Clinical data informs the personalization of health care with a potential for
more effective disease management. In practice, this is achieved by
subgrouping, whereby clusters with similar patient characteristics are
identified and then receive customized treatment plans with the goal of
targeting subgroup-specific disease dynamics. In this paper, we propose a novel
mixture hidden Markov model for subgrouping patient trajectories from chronic
diseases. Our model is probabilistic and carefully designed to capture
different trajectory phases of chronic diseases (i.e., "severe", "moderate",
and "mild") through tailored latent states. We demonstrate our subgrouping
framework based on a longitudinal study across 847 patients with non-specific
low back pain. Here, our subgrouping framework identifies 8 subgroups. Further,
we show that our subgrouping framework outperforms common baselines in terms of
cluster validity indices. Finally, we discuss the applicability of the model to
other chronic and long-lasting diseases.

通过混合隐马尔可夫模型对长期疾病患者轨迹进行亚群分组，从而实现个性化医疗，该模型在研究中表现出较常见基准的优势

慢性病患者轨迹的数据驱动分组：以腰痛为例的证据

Data-driven subgrouping of patient trajectories with chronic diseases:  Evidence from low back pain

Selecting the number of clusters is one of the key processes when applying
clustering algorithms. To fulfill this task, various cluster validity indices
(CVIs) have been introduced. Most of the cluster validity indices are defined
to detect the optimal number of clusters hidden in a dataset. However, users
sometimes do not expect to get the optimal number of groups but a secondary one
which is more reasonable for their applications. This has motivated us to
introduce a Bayesian cluster validity index (BCVI) based on existing underlying
indices. This index is defined based on either Dirichlet or Generalized
Dirichlet priors which result in the same posterior distribution. Our BCVI is
then tested based on the Wiroonsri index (WI), and the Wiroonsri-Preedasawakul
index (WP) as underlying indices for hard and soft clustering, respectively. We
compare their outcomes with the original underlying indices, as well as a few
more existing CVIs including Davies and Bouldin (DB), Starczewski (STR), Xie
and Beni (XB), and KWON2 indices. Our proposed BCVI clearly benefits the use of
CVIs when experiences matter where users can specify their expected range of
the final number of clusters. This aspect is emphasized by our experiment
classified into three different cases. Finally, we present some applications to
real-world datasets including MRI brain tumor images. Our tools will be added
to a new version of the recently developed R package ``UniversalCVI''.

通过引入贝叶斯聚类验证指数（BCVI），本研究基于现有的基础指数，构建了一个可根据使用者应用的可行性，选择次优聚类数量的方法，并通过对真实世界数据集（包括 MRI 脑肿瘤图像）的应用验证了算法的有效性和应用潜力。