Pattern discovery of health curves using an ordered probit model with Bayesian smoothing and functional principal component analysis.

This article is motivated by the need for discovering patterns of patients' health based on their daily settings of care to aid the health policy-makers to improve the effectiveness of distributing funding for health services. The hidden process of one's health status is assumed to be a continuous smooth function, called the health curve, ranging from perfectly healthy to dead. The health curves are linked to the categorical setting of care using an ordered probit model and are inferred through Bayesian smoothing. The challenges include the nontrivial constraints on the lower bound of the health status (death) and on the model parameters to ensure model identifiability. We use the Markov chain Monte Carlo method to estimate the parameters and health curves. The functional principal component analysis is applied to the patients' estimated health curves to discover common health patterns. The proposed method is demonstrated through an application to patients hospitalized from strokes in Ontario. Whilst this paper focuses on the method's application to a health care problem, the proposed model and its implementation have the potential to be applied to many application domains in which the response variable is ordinal and there is a hidden process. Our implementation is available at https://github.com/liangliangwangsfu/healthCurveCode.