# Semiparametric Estimation for the Transformation Model with Length-Biased Data and Covariate Measurement Error

## TL;DR

This paper develops a new semiparametric inference method for transformation models applied to length-biased survival data contaminated with measurement error, addressing a gap in existing survival analysis techniques.

## Contribution

It introduces a novel estimation approach that handles complex features like length-biased sampling and measurement error without requiring covariate distribution specification.

## Key findings

- Establishes asymptotic properties of the estimators
- Demonstrates the method's effectiveness through numerical studies
- No need to specify covariate distribution or transformation function

## Abstract

Analysis of survival data with biased samples caused by left-truncation or length-biased sampling has received extensive interest. Many inference methods have been developed for various survival models. These methods, however, break down when survival data are typically error-contaminated. Although error-prone survival data commonly arise in practice, little work has been available in the literature for handling length-biased data with measurement error. In survival analysis, the transformation model is one of the frequently used models. However, methods of analyzing the transformation model with those complex features have not been fully explored. In this paper, we study this important problem and develop a valid inference method under the transformation model. We establish asymptotic results for the proposed estimators. The proposed method enjoys appealing features in that there is no need to specify the distribution of the covariates and the increasing function in the transformation model. Numerical studies are reported to assess the performance of the proposed method.