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. 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. Adding stochasticity to HMMs results in mixed HMMs (MHMMs) which potentially allow for the characterization of variability in unobservable processes. Further, HMMs can be extended to include more than one observation source and are then multivariate HMMs. In this work MHMMs were developed and applied in a chronic obstructive pulmonary disease example. 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). Estimation properties in the software NONMEM of model parameters were investigated with and without random and covariate effect parameters. 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. A bivariate MHMM was developed for simulating and analysing hypothetical COPD data consisting of PRO and FEV1 measurements collected every week for 60 weeks. 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 [RRMSE] > 150%). Parameter precision was better with higher magnitudes of the transition probability parameters. A drug effect was included on the transition rate probability and the precision of the drug effect parameter improved with increasing magnitude of the parameter. The power to detect the drug effect was improved by utilizing a bivariate MHMM model over the univariate MHMM models where the number of subject required for 80% power was 25 with the bivariate MHMM model versus 63 in the univariate MHMM FEV1 model and > 100 in the univariate MHMM PRO model. The results advocates for the use of bivariate MHMM models when implementation is possible.

中文翻译：

---

使用 NOMMEM 中的二元混合隐马尔可夫模型处理基础离散变量。

非线性混合效应模型通常处理观察过程中的随机性，但仅考虑观察过程的模型可能并不最适合所有数据。隐马尔可夫模型 (HMM) 描述了观察变量和隐藏变量之间的关系，其中隐藏变量可以代表潜在的且不可测量的疾病状态。向 HMM 添加随机性会产生混合 HMM (MHMM)，这可能允许表征不可观测过程中的变异性。此外，HMM 可以扩展到包括多个观察源，从而成为多元 HMM。在这项工作中，MHMM 被开发出来并应用于慢性阻塞性肺病的例子。模型中包含的两个隐藏状态是缓解和恶化，并考虑了两个观察来源：患者报告结果 (PRO) 和用力呼气量 (FEV1)。在有或没有随机和协变量效应参数的情况下，研究了模型参数 NONMEM 软件中的估计属性。量化了模型中参数的随机效应和协变量效应对参数的影响，并进行功效分析以比较单个双变量 MHMM 与两个单独的单变量 MHMM 的功效。开发了双变量 MHMM，用于模拟和分析假设的 COPD 数据，其中包括 60 周内每周收集的 PRO 和 FEV1 测量值。除了决定从缓解到恶化的转变的转变率方差（相对均方根误差 [RRMSE] > 150%）之外，所有参数的参数精度都很高。转移概率参数的幅值越高，参数精度越好。药物效应包含在转变率概率中，并且药物效应参数的精度随着参数大小的增加而提高。与单变量 MHMM 模型相比，使用双变量 MHMM 模型提高了检测药物效果的功效，其中双变量 MHMM 模型达到 80% 功效所需的受试者数量为 25 人，而单变量 MHMM FEV1 模型为 63 人，而单变量 MHMM FEV1 模型为 > 100 人。单变量 MHMM PRO 模型。结果提倡在可行的情况下使用双变量 MHMM 模型。