. Author manuscript; available in PMC: 2018 Jan 17.

Published in final edited form as: Stat Methods Med Res. 2014 Mar 11;25(6):2488–2505. doi: 10.1177/0962280214526193

Table 4.

Results for fitting the three subhazard models to Type 1 event of the breast cancer data

Model

Treatment

{\hat{β}}_{1}

(SE)

Age

{\hat{β}}_{2}

(SE)

Tumor size

{\hat{β}}_{3}

(SE)

{\hat{σ}}_{0}^{2}

(SE)

{\hat{σ}}_{1}^{2}

(SE)

{\hat{σ}}_{01} [\hat{ρ}]

(SE)

- 2 p_{β, v} (h_{w}^{*})

M1 (F-G)

−0.667
(0.119)

−0.026
(0.005)

0.082
(0.042)

–

4870.5

M2 (Center)

−0.672
(0.119)

−0.026
(0.005)

0.081
(0.042)

0.043
(0.051)

–

4869.4

M3 (Corr)

−0.658
(0.137)

−0.026
(0.005)

0.079
(0.043)

0.091
(0.026)

0.249
(0.073)

−0.108 [−0.721]
(0.037)

4865.7

M1, proportional subhazard model (Fine-Gray model) without frailties;

M2, subhazard shared frailty model with random center effect only;

M3, subhazard correlated frailty model with ρ;

${\hat{σ}}_{0}^{2}$ and ${\hat{σ}}_{1}^{2}$ , the variances of random center effect and random treatment-by-center interaction, respectively;

σ₀₁ and ρ, the corresponding covariance and correlation with ρ = σ₀₁/(σ₀σ₁);

SE, the estimated standard error for regression and frailty parameters;

$p_{β, v} (h_{w}^{*})$ , restricted h-likelihood in (9).