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. Author manuscript; available in PMC: 2017 Aug 18.
Published in final edited form as: J Am Stat Assoc. 2016 Aug 18;111(514):787–799. doi: 10.1080/01621459.2015.1044090

Table 3.

Summary statistics for the estimation of Model (A) λ(t | X1, X2) = λ0(t) exp(β1X1 + β2X2) when ρ = 1.5.

Proportion censored β1 β2 ρ Λ(0.3) Λ(0.7)
n Coef Bias ES RE Bias ES RE Bias ES Bias ES RE Bias ES RE
0% 100 PL -1 12 2 22 0 3 0 10
DEL 0 5 5.99 -22 15 1.88 4 3 0.76 15 7 1.92
DELρ -1 5 4.71 1 22 1.02 8 38 0 3 1.02 0 10 1.03
400 PL 0 6 1 11 0 1 0 5
DEL 2 2 6.26 -21 8 1.81 4 2 0.88 15 3 1.90
DELρ 1 2 5.68 0 11 1.02 2 17 0 1 1.04 0 5 1.05
30% 100 PL -2 14 2 27 0 3 0 12
DEL 1 5 8.39 -25 19 1.99 4 3 0.82 16 8 2.01
DELρ 0 2 5.20 0 11 1.01 2 17 0 1 1.03 0 5 1.04
400 PL -1 7 1 13 0 2 0 5
DEL 1 2 7.59 -23 9 1.92 4 2 0.90 15 4 1.88
DELρ 0 2 7.01 0 13 1.02 2 19 0 1 1.04 0 5 1.04
50% 100 PL -2 16 2 32 0 3 0 13
DEL 1 5 8.84 -28 22 2.09 4 3 0.97 16 10 1.84
DELρ 0 6 8.29 1 31 1.04 12 50 0 3 1.02 1 13 1.03
400 PL -1 8 1 15 0 2 0 6
DEL 2 2 9.99 -27 11 2.01 4 2 0.90 16 4 1.96
DELρ 1 2 9.39 0 15 1.02 2 21 0 2 1.05 0 6 1.04

NOTE: β1 and β2 are the regression coefficients, where the true parameter values are (−0.5, 0.5); Λ(t) = t2 is the baseline cumulative hazard function evaluated at t; PL, the maximum partial likelihood estimator β̂PL; DEL, the double empirical likelihood estimator β̂; DELρ, the extended double empirical likelihood estimator β̂ρ that allows for a different baseline hazard function for the aggregate data; Bias and ES, empirical bias (×100) and empirical standard deviation (×100) of 1,000 regression parameter estimates; RE, the empirical variance of the maximum partial likelihood estimator divided by that of the double empirical likelihood estimators.