Estimation of Proportional Hazards Models for Survival Times with Nested Errors
Rick L. Williams
and Gayle S. Bieler
1993, American
Statistical Association, Proceedings
of the Biopharmaceutical Section,
115-120.
Keywords:
Correlated failure times; Taylor series variance approximation; Cox regression
Abstract
A simple
variance estimation method is demonstrated for proportional hazards
models of survival times with a nested error structure. For example,
this method is appropriate when repeated measurements are taken on a
single animal in neurobehavioral toxicology experiments, when
analyzing littermates in teratology studies, or whenever survival
times are clustered, as in families or clinics. The method derives
from Binder's (1992) work for complex sample surveys using a Taylor
series approach which yields consistent estimates of the model
parameters and their variance-covariance matrix. In a simulation
study of the level and power of significance tests of model
parameters, we find that the method maintains the specified Type l
error rate. We further demonstrate the method using repeated
measurements of time to avoidance in a neurobehavioral toxicology
experiment. This approach is implemented in the SUDAAN software package.