Quasi-Likelihood for Right-Censored Data in the Generalized Linear Model

Abstract

This article proposes a method for estimation in a generalized linear model with right-censored data. Consider the model , μ _i (β) = g(β ^T X _i ), where v and g are known functions, e _i , i = 1,…,n are identically and independently distributed with mean 0 and finite variance φ², but the distribution is unspecified. We use Kaplan–Meier estimates to replace the censored observations and employ quasi-likelihood to estimate the parameters. Consistency and asymptotic normality of the parameter estimates are derived. The performance of the proposed method for small sample sizes is investigated by simulation study. The new method is illustrated with the Stanford heart transplant data.

Keywords:

• First two moments
• Kaplan–Meier estimate
• Survival analysis

Mathematics Subject Classification:

• Primary 62N02
• Secondary 62F12

Notes

Note: Bias = Ave( ₁ − β₁), var^1/2 = (Ave( ₁ − β₁)²)^1/2. Extreme denotes the extreme value distribution.

Note: Bias = Ave( ₁ − β₁), var^1/2 = (Ave( ₁ − β₁)²)^1/2