Medical imaging data have been widely used in modern health care, particularly in the prognosis, screening, diagnosis, and treatment of various diseases. In this study, we consider a latent factor‐on‐image (LoI) regression model that regresses a latent factor on ultrahigh dimensional imaging covariates. The latent factor is characterized by multiple manifest variables through a factor analysis model, while the manifest variables are subject to nonignorable missingness. We propose a two‐stage approach for statistical inference. At the first stage, an efficient functional principal component analysis method is applied to reduce the dimension and extract useful features/eigenimages. At the second stage, a factor analysis mode is proposed to characterize the latent response variable. Moreover, an LoI model is used to detect influential risk factors, and an exponential tiling model applied to accommodate nonignoreable nonresponses. A fully Bayesian method with an adjust spike‐and‐slab absolute shrinkage and selection operator (lasso) procedure is developed for the estimation and selection of influential features/eigenimages. Simulation studies show the proposed method exhibits satisfactory performance. The proposed methodology is applied to a study on the Alzheimer's Disease Neuroimaging Initiative data set.

中文翻译：

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具有不可忽略缺失数据的图像回归的贝叶斯潜在因子

医学成像数据已广泛用于现代医疗保健中，尤其是在各种疾病的预后，筛查，诊断和治疗中。在这项研究中，我们考虑了潜在的图像潜能因素（LoI）回归模型，该模型可以回归超高维成像协变量的潜在潜能。通过因子分析模型，潜在因子的特征是多个清单变量，而清单变量易失。我们提出了一种统计推断的两阶段方法。在第一阶段，一种有效的功能主成分分析方法被应用于减小尺寸并提取有用的特征/特征图像。在第二阶段，提出了一种因子分析模式来表征潜在响应变量。此外，LoI模型用于检测有影响力的风险因素，并采用指数化切片模型来适应不可忽略的无响应。为估计和选择有影响的特征/特征图像，开发了一种具有调整后的尖峰和台阶绝对收缩和选择算子（套索）程序的完全贝叶斯方法。仿真研究表明，该方法具有令人满意的性能。拟议的方法应用于阿尔茨海默氏病神经影像学倡议数据集的研究。