This paper investigates the urn sampling analogue for the score statistic relating survival to covariates assuming a proportional hazard model. The exact permutation distribution can be calculated as well as the exact low order moments for arbitrary censoring patterns. The asymptotic distribution of the score statistic is an easy consequence. The method is naturally extended to deal with the multivariate case, time varying covariates and interval censoring. Finally the relationship between the censoring process, the survival times and covariates are studied considering different reference sets for the distribution of the score statistic. Some assumptions about the censoring process are investigated and as a consequence the effect of censoring is clarified.
Bibliographical noteFunding Information:
This work was supported in part by grants from the National Institute of Health and originated as part of the first author’s doctoral dissertation at the Department of Biostatistics at the Harvard School of Public Health.
- Permutation distribution
- Proportional hazards
- Urn sampling
ASJC Scopus subject areas
- Applied Mathematics