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

Abstract

A discretely observed two-state process may misclassify the state of an unobservable continuous-time, two-state Markov process. We examine the behaviour of maximum likelihood transition probability estimates as functions of known misclassification probabilities. Since maximum likelihood estimators are not available in closed form, we provide two alternatives for bias-adjusted estimation. In the case of large samples, the asymptotic bias is quantified and estimators are constructed iteratively using transition counts and specified misclassification probabilities. For finite samples, we provide an approximation based on partial derivatives. Estimators that are bias-adjusted to a first approximation are easily constructed and may serve well when misclassification probabilities are known to be small. Simulation studies reveal the effect of misclassification on estimation. Repeated diagnostic testing data illustrate the approaches.