Semiparametric Estimation for the Additive Inverse Gaussian Frailty Model

Abstract

In survival analysis it is usually assumed that, conditional on observable covariates, life times are statistically independent. In many situations this assumption is not reasonable because individuals are naturally or artificially grouped, and within groups survival times may be associated. Frailty models are commonly employed to model dependent event times. In this article, the additive inverse Gaussian frailty model is studied. This model assumes that within each group individual frailties are correlated. Each frailty is the sum of two parts, a part shared by all group members and an individual specific part, and both parts follow the inverse Gaussian distribution. The EM algorithm is used to estimate frailty parameters and risk coefficients. Variances of these estimates are also computed. Testing procedures are discussed to discriminate between submodels.

Keywords:

• EM algorithm
• Frailty models
• Inverse Gaussian distribution
• Semiparametric estimation

Mathematics Subject Classification:

• 62N01
• 62P10

Notes

Note: “–” means not applicable, and “NA” means not available. Numbers in the parenthesis are the corresponding standard errors.

Note: “–” means not applicable, and “NA” means not available. Numbers in the parenthesis are the corresponding standard errors.