Bias correction of two-state latent Markov process parameter estimates under misclassification.

Area of Science:

• Statistics
• Stochastic Processes
• Biostatistics

Background:

• Discretely observed processes can misclassify states of continuous-time Markov processes.
• Accurate estimation of transition probabilities is crucial for understanding underlying dynamics.
• Maximum likelihood estimators are often intractable in the presence of misclassification.

Purpose of the Study:

• To investigate the impact of known misclassification probabilities on transition probability estimates.
• To develop bias-adjusted estimation methods for continuous-time, two-state Markov processes.
• To provide practical approaches for both large and finite sample sizes.

Main Methods:

• Quantification of asymptotic bias for large samples.
• Iterative construction of estimators using transition counts and misclassification probabilities.
• Approximation using partial derivatives for finite samples.

Main Results:

• Bias-adjusted estimators are proposed for scenarios with known misclassification.
• First-order bias-adjusted estimators are effective when misclassification probabilities are small.
• Simulation studies demonstrate the influence of misclassification on estimation accuracy.

Conclusions:

• Bias-adjusted estimation provides a viable solution for misclassified Markov process data.
• The proposed methods are applicable to real-world data, such as repeated diagnostic testing.
• Accurate state classification is essential for reliable process modeling.