Analysis of testicular cancer data using a frailty modelwith familial dependence



Previously published papers have indicated a fairly strong familial dependence intesticular cancer patients. This is particularly evident in brothers. We have applied a frailty model with familial dependence to family data on brothers of testicular cancer patients from the Norwegian Radium Hospital. The model is a two-level frailty, with variation in susceptibility at both the family and the individual level. Specifically, the frailty variable is assumed to be compound Poisson distributed to allow individuals to be non-susceptible. The underlying Poisson parameter is gamma distributed to model how testicular cancer is distributed among families. This is an extension of a previous compound Poisson frailty model developed for individual testicular cancer data, and an alternative to traditional modelling of survival time family data. The likelihood construction and ascertainment problems are looked at in detail. To avoid ascertainment bias, the likelihood is based on the probability of observing the disease status for each brother in a family, given that at least one brother is ascertained. The estimated relative risk for brothers is 7.4. This paper expands on a previous analysis of the data by using a frailty model, which makes it possible to examine how the cancer is distributed among families. The estimated gamma-shaped parameter is 0.151 (95 per cent confidence interval 0.078–0.294), and this indicates that in order to obtain the high relative risks observed for brothers of testicular cancer patients, the distribution of susceptibility has to be strongly skewed among the families. The vast majority of families have a very low risk and a small proportion have a high risk. In addition, a quantity similar to the relative risk is derived to show that the susceptibility is skewly distributed also if the Poisson parameter is Bernoulli or stable distributed. This indicates that the results are valid also if other distributions are used to model familial dependence in the compound Poisson frailty model. Copyright © 2004 John Wiley & Sons, Ltd.