 (4.63,4.84)
|
Hypertension
|
19.39 (19.02,19.76)
|
Gout
|
4.74 (4.64,4.84)
|
Osteoporosis/Paget’s
|
19.88 (19.53,20.23)
|
Chronic Airways Disease
|
4.78 (4.66,4.9)
|
Anticoagulants
|
21.74 (21.37,22.12)
|
Femoral cement
|
4.86 (4.74,4.98)
|
Inflammation pain
|
22.09 (21.76,22.42)
|
Glaucoma
|
4.93 (4.81,5.05)
|
Chronic Airways Disease
|
22.96 (22.61,23.31)
|
Anticoagulants
|
4.93 (4.82,5.04)
|
Diabetes
|
23.9 (23.58,24.22)
|
Osteoporosis/Paget’s
|
5.1 (4.99,5.21)
|
Hyperlipidaemia
|
24.12 (23.82,24.41)
|
Arrhythmia
|
5.11 (5,5.21)
|
Antiplatelet medication
|
24.28 (23.96,24.6)
|
Diabetes
|
5.17 (5.07,5.27)
|
Gout
|
24.86 (24.59,25.14)
|
Antiplatelet medication
|
5.18 (5.07,5.29)
|
Glaucoma
|
25.23 (24.95,25.52)
|
Hypothyroidism
|
5.19 (5.1,5.29)
|
Femoral cement
|
25.24 (24.97,25.51)
|
Hyperlipidaemia
|
5.26 (5.16,5.36
|
Table 6
Ranked importance of variables from backward elimination in Cox model compared to minimal depth from random survival forest, for prediction of THA revision. Variables are displayed in decreasing order of importance.
Bootstrap backwards elimination in Cox model (95% CI)
|
Minimal depth from random survival forest (95% CI)
|
Femoral cement
|
1.46 (1.43,1.49)
|
Femoral cement
|
0.66 (0.62,0.7)
|
Depression
|
1.92 (1.87,1.98)
|
Depression
|
0.99 (0.93,1.04)
|
Pain
|
2.82 (2.76,2.89)
|
Pain
|
1.5 (1.44,1.55)
|
Gastro-oesophageal reflux disease
|
5.33 (5.19,5.46)
|
Gastro-oesophageal reflux disease
|
2.44 (2.36,2.51)
|
Sex
|
5.58 (5.49,5.67)
|
Sex
|
2.7 (2.65,2.76)
|
Age
|
7.49 (7.32,7.67)
|
Steroid responsive diseases
|
2.77 (2.69,2.85)
|
Steroid responsive diseases
|
8.29 (8.06,8.52)
|
Age
|
3.1 (3.05,3.15)
|
Inflammation pain
|
8.96 (8.79,9.13)
|
Congestive heart failure
|
3.25 (3.18,3.32)
|
Anxiety
|
9.74 (9.53,9.95)
|
Anxiety
|
3.64 (3.55,3.74)
|
Congestive heart failure
|
12.22 (11.93,12.5)
|
Bearing Surface
|
3.74 (3.67,3.81)
|
Osteoporosis/Paget’s
|
12.22 (11.98,12.46)
|
Head size
|
3.88 (3.83,3.94)
|
Head size
|
12.23 (11.97,12.49)
|
Osteoporosis/Paget’s
|
3.93 (3.84,4.02)
|
Bearing surface
|
12.32 (12.1,12.55)
|
Gout
|
4.18 (4.1,4.26)
|
Hyperlipidaemia
|
12.37 (12.19,12.54)
|
Inflammation pain
|
4.32 (4.23,4.41)
|
Anticoagulant
|
15.47 (15.18,15.76)
|
Acetabular cement
|
4.33 (4.26,4.41)
|
Hypothyroidism
|
16.74 (16.48,17)
|
Hyperlipidaemia
|
4.6 (4.51,4.69)
|
Chronic Airways Disease
|
17.61 (17.34,17.88)
|
Chronic Airways Disease
|
4.78 (4.69,4.87)
|
Gout
|
19.13 (18.86,19.4)
|
Anticoagulants
|
4.95 (4.85,5.04)
|
Arrhythmia
|
19.92 (19.64,20.2)
|
Arrhythmia
|
5.05 (4.95,5.15)
|
Ischaemic heart disease hypertension
|
20 (19.76,20.23)
|
Hypothyroidism
|
5.28 (5.19,5.38)
|
Antiplatelet medications
|
21.3 (21.09,21.52)
|
Ischaemic heart disease angina
|
5.32 (5.22,5.43)
|
Glaucoma
|
21.4 (21.2,21.6)
|
Hypertension
|
5.48 (5.38,5.58)
|
Diabetes
|
21.53 (21.33,21.74)
|
Ischaemic heart disease hypertension
|
5.55 (5.46,5.64)
|
Ischaemic heart disease angina
|
21.62 (21.42,21.82)
|
Antiplatelet medications
|
5.57 (5.47,5.67)
|
Acetabular cement
|
21.64 (21.45,21.84)
|
Diabetes
|
5.74 (5.64,5.85)
|
Hypertension
|
21.69 (21.48,21.89)
|
Glaucoma
|
6.11 (6,6.21)
|