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NONPARAMETRIC INFERENCE FOR MARKOV PROCESSES WITH MISSING ABSORBING STATE.

Giorgos Bakoyannis1, Ying Zhang1, Constantin T Yiannoutsos1

  • 1Indiana University.

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|September 14, 2019
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Summary
This summary is machine-generated.

This study introduces a new nonparametric maximum pseudolikelihood estimator (NPMPLE) for estimating transition probabilities in partially observed Markov processes. The method is efficient, robust, and performs well even with small sample sizes.

Keywords:
Aalen-Johansen estimatorCompeting risksCumulative incidence functionDouble-samplingFinite state spaceMissing cause of failurePseudolikelihood

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Area of Science:

  • Statistics
  • Biostatistics
  • Epidemiology

Background:

  • Estimating transition probabilities in non-homogeneous Markov processes with partially observed absorbing states is challenging.
  • Existing methods may lack efficiency or robustness when dealing with missing data.

Purpose of the Study:

  • To develop a computationally efficient nonparametric maximum pseudolikelihood estimator (NPMPLE) for transition probability matrices.
  • To address the issue of partially observed absorbing states under a missing at random assumption.
  • To provide a formal goodness-of-fit test for the parametric model used for missing observations.

Main Methods:

  • Proposed a nonparametric maximum pseudolikelihood estimator (NPMPLE).
  • Utilized a parametric model for estimating probabilities of absorbing states for missing observations.
  • Employed modern empirical process theory for theoretical analysis and developed a residual process for goodness-of-fit testing.

Main Results:

  • The NPMPLE is shown to be uniformly consistent and converges weakly to a Gaussian random field.
  • Methodology for simultaneous confidence band construction is provided.
  • Simulation studies indicate good performance with small sample sizes and robustness to model misspecification.

Conclusions:

  • The proposed NPMPLE offers an efficient and robust approach for estimating transition probabilities in complex Markov processes.
  • The method is validated through simulations and demonstrated on HIV data for estimating mortality and disengagement probabilities.