It is well-known that the nonparametric maximum likelihood estimator (NPMLE) may severely under-estimate the survival function with left truncated data. Based on the Nelson estimator (for right censored data) and self-consistency we suggest a nonparametric estimator of the survival function, the iterative Nelson estimator (INE), for arbitrarily truncated and censored data, where only few nonparametric estimators are available. By simulation we show that the INE does well in overcoming the under-estimation of the survival function from the NPMLE for left-truncated and interval-censored data. An interesting application of the INE is as a diagnostic tool for other estimators, such as the monotone MLE or parametric MLEs. The methodology is illustrated by application to two real world problems: the Channing House and the Massachusetts Health Care Panel Study data sets.
Bibliographical noteFunding Information:
The first author would like to thank Yunlei Zhang for his stimulating discussions. We are very grateful to three anonymous referees for their insightful comments, which greatly improved our presentation. This research was supported by the NIH Grant R29-EY10769.
- Cumulative hazard
- EM algorithm
- Nelson estimator
- Nonparametric maximum likelihood