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Beyond time-homogeneity for continuous-time multistate Markov models.

Emmett B Kendall1, Jonathan P Williams1,2, Gudmund H Hermansen2,3,4

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Summary
This summary is machine-generated.

Continuous-time Markov models can be biased if assumed time-homogeneous. This study presents a method for time-inhomogeneous models, improving parameter estimation accuracy for complex data like medical records.

Keywords:
Aalen-Johansen estimatorHidden Markov modelHierarchical Bayesian modelingLongitudinal studyState space model

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Area of Science:

  • Statistics
  • Biostatistics
  • Computational Biology

Background:

  • Multistate Markov models are standard for stochastic processes.
  • Continuous-time Markov processes model irregularly observed data, common in longitudinal studies.
  • Time-homogeneous models have analytical solutions, but time-inhomogeneous models do not.

Purpose of the Study:

  • To illustrate biases in parameter estimation when assuming piecewise time-homogeneity.
  • To propose a method for likelihood computation in truly time-inhomogeneous Markov models.
  • To address state label misclassifications within multistate Markov models.

Main Methods:

  • Derivation of likelihood functions from Kolmogorov forward equations.
  • Utilizing matrix-exponential solutions for time-homogeneous processes.
  • Advocating for Bayesian computation to avoid numerical gradient approximations for MLEs.

Main Results:

  • Demonstration of potential parameter estimation biases when the piecewise-homogeneous assumption is violated.
  • Development of a framework for time-inhomogeneous likelihood computation.
  • Application to multistate Markov models with state misclassification.

Conclusions:

  • The assumption of piecewise time-homogeneity can lead to significant biases.
  • A time-inhomogeneous approach is necessary for accurate modeling of complex stochastic processes.
  • Bayesian methods offer an efficient alternative for parameter estimation in these models.