It is well-known that the nonparametric maximum likelihood estimator (NPMLE) of a survival function may severely under-estimate the survival probabilities at very early times for left truncated data. This problem might be overcome by instead computing a smoothed nonparametric estimator (SNE) via the EMS algorithm. The close connection between the SNE and the maximum penalized likelihood estimator is also established. Extensive Monte Carlo simulations demonstrate the superior performance of the SNE over that of the NPMLE, in terms of cither bias or variance, even for moderately large samples. The methodology is illustrated with an application to the Massachusetts Health Care Panel Study dataset to estimate the probability of being functionally independent for non-poor male and female groups respectively.
- EM algorithm
- Maximum penalized likelihood
- Non-parametric maximum likelihood