Estimation of excess hazard using compound Poisson frailty model

Abstract

Background & Aim: The excess hazard rate proposed by Andersen and Vaeth may underestimate the long-term excess hazard rate for cancer survival. Zahl explained the phenomenon by continuous selection of the most robust individuals after diagnosis. He applied correlated inverse Gaussian and gamma  frailty  models  to estimate  excess intensity  and reached  a better  estimate  of the rate and called it the corrected excess hazard. The compound Poisson distribution has more parameters and therefore owns more flexibility and includes gamma and inverse Gaussian distributions as special cases. Therefore, the aim of this study was to estimate the excess hazard using compound poisson frailty model
Methods  &  Materials:  Both  shared  and  correlated  frailty  (CF)  variables based  on  compound Poisson distribution  were used to model  unobserved common  covariates.  A data  set  of patients diagnosed  with localized or  regional  gastrointestinal  tract  cancer  collected  at  the  Mazandaran province of Iran was studied. As registration systems in Iran are so affected by omission and various errors,  a  number  of  five  West  Coale- Demeny  life  tables for men  and  four  for  women  were constructed corresponding to each birth cohort, which was considered as the reference life tables. Thus, population-based mortality rates [h1(t)] were simply replaced by the appropriate values of the West tables depending on the sex (male or female) and birth cohort of the patient. 
Results: The CF model with unequal variances could best estimate the long-term excess hazard.
Conclusion:  This study advocates  the CF models can best estimate  the long-term  excess hazard rates regardless of the distribution of the frailty variable.