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Semiparametric Analysis of Interval-Censored Data Subject to Inaccurate Diagnoses with A Terminal Event

Yuhao Deng, Donglin Zeng, Yuanjia Wang

TL;DR

This work tackles interval-censored survival data subject to misdiagnosis and possible terminal events by extending the Cox model with a semiparametric, NPMLE framework that incorporates diagnosis sensitivity $p$ and specificity $q$ and a shared random effect $b_i$. By recasting the likelihood as a mixture over diagnosis-intervals and employing an EM algorithm with latent Poisson variables, the authors achieve computationally feasible estimation and prove asymptotic efficiency for the parametric components. The approach is extended to include postmortem pathological diagnoses, and it provides population-level and individual dynamic predictions for disease incidence and survival. In an Alzheimer’s disease application to the ADNI data, the method reveals that amyloid-beta is negatively associated with AD while Tau is positively associated with both AD and mortality, with a strong shared risk between disease and death reflected in the random effect variance. Overall, the methodology offers robust, misdiagnosis-aware inference for interval-censored, semi-competing risk settings with practical implications for dynamic risk prediction in aging-related diseases.

Abstract

Interval-censoring frequently occurs in studies of chronic diseases where disease status is inferred from intermittently collected biomarkers. Although many methods have been developed to analyze such data, they typically assume perfect disease diagnosis, which often does not hold in practice due to the inherent imperfect clinical diagnosis of cognitive functions or measurement errors of biomarkers such as cerebrospinal fluid. In this work, we introduce a semiparametric modeling framework using the Cox proportional hazards model to address interval-censored data in the presence of inaccurate disease diagnosis. Our model incorporates sensitivity and specificity of the diagnosis to account for uncertainty in whether the interval truly contains the disease onset. Furthermore, the framework accommodates scenarios involving a terminal event and when diagnosis is accurate, such as through postmortem analysis. We propose a nonparametric maximum likelihood estimation method for inference and develop an efficient EM algorithm to ensure computational feasibility. The regression coefficient estimators are shown to be asymptotically normal, achieving semiparametric efficiency bounds. We further validate our approach through extensive simulation studies and an application assessing Alzheimer's disease (AD) risk. We find that amyloid-beta is significantly associated with AD, but Tau is predictive of both AD and mortality.

Semiparametric Analysis of Interval-Censored Data Subject to Inaccurate Diagnoses with A Terminal Event

TL;DR

This work tackles interval-censored survival data subject to misdiagnosis and possible terminal events by extending the Cox model with a semiparametric, NPMLE framework that incorporates diagnosis sensitivity and specificity and a shared random effect . By recasting the likelihood as a mixture over diagnosis-intervals and employing an EM algorithm with latent Poisson variables, the authors achieve computationally feasible estimation and prove asymptotic efficiency for the parametric components. The approach is extended to include postmortem pathological diagnoses, and it provides population-level and individual dynamic predictions for disease incidence and survival. In an Alzheimer’s disease application to the ADNI data, the method reveals that amyloid-beta is negatively associated with AD while Tau is positively associated with both AD and mortality, with a strong shared risk between disease and death reflected in the random effect variance. Overall, the methodology offers robust, misdiagnosis-aware inference for interval-censored, semi-competing risk settings with practical implications for dynamic risk prediction in aging-related diseases.

Abstract

Interval-censoring frequently occurs in studies of chronic diseases where disease status is inferred from intermittently collected biomarkers. Although many methods have been developed to analyze such data, they typically assume perfect disease diagnosis, which often does not hold in practice due to the inherent imperfect clinical diagnosis of cognitive functions or measurement errors of biomarkers such as cerebrospinal fluid. In this work, we introduce a semiparametric modeling framework using the Cox proportional hazards model to address interval-censored data in the presence of inaccurate disease diagnosis. Our model incorporates sensitivity and specificity of the diagnosis to account for uncertainty in whether the interval truly contains the disease onset. Furthermore, the framework accommodates scenarios involving a terminal event and when diagnosis is accurate, such as through postmortem analysis. We propose a nonparametric maximum likelihood estimation method for inference and develop an efficient EM algorithm to ensure computational feasibility. The regression coefficient estimators are shown to be asymptotically normal, achieving semiparametric efficiency bounds. We further validate our approach through extensive simulation studies and an application assessing Alzheimer's disease (AD) risk. We find that amyloid-beta is significantly associated with AD, but Tau is predictive of both AD and mortality.
Paper Structure (12 sections, 3 theorems, 23 equations, 3 figures, 2 tables)

This paper contains 12 sections, 3 theorems, 23 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Motivating Application
  3. Method
  4. Models and data likelihood
  5. Nonparametric maximum likelihood estimation and EM algorithm
  6. Extension to incorporate accurate pathological diagnoses
  7. Model prediction
  8. Asymptotic Theory
  9. Simulation Studies
  10. Application to The ADNI Data
  11. Discussion
  12. Significance Statement

Key Result

Lemma 1

Under Conditions 1--5, if the density function of the observed data $p(\bm{\theta}_*,\mathcal{A}_*) = p(\bm{\theta}_0,\mathcal{A}_0)$ for some parameters $(\bm{\theta}_*,\mathcal{A}_*)$ with probability 1, then $\bm{\theta}_*=\bm{\theta}_0$ and $\mathcal{A}_*=\mathcal{A}_0$ in $[0,\tau]\times\mathca

Figures (3)

  • Figure 1: The average estimated cumulative baseline hazards with $p=0.9$, $q=0.6$, $r=0.5$ and $n=500$. The true values are plotted in solid lines. The average estimated curves are plotted in dotted/dashed lines.
  • Figure 2: Estimated cumulative incidence function of Alzheimer's disease (AD) and death. Upper: estimated curves using different methods. Lower: estimated curves categorized by sex using the proposed method (47.4% of the sample were female, and 52.6% were male).
  • Figure 3: Estimated survival probability (in solid lines) and disease-free survival probability (in dashed lines) for an individual (ID=41) since the last visit.

Theorems & Definitions (3)

  • Lemma 1
  • Theorem 2
  • Theorem 3