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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 4.

Summary statistics for the estimation of Model (B) λ(t | X1, X2) = λ0(t)exp(β1X1 + β2X2 + β3X1X2) when ρ = 1.5.

Proportion censored β1 β2 β3 ρ Λ(0.3) Λ(0.7)
n Coef Bias ES RE Bias ES RE Bias ES RE Bias ES Bias ES RE Bias ES RE
0% 100 PL -1 17 2 24 -2 24 0 3 10
DEL 0 5 9.70 -24 16 2.10 6 17 2.04 4 3 0.88 15 7 2.02
DELρ 0 6 9.38 2 23 1.02 -2 18 1.73 9 40 0 3 1.01 0 10 1.04
400 PL -1 8 1 12 0 11 0 1 0 5
DEL 2 2 10.1 -24 8 2.08 6 8 1.82 4 1 0.95 15 4 1.90
DELρ 1 2 9.75 1 12 1.02 -1 9 1.51 2 19 0 1 1.02 0 5 1.03
30% 100 PL -2 21 3 29 -2 28 0 3 0 12
DEL 0 6 14.1 -27 19 2.20 4 20 2.09 4 3 0.95 16 9 1.93
DELρ -1 6 13.6 2 28 1.04 -2 21 1.84 12 46 0 3 1.03 0 12 1.05
400 PL -1 9 1 14 0 13 0 2 0 6
DEL 1 3 14.2 -26 9 2.17 5 10 1.92 4 2 0.98 15 4 1.94
DELρ 0 3 13.7 1 13 1.04 -1 10 1.70 3 21 0 1 1.04 0 6 1.05
50% 100 PL -2 27 4 35 -2 36 0 3 0 14
DEL 0 6 23.5 -30 23 2.36 0 24 2.23 4 3 1.00 16 10 1.93
DELρ 0 6 22.6 2 33 1.09 -4 25 2.11 14 53 0 3 1.06 0 14 1.08
400 PL -1 12 1 16 0 16 0 0 7
DEL 2 3 21.3 -29 11 2.19 2 11 2.05 4 2 0.99 16 5 1.88
DELρ 1 3 20.6 0 16 1.03 -2 11 1.90 3 23 0 2 1.04 0 6 1.06

NOTE: β1, β2, and β3 are the regression coefficients, where the true parameter values are (−0.5, 1, −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.