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Nonparametric estimation of a state entry time distribution conditional on a "past" state occupation in a progressive multistate model with current status data

Samuel Anyaso-Samuel, Somnath Datta

Abstract

Case-I interval-censored (current status) data from multistate systems are often encountered in biomedical and epidemiological studies. In this article, we focus on the problem of estimating state entry distribution and occupation probabilities, contingent on a preceding state occupation. This endeavor is particularly complex owing to the inherent challenge of the unavailability of directly observed counts of individuals at risk of transitioning from a state, due to severe interval censoring. We propose two nonparametric approaches, one using the fractional at-risk set approach recently adopted in the right-censoring framework and the other a new estimator based on the ratio of marginal state occupation probabilities. Both estimation approaches utilize innovative applications of concepts from the competing risks paradigm. The finite-sample behavior of the proposed estimators is studied via extensive simulation studies where we show that the estimators based on severely censored current status data have good performance when compared with those based on complete data. We demonstrate the application of the two methods to analyze data from patients diagnosed with breast cancer.

Nonparametric estimation of a state entry time distribution conditional on a "past" state occupation in a progressive multistate model with current status data

Abstract

Case-I interval-censored (current status) data from multistate systems are often encountered in biomedical and epidemiological studies. In this article, we focus on the problem of estimating state entry distribution and occupation probabilities, contingent on a preceding state occupation. This endeavor is particularly complex owing to the inherent challenge of the unavailability of directly observed counts of individuals at risk of transitioning from a state, due to severe interval censoring. We propose two nonparametric approaches, one using the fractional at-risk set approach recently adopted in the right-censoring framework and the other a new estimator based on the ratio of marginal state occupation probabilities. Both estimation approaches utilize innovative applications of concepts from the competing risks paradigm. The finite-sample behavior of the proposed estimators is studied via extensive simulation studies where we show that the estimators based on severely censored current status data have good performance when compared with those based on complete data. We demonstrate the application of the two methods to analyze data from patients diagnosed with breast cancer.
Paper Structure (22 sections, 32 equations, 4 figures, 5 tables)

This paper contains 22 sections, 32 equations, 4 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Study Design: Single-Inspection Multistate Sampling
  3. What is observed under multistate current status?
  4. How common is the design in practice?
  5. Notation and Convention
  6. Estimators based on fractional at-risk sets
  7. An illustration using a five-state model
  8. Extension to general multistate model with a tree structure
  9. Product limit estimators
  10. A toy example
  11. Bootstrap-based Confidence Intervals
  12. Testing of covariate effects via pseudo-value regression
  13. Simulation studies
  14. Five-State Illness-Death Model
  15. Seven-State Multistate Model
  16. ...and 7 more sections

Figures (4)

  • Figure 1: A five-state illness-death model.
  • Figure 2: A seven-state multistate system.
  • Figure 3: Estimated probability curves for $\Psi_{5|1}(t)$ using the two proposed methods, along with 95% pointwise bootstrap confidence intervals, based on simulated data from a seven-state model. For $N=1000$ individuals, true transition times were generated from a lognormal distribution, while inspection times followed a uniform distribution.
  • Figure 4: Multistate system for the breast cancer study from EORTC-trial 10854.