Analysis of Proportional Odds Models With Censoring and Errors-in-Covariates

ABSTRACT

We propose a consistent method for estimating both the finite- and infinite-dimensional parameters of the proportional odds model when a covariate is subject to measurement error and time-to-events are subject to right censoring. The proposed method does not rely on the distributional assumption of the true covariate, which is not observed in the data. In addition, the proposed estimator does not require the measurement error to be normally distributed or to have any other specific distribution, and we do not attempt to assess the error distribution. Instead, we construct martingale-based estimators through inversion, using only the moment properties of the error distribution, estimable from multiple erroneous measurements of the true covariate. The theoretical properties of the estimators are established and the finite sample performance is demonstrated via simulations. We illustrate the usefulness of the method by analyzing a dataset from a clinical study on AIDS. Supplementary materials for this article are available online.

Keywords:

• Estimating equations
• Functional approach
• Martingale
• Measurement error
• Proportional odds model
• U-statistics

Supplementary Materials

The supplementary materials contain a detailed derivation of whγ₂, regularity conditions, necessary lemmas, and the proof of the Theorems and Corollary 1.

Acknowledgment

The authors are grateful to the review team for insightful comments that led to a significant improvement of the article.

Funding

The work was partially supported by the National Science Foundation (DMS-1206693), the National Institute of Neurological Disorders and Stroke (R01-NS073671), and the National Cancer Institute (R03-CA176760).