Estimation of Competing Risks with General Missing Pattern in Failure Types
Article first published online: 11 DEC 2003
Volume 59, Issue 4, pages 1063–1070, December 2003
How to Cite
Dewanji, A. and Sengupta, D. (2003), Estimation of Competing Risks with General Missing Pattern in Failure Types. Biometrics, 59: 1063–1070. doi: 10.1111/j.0006-341X.2003.00122.x
- Issue published online: 11 DEC 2003
- Article first published online: 11 DEC 2003
- Received September 2001. Revised June 2003. Accepted June 2003.
- Competing risks;
- Cause-specific hazard;
- Missing failure type;
- Missing at random;
- EM algorithm;
- Nelson-Aalen estimator
Summary. In competing risks data, missing failure types (causes) is a very common phenomenon. In this work, we consider a general missing pattern in which, if a failure type is not observed, one observes a set of possible types containing the true type, along with the failure time. We first consider maximum likelihood estimation with missing-at-random assumption via the expectation maximization (EM) algorithm. We then propose a Nelson-Aalen type estimator for situations when certain information on the conditional probability of the true type given a set of possible failure types is available from the experimentalists. This is based on a least-squares type method using the relationships between hazards for different types and hazards for different combinations of missing types. We conduct a simulation study to investigate the performance of this method, which indicates that bias may be small, even for high proportion of missing data, for sufficiently large number of observations. The estimates are somewhat sensitive to misspecification of the conditional probabilities of the true types when the missing proportion is high. We also consider an example from an animal experiment to illustrate our methodology.