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.

Keywords

• excess hazard
• frailty models
• shared and correlated Gaussian frailty models
• compound Poisson frailty model
• Coale–Demeny life table models
• Mazandaran province of Iran