# Proportional hazards model with partly interval censoring and its penalized likelihood estimation

## TL;DR

This paper introduces a flexible penalized likelihood approach for semi-parametric proportional hazards models with various censoring types, providing asymptotic analysis, an automatic regularization method, and demonstrating superior performance through simulations and real data application.

## Contribution

It develops a novel penalized likelihood method for semi-parametric proportional hazards models with interval, left, and right censoring, including asymptotic properties and an automatic regularization procedure.

## Key findings

- The method performs favorably in simulations.
- It effectively estimates baseline hazards and regression coefficients.
- The approach is validated on real melanoma recurrence data.

## Abstract

This paper considers the problem of semi-parametric proportional hazards model fitting for interval, left and right censored survival times. We adopt a more versatile penalized likelihood method to estimate the baseline hazard and the regression coefficients simultaneously, where the penalty is introduced in order to regularize the baseline hazard estimate. We present asymptotic properties of our estimate, allowing for the possibility that it may lie on the boundary of the parameter space. We also provide a computational method based on marginal likelihood, which allows the regularization parameter to be determined automatically. Comparisons of our method with other approaches are given in simulations which demonstrate that our method has favourable performance. A real data application involving a model for melanoma recurrence is presented and an R package implementing the methods is available.