Comparison of variance estimation approaches in a two‐state Markov model for longitudinal data with misclassification

We examine the behaviour of the variance-covariance parameter estimates in an alternating binary Markov model with misclassification. Transition probabilities specify the state transitions for a process that is not directly observable. The state of an observable process, which may not correctly classify the state of the unobservable process, is obtained at discrete time points. Misclassification probabilities capture the two types of classification errors. Variance components of the estimated transition parameters are calculated with three estimation procedures: observed information, jackknife, and bootstrap techniques. Simulation studies are used to compare variance estimates and reveal the effect of misclassification on transition parameter estimation. The three approaches generally provide similar variance estimates for large samples and moderate misclassification. In these situations, the resampling methods are reasonable alternatives when programming partial derivatives is not appealing. With smaller chains or higher misclassification probabilities, the bootstrap method appears to be the best choice.

[1]  N. Nagelkerke,et al.  Estimation of parasitic infection dynamics when detectability is imperfect. , 1990, Statistics in medicine.

[2]  B. Efron.  Nonparametric estimates of standard error: The jackknife, the bootstrap and other methods , 1981 .

[3]  J. Kalbfleisch,et al.  The Analysis of Panel Data under a Markov Assumption , 1985 .

[4]  Alexandre Bureau,et al.  Applications of continuous time hidden Markov models to the study of misclassified disease outcomes , 2003, Statistics in medicine.

[5]  B. Efron,et al.  Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information , 1978 .

[6]  Glen A. Satten,et al.  Markov Chains with Measurement Error: Estimating the ‘True’ Course of a Marker of the Progression of Human Immunodeficiency Virus Disease , 1996 .

[7]  L. Baum,et al.  Statistical Inference for Probabilistic Functions of Finite State Markov Chains , 1966 .

[8]  R J Cook,et al.  Estimation of Operating Characteristics for Dependent Diagnostic Tests Based on Latent Markov Models , 2000, Biometrics.

[9]  James P. Hughes,et al.  Computing the observed information in the hidden Markov model using the EM algorithm , 1997 .

[10]  P C Molenaar,et al.  Confidence intervals for hidden Markov model parameters. , 2000, The British journal of mathematical and statistical psychology.

[11]  B. Leroux.  Maximum-likelihood estimation for hidden Markov models , 1992 .

[12]  B. Efron.  Bootstrap Methods: Another Look at the Jackknife , 1979 .

[13]  Lain L. MacDonald,et al.  Hidden Markov and Other Models for Discrete- valued Time Series , 1997 .

[14]  Robert Tibshirani,et al.  Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy , 1986 .

[15]  J. Kingman.  The imbedding problem for finite Markov chains , 1962 .

[16]  Peter J. Bickel,et al.  Inference in hidden Markov models I: Local asymptotic normality in the stationary case , 1996 .

[17]  J. Booth,et al.  Monte Carlo Approximation of Bootstrap Variances , 1998 .

[18]  T. Rydén.  Consistent and Asymptotically Normal Parameter Estimates for Hidden Markov Models , 1994 .

[19]  Rhonda J Rosychuk,et al.  Bias correction of two‐state latent Markov process parameter estimates under misclassification , 2003, Statistics in medicine.