Table 1.
Simulation results for nonparametric estimators under the assumptions of independent and informative observation times
| (a) Independent observation times | ||||||||
|---|---|---|---|---|---|---|---|---|
| n | t | Λ0(t) | Proposed | NPMLE | NPMPLE | |||
| Bias | SE | Bias | SE | Bias | SE | |||
| 100 | 1·0 | 2 | −0·031 | 0·397 | −0·030 | 0·392 | −0·060 | 0·418 |
| 3·0 | 6 | −0·006 | 0·488 | −0·019 | 0·476 | −0·058 | 0·633 | |
| 5·0 | 10 | −0·024 | 0·542 | −0·047 | 0·505 | −0·063 | 0·723 | |
| 7·0 | 14 | −0·015 | 0·654 | −0·055 | 0·559 | −0·065 | 0·844 | |
| 9·0 | 18 | 0·004 | 0·804 | −0·051 | 0·643 | −0·045 | 0·904 | |
| 1000 | 1·0 | 2 | 0·011 | 0·156 | 0·010 | 0·154 | 0·007 | 0·200 |
| 3·0 | 6 | 0·005 | 0·202 | −0·002 | 0·189 | −0·017 | 0·276 | |
| 5·0 | 10 | 0·014 | 0·210 | −0·002 | 0·193 | −0·030 | 0·336 | |
| 7·0 | 14 | 0·011 | 0·241 | −0·009 | 0·211 | −0·019 | 0·374 | |
| 9·0 | 18 | 0·025 | 0·277 | −0·003 | 0·218 | −0·023 | 0·408 | |
| (b) Informative observation times | ||||||||
|---|---|---|---|---|---|---|---|---|
| n | t | Λ0(t) | Proposed | NPMLE | NPMPLE | |||
| Bias | SE | Bias | SE | Bias | SE | |||
| 100 | 1·0 | 2 | −0·009 | 0·271 | 0·015 | 0·271 | 0·447 | 0·454 |
| 3·0 | 6 | −0·007 | 0·553 | −0·040 | 0·512 | 0·361 | 0·795 | |
| 5·0 | 10 | 0·049 | 0·874 | −0·543 | 0·722 | −1·183 | 0·949 | |
| 7·0 | 14 | 0·008 | 1·198 | −1·699 | 0·859 | −3·395 | 1·067 | |
| 9·0 | 18 | 0·127 | 1·532 | −2·987 | 1·021 | −5·324 | 1·349 | |
| 1000 | 1·0 | 2 | 0·000 | 0·104 | 0·021 | 0·101 | 0·484 | 0·194 |
| 3·0 | 6 | 0·015 | 0·214 | −0·021 | 0·182 | 0·431 | 0·345 | |
| 5·0 | 10 | 0·031 | 0·343 | −0·509 | 0·258 | −1·157 | 0·407 | |
| 7·0 | 14 | 0·035 | 0·459 | −1·580 | 0·309 | −3·321 | 0·459 | |
| 9·0 | 18 | 0·038 | 0·564 | −2·901 | 0·340 | −5·448 | 0·508 | |
NPMLE, nonparametric maximum likelihood estimator; NPMPLE, nonparametric maximum pseudolikelihood estimator; Bias and SE are the Monte Carlo sample mean and standard deviation of the 1000 estimates of Λ0(t).