Digital technologies (e.g., mobile phones) can be used to obtain objective, frequent, and real-world digital phenotypes from individuals. However, modeling these data poses substantial challenges since observational data are subject to confounding and various sources of variabilities. For example, signals on patients' underlying health status and treatment effects are mixed with variation due to the living environment and measurement noises. The digital phenotype data thus shows extensive variabilities between- and within-patient as well as across different health domains (e.g., motor, cognitive, and speaking). Motivated by a mobile health study of Parkinson's disease (PD), we develop a mixed-response state-space (MRSS) model to jointly capture multi-dimensional, multi-modal digital phenotypes and their measurement processes by a finite number of latent state time series. These latent states reflect the dynamic health status and personalized time-varying treatment effects and can be used to adjust for informative measurements. For computation, we use the Kalman filter for Gaussian phenotypes and importance sampling with Laplace approximation for non-Gaussian phenotypes. We conduct comprehensive simulation studies and demonstrate the advantage of MRSS in modeling a mobile health study that remotely collects real-time digital phenotypes from PD patients.

翻译：数字技术（如手机）可用于从个体中获取客观、频繁且真实世界的数字表型。然而，对这些数据进行建模面临重大挑战，因为观测数据容易受到混杂因素和多种变异源的影响。例如，反映患者潜在健康状况和治疗效果的信号与生活环境变化和测量噪声混杂在一起。因此，数字表型数据在患者间、患者内部以及不同健康领域（如运动、认知和语言）均表现出广泛的变异性。受一项帕金森病（PD）移动健康研究的启发，我们开发了一种混合响应状态空间（MRSS）模型，通过有限数量的潜在状态时间序列来联合捕捉多维度、多模态的数字表型及其测量过程。这些潜在状态反映了动态的健康状态和个体化的时变治疗效果，并可用于调整信息性测量。在计算方面，我们对高斯表型使用卡尔曼滤波器，对非高斯表型采用拉普拉斯近似结合重要性采样。我们进行了全面的模拟研究，并展示了MRSS在建模一项远程收集PD患者实时数字表型的移动健康研究中的优势。