Uncovering the heterogeneity in the disease progression of Alzheimer's is a key factor to disease understanding and treatment development, so that interventions can be tailored to target the subgroups that will benefit most from the treatment, which is an important goal of precision medicine. However, in practice, one top methodological challenge hindering the heterogeneity investigation is that the true subgroup membership of each individual is often unknown. In this paper, we aim to identify latent subgroups of individuals who share a common disorder progress over time, to predict latent subgroup memberships, and to estimate and infer the heterogeneous trajectories among the subgroups. To achieve these goals, we propose a nonparametric fusion learning method that can automatically identify subgroups and recover the heterogeneous trajectories, which are represented by subject-specific unknown functions. We approximate the unknown functions by B-splines, and apply a concave fusion penalization method that can merge the estimated functions together for the subjects belonging to the same subgroup. The resulting estimator of the disease trajectory of each subgroup is supported by an asymptotic distribution. It provides a sound theoretical basis for further conducting statistical inference in subgroup analysis. Our method is applied to a longitudinal Alzheimer's Disease data set.
翻译:阿尔茨海默氏病发作过程中的疾病变异性没有覆盖阿尔茨海默氏病变异性,这是疾病理解和治疗发展的一个关键因素,因此干预措施可以针对最能从治疗中受益的分组进行量身定做,这是精确医学的一个重要目标。然而,在实践中,阻碍异质性调查的最主要方法挑战是,每个人的真正分组成员身份往往不为人所知。在本文件中,我们的目标是确定个人的潜在分组,这些分组在一段时间内具有共同的紊乱进展,预测潜在的分组成员身份,估计和推断各分组的不同轨迹。为了实现这些目标,我们建议采用非对准聚变异性学习方法,可以自动识别分组,并恢复由特定主题未知功能代表的异异异性轨迹。我们比较了B-splines的未知功能,并应用了连接聚变法惩罚方法,可以将同一分组的主体的估计函数合并在一起。每个分组的疾病轨迹估计结果得到一个随机分布的支持。为了实现这些目标,我们建议采用一种非对准的聚合学习方法,可以自动识别分解,并恢复由不同对象组成的不同轨迹。我们用于进一步进行统计分析的理论基础。