Analysis of childhood brain tumour data in New York City using frailty models

This paper uses frailty models to analyse overall survival and progression-free survival times for children with a brain tumour. We are interested in how surgery resection affects survival times. We are also interested in how strong a child's progression-free survival correlates with his/her overall survival and if the association differs with age. Traditionally the frailty is modelled parametrically and a maximum likelihood approach is used to estimate the parameters of interest. However, the result is sensitive to the misspecification of the frailty distribution and the currently developed algorithms for the maximum likelihood approach do not allow the association parameter to depend on covariates. Xue formulates a Poisson regression model and applies an estimating equation approach to obtain a consistent estimate of the covariate effect on survival. This paper extends that approach to obtain consistent and efficient estimates of the association parameter as well as the covariate effect and to allow the association parameter to depend on the covariates. The approach does not require the specification of the frailty distribution. The performance of the method is evaluated through simulation studies. We apply this method to a childhood brain tumour data set in New York City.