Parameter precision was better with higher magnitudes of the transition probability parameters. Parameter precision was high for all parameters with the exception of the variance of the transition rate dictating the transition from remission to exacerbation (relative root mean squared error > 150%).
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A bivariate MHMM was developed for simulating and analysing hypothetical COPD data consisting of PRO and FEV1 measurements collected every week for 60 weeks.
![$ estimate nonmem important sampling $ estimate nonmem important sampling](https://s3.studylib.net/store/data/025271356_1-04971b1d8d03579fe6c196d2cafe46a9.png)
The influence of including random and covariate effects of varying magnitudes on the parameters in the model was quantified and a power analysis was performed to compare the power of a single bivariate MHMM with two separate univariate MHMMs. Estimation properties in the software NONMEM of model parameters were investigated with and without random and covariate effect parameters. The two hidden states included in the model were remission and exacerbation and two observation sources were considered, patient reported outcomes (PROs) and forced expiratory volume (FEV1). In this work MHMMs were developed and applied in a chronic obstructive pulmonary disease example.
![$ estimate nonmem important sampling $ estimate nonmem important sampling](https://i0.wp.com/www.theurbanist.org/wp-content/uploads/2015/12/appraised-land-values.png)
Further, HMMs can be extended to include more than one observation source and are then multivariate HMMs.
![$ estimate nonmem important sampling $ estimate nonmem important sampling](https://media.springernature.com/full/springer-static/image/art%3A10.1038%2Fs42256-021-00357-4/MediaObjects/42256_2021_357_Fig1_HTML.png)
Adding stochasticity to HMMs results in mixed HMMs (MHMMs) which potentially allow for the characterization of variability in unobservable processes. Hidden Markov models (HMMs) characterize the relationship between observed and hidden variables where the hidden variables can represent an underlying and unmeasurable disease status for example. Non-linear mixed effects models typically deal with stochasticity in observed processes but models accounting for only observed processes may not be the most appropriate for all data.