A joint model for multistate disease processes and random informative observation times, with applications to electronic medical records data

Abstract

Multistate models are used to characterize individuals' natural histories through diseases with discrete states. Observational data resources based on electronic medical records pose new opportunities for studying such diseases. However, these data consist of observations of the process at discrete sampling times, which may either be pre-scheduled and non-informative, or symptom-driven and informative about an individual's underlying disease status. We have developed a novel joint observation and disease transition model for this setting. The disease process is modeled according to a latent continuous-time Markov chain; and the observation process, according to a Markov-modulated Poisson process with observation rates that depend on the individual's underlying disease status. The disease process is observed at a combination of informative and non-informative sampling times, with possible misclassification error. We demonstrate that the model is computationally tractable and devise an expectation-maximization algorithm for parameter estimation. Using simulated data, we show how estimates from our joint observation and disease transition model lead to less biased and more precise estimates of the disease rate parameters. We apply the model to a study of secondary breast cancer events, utilizing mammography and biopsy records from a sample of women with a history of primary breast cancer.

Keywords: Disease process; Electronic medical records; Informative observations; Markov-modulated Poisson process; Multistate model; Panel data.

Figure 1

A. Example of a joint informative observation and disease process, Y (t) = (X (t), N(t)). B. The informative observation time process and the disease process observed at DDO and scheduled times. C. Same as B, with misclassification error.

Figure 2

Simulation results demonstrating bias that occurs when informative visit times are ignored. Data were simulated from discretely observed 2-state standard and latent CTMC multistate-DDO models on the interval t=[0,8] at DDO times or a combination of DDO and scheduled visits (See Web Appendix Figure D-1 and Table D-1 for simulation details). Data were fit with correctly specified multistate-DDO models and incorrectly specified panel models. Box plots/functional box plots are shown for hazard estimates of H →D and D →H transitions from both DDO and panel models. The different DDO rates in the model states varied across simulations, with more discrepant rates inducing more bias under model misspecification. A. DDO rates are q_D = 2, q_H = .25; data also included fixed observation times t = (0, 2, 4, 6, 8). B. DDO rates are q_D = 2, q_H = .25. C. DDO rates are q_D = .35, q_H = .25. D. DDO rates are q_H = .25 and q_D = 2.

Figure 3

SBCE competing risks disease models. A. Standard CTMC, where H=healthy, C=contralateral SBCE, I=ipsilateral SBCE, and D=death before SBCE. B. Latent CTMC with Coxian structure. States H₁ and H₂ map to the healthy state.

Figure 4

Estimated cumulative incidence for ipsilateral and contralateral SBCEs and death, via empirical estimates of the diagnosis times or using the BIC-selected multistate-DDO model (Web Appendix Table E-2, model 6). The bands are point-wise standard errors. Abbreviations: Dx empirical=empirical estimate of cumulative incidence of diagnosed SBCE events; SE=standard error.