Table 3.
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.