Maximum likelihood estimation in a partially observed stratified regression model with censored data

TL;DR

This paper develops nonparametric maximum likelihood estimators for a stratified proportional intensity model with censored data, where the stratum variable is partially unobserved, and proves their statistical properties.

Contribution

It introduces consistent and asymptotically normal estimators for a stratified model with unobserved stratification, extending Cox's model to incomplete data scenarios.

Findings

Establishes consistency of the proposed estimators.

Proves asymptotic normality of the estimators.

Provides methods for estimating variances.

Abstract

The stratified proportional intensity model generalizes Cox's proportional intensity model by allowing different groups of the population under study to have distinct baseline intensity functions. In this article, we consider the problem of estimation in this model when the variable indicating the stratum is unobserved for some individuals in the studied sample. In this setting, we construct nonparametric maximum likelihood estimators for the parameters of the stratified model and we establish their consistency and asymptotic normality. Consistent estimators for the limiting variances are also obtained.