Intermittent Missing Observations in Discrete-Time Hidden Markov Models
Hung‐Wen Yeh, Wenyaw Chan, Elaine Symanski · Communications in Statistics - Simulation and Computation · 2011
In medical and public health research, hidden Markov models (HMM) are applied in longitudinal studies to model the progression of disease based on clinical classifications that may not be accurate. While missing data are common in longitudinal studies, their impact on HMM has not been well studied. We conduct a simulation study to evaluate effects on the parameter estimates of HMM by simulating complete data, along with incomplete data with intermittent missing values generated by ignorable and non ignorable missing mechanisms. Three scenarios with different sets of parameters were simulated. For incomplete data due to an ignorable mechanism, the accuracy and precision of parameter estimates are generally similar to those obtained from complete data in all examined parameter sets. Under the non ignorable mechanism, the estimation bias is substantial for most parameters when the latent outcome is equally likely to stay at the current state or to move to other states. The bias is dramatically smaller when subjects are more likely to stay at the current state than moving to other states. An example from the mental health arena is used to illustrate the application of intermittent missing observations using HMM. Some computational issues are also discussed.