Table 4.
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.