Table 3.

Analyses of cause-specific and subdistribution hazards models for characterizing levels of FGF-23 associated with development of ESRD from the motivating example

Cause-Specific Hazards ModelsSubdistribution Hazards Models
ESRDCoefficient (P Value)HRESRD, CS (95% CI)Coefficient (P Value)SHRESRD (95% CI)
With time-dependent coefficient for FGF-23
 FGF-23>180 RU/ml1.78 (<0.001)5.90 (4.21 to 8.27) at year 11.75 (<0.001)5.76 (4.17 to 7.97) at year 1
 Interaction of FGF-23>180 RU/ml and time−0.56 (0.002)4.02 (3.25 to 4.96) at year 2−0.62 (0.002)3.76 (3.05 to 4.65) at year 2
3.21 (2.51 to 4.10) at year 32.93 (2.30 to 3.75) at year 3
2.73 (2.00 to 3.73) at year 42.46 (1.81 to 3.34) at year 4
2.41 (1.66 to 3.51) at year 52.14 (1.45 to 3.08) at year 5
Without time-dependent coefficient for FGF-23a
 FGF-23>180 RU/ml1.39 (<0.001)4.01 (3.26 to 4.93)1.33 (<0.001)3.77 (3.07 to 4.62)
  • For the purpose of illustration, all models are unadjusted. Time-dependent FGF-23>180 RU/ml is defined as an interaction between FGF-23>180 RU/ml and logarithm of survival time. FGF-23, fibroblast growth factor 23; HRESRD, CS, cause-specific hazard ratio for ESRD; 95% CI, 95% confidence interval; SHRESRD, sub-distribution hazard ratio for ESRD.

  • a Models without time-dependent coefficient for levels of FGF-23 are presented here for the purpose of comparison. We do not need them in practice because of the presence of significant time-dependent coefficient for levels of FGF-23.