Variational Approximation Approaches for Efficient Clinical Predictions

动机：高维数据现在在许多医疗环境中被常规收集。由于在单个患者上测量的不同变量的数量（例如遗传或代谢组学研究）或重复测量变量的次数（例如纵向研究），数据可能是高维的。此外，研究中有可用数据的个人数量正在增加（例如通过提供生物库）。可以使用这些数据的一种方式是筛选或监测患者，以确定他们患上疾病或需要干预的风险，或将患者分为不同的风险组。近年来，已经开发了多个纵向（主要是连续的）和时间到事件数据的联合模型，这些模型使用混合模型。关节模型软件包的成功证明了这些方法的流行，这些方法提供了对患者经历事件风险的个性化预测。然而，当前模型的一个关键限制是拟合这些模型所需的计算负担。如果有大量患者（数千而不是几百），每个患者多次重复观察，或考虑多种临床生物标志物，则会发生这种负担。这些因素限制了联合建模方法的采用，通常小样本量和只有几个（2-4）纵向生物标志物。在机器学习文献中，变分逼近方法已被证明可以在各种设置中快速准确地估计模型参数。最近的统计工作已经将这些方法引入单变量广义线性混合模型和一些遗传环境中，我的建议是导出一种均值场变分贝叶斯（MFVB）方法来估计不同类型（连续，计数，二进制等）的多个纵向生物标志物的联合模型。和事件发生时间数据。该方法的基本思想是避免从完整的似然函数估计模型参数，而是将似然函数拆分为更易于处理的函数的乘积，然后可以更容易地估计。基本原理是，通过牺牲一点模型精度，我们获得了在合理的时间段内（秒/分钟而不是小时/天）拟合多变量联合模型的能力。在合理的时间范围内拟合这些模型是可行的，将允许实时执行个性化的风险预测和诊断，并为分层医疗和智能医疗系统做出重大贡献。临床应用：开发的模型将用于评估协变量的影响，以及至少10种标记物之间随时间的相关性，所述标记物已知与患者发展成威胁视力的糖尿病视网膜病变（STDR）有关。考虑到ISDR数据集包含超过20，000名患者，即使拟合单变量混合模型来评估随时间的演变，使用当前方法也是计算密集型的。拟合一个模型来评估所有这些标志物之间随时间的相关性是不可行的。我的方法将导致更好地理解各种临床标志物之间的复杂关系及其随时间的变化。我将推导出STDR的个性化风险预测模型，该模型将增加对风险因素的理解，并将在临床相关时间范围内提供患者特定的STDR风险评估。一些在单变量分析中表现出显著相关性的标志物在考虑多个标志物时可能不再显著。这些模型将使我们能够告知临床医生影响疾病发生风险的最关键标志物，并确定计划患者下次就诊的最佳时间。

Motivation: High-dimensional data is now routinely collected in many medical settings. The data may be high-dimensional due to the number of different variables being measured on a single patient (e.g. genetic or metabolomics studies) or the number of times a variable is repeatedly measured (e.g. longitudinal studies). In addition the number of individuals with available data in a study is now increasing (through the availability of Biobanks for example).One way in which this data can be used is in screening or monitoring patients to determine their risk of developing a disease or requiring an intervention, or to classify patients into various risk groups.Objective: In recent years joint models for multiple longitudinal (mainly continuous) and time-to-event data have been developed, which make use of mixed models. The popularity of these methods is evidenced by the success of software packages for joint models.These methods provide personalised predictions of a patient's risk of experiencing an event. However, a key limitation of current models is the computational burden required to fit such models. This burden occurs if there is a high number of patients (many thousands instead of a few hundred), many repeated observations per patient, or multiple clinical biomarkers under consideration. These factors have limited the uptake of joint-modelling methodology to generally small sample sizes and only a few (2-4) longitudinal biomarkers.In the machine learning literature variational approximation methods have been shown to give fast and accurate estimates of model parameters in a variety of settings. Recent statistical work has introduced these methods in univariate generalised linear mixed models, and in some genetic settings.My proposal is to derive a mean-field variational Bayes (MFVB) approach to estimating joint models for multiple longitudinal biomarkers of different type (continuous, counts, binary, etc.) and time-to-event data. The basic idea of the approach is to avoid estimating the model parameters from the full likelihood function but instead, split the likelihood function into a product of more tractable functions, which can then be more easily estimated. The rationale is that by sacrificing a little in terms of model accuracy, we gain the ability to fit multivariate joint model within a reasonable period of time (seconds/minutes instead of hours/days). Making it practicable to fit such models in a reasonable time frame, will allow personalised risk-prediction and diagnostics to be performed in real-time and make a substantial contribution towards stratified medical treatment and intelligent medical systems.Clinical Applications: The models developed will be used to assess the influence of covariates, and the correlation between at least 10 markers over time that have known links to a patient developing sight threatening diabetic retinopathy (STDR). Considering that the ISDR dataset contains over 20,000 patients, even fitting a univariate mixed model to assess the evolution over time is computationally intensive with current methods. Fitting a model to assess the correlation over time between all of these markers would be infeasible. My approach will lead to an improved understanding of the complex relationship between various clinical markers and their changes over time. I will derive personalised risk prediction models for STDR, which will provide increased understanding of risk factors and will provide patient specific assessment of their risk of STDR within clinically relevant timeframes. Some markers that appear to have a significant association in univariate analysis may be found to be no longer significant when multiple markers are considered. The models will allow us to inform clinicians as to the most crucial markers influencing risk of developing a disease and also to determine the best time to plan the patient's next visit.