# Revisiting Non-Parametric Maximum Likelihood Estimation of Current Status Data with Competing Risks

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## Abstract

Re-parametrization is often done to make a constrained optimization problem an unconstrained one. This paper focuses on the non-parametric maximum likelihood estimation of the sub-distribution functions for current status data with competing risks. Our main aim is to propose a method using re-parametrization, which is simpler and easier to handle with compared to the constrained maximization methods discussed in Jewell and Kalbfleisch (Biostatistics. **5**, 291–306, 2004) and Maathuis (2006), when both the monitoring times and the number of individuals observed at these times are fixed. Then the Expectation-Maximization (EM) algorithm is used for estimating the unknown parameters. We have also established some asymptotic results of these maximum likelihood estimators. Finite sample properties of these estimators are investigated through an extensive simulation study. Some generalizations have been discussed.

## Keywords and phrases.

Monitoring time Isotonic constraints Re-parametrization Cover percentage Observed Mahalanobis distance Interval hazards EM algorithm Complete data likelihood## AMS (2000) subject classification.

Primary 62N01, 62N02 Secondary 62P10## Preview

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## Notes

### Acknowledgments

We would like to thank the Associate Editor and the anonymous reviewers for a careful reading of the manuscript and several helpful suggestions.

## References

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