Time-dependent diagnostic accuracy analysis with censored outcome and censored predictor

A local agreement pattern measure based on hazard functions for survival outcomes

Assessing agreement is often of interest in biomedical and clinical research when measurements are obtained on the same subjects by different raters or methods. Most classical agreement methods have been focused on global summary statistics, which cannot be used to describe various local agreement patterns. The objective of this work is to study the local agreement pattern between two continuous measurements subject to censoring. In this article, we propose a new agreement measure based on bivariate hazard functions to characterize the local agreement pattern between two correlated survival outcomes. The proposed measure naturally accommodates censored observations, fully captures the dependence structure between bivariate survival times and provides detailed information on how the strength of agreement evolves over time. We develop a nonparametric estimation method for the proposed local agreement pattern measure and study theoretical properties including strong consistency and asymptotical normality. We then evaluate the performance of the estimator through simulation studies and illustrate the method using a prostate cancer data example.

Inference for reclassification statistics under nested and non-nested models for biomarker evaluation

The Net Reclassification Improvement (NRI) and the Integrated Discrimination Improvement (IDI) are used to evaluate the diagnostic accuracy improvement for biomarkers in a wide range of applications. Most applications for these reclassification metrics are confined to nested model comparison. We emphasize the important extensions of these metrics to the non-nested comparison. Non-nested models are important in practice, in particular, in high-dimensional data analysis and in sophisticated semiparametric modeling. We demonstrate that the assessment of accuracy improvement may follow the familiar NRI and IDI evaluation. While the statistical properties of the estimators for NRI and IDI have been well studied in the nested setting, one cannot always rely on these asymptotic results to implement the inference procedure for practical data, especially for testing the null hypothesis of no improvement, and these properties have not been established for the non-nested setting. We propose a generic bootstrap re-sampling procedure for the construction of confidence intervals and hypothesis tests. Extensive simulations and real biomedical data examples illustrate the applicability of the proposed inference methods for both nested and non-nested models.