Statistical Modelling 9 (2009), 361–379
Urn sampling, interval censoring and proportional hazard models: tests and
relationships
Lu Zheng
Department of Biostatistics
Harvard School of Public Health
655 Huntington Avenue
Boston, MA 02115
USA
eMail: lzheng@hsph.harvard.edu
Marvin Zelen
Department of Biostatistics
Harvard School of Public Health
USA
Abstract:
This paper proposes a new distribution-free statistical method for
testing hypotheses about covariates for survival data having
simultaneously right-, left- and interval-censored survival times.
The new test is motivated by the analogue between urn sampling and
the Cox’s proportional hazard models. Investigations of the
significance levels and power as a function of the proportion of
interval-censored observations and interval length show that the
test performs well for most censoring situations encountered in
practice. Simulation results also suggest that there is negligible
loss of power in the practical situation in which the mean interval
length for interval-censored observations is less than the mean
survival time. This holds even with heavy interval censoring.
Comparison with the widely used Mantel’s method for comparing
two groups shows that the power of the new method appears to be
superior. Furthermore, the test is relatively simple to carry out
and generalizes to comparing k populations as well as the testing
of general linear hypothesis for arbitrary covariates.
Keywords:
interval censoring; mid-rank; rank-based tests; time to events; urn sampling
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