Lifespan AI - Project M1: Normalizing Flows for Lifespan Health Data

健康科学使用统计模型来量化健康状况和结果，因为它随着时间的推移而演变，并受到风险因素和/或治疗的影响。因此，不确定性的量化是统计学在方法上的一个重要贡献。由于趋势和不确定性最好用分布来描述，因此考虑中的所有时间点的所有变量和特征的联合分布模型提供了最完整的统计图像。这种方法允许--至少在形式上允许--统计学在没有不可检验的假设的情况下提供所有的结论。这种方法并不简单，当数据是高维数据时需要机器学习方法。在寿命数据方面出现了进一步的挑战，其中数据具有不同的尺度，在个别特定时间点进行测量，来自不同的数据来源，只有部分重叠，或来自变量集随时间变化的研究队列。在这个项目中，我们通过开发利用可逆残差神经网络的规范化流来解决这些挑战，并使用广义线性混合模型（GLMM）进行基础分布。使用Glucose对健康科学家特别有吸引力，因为它们经常用于应用。基于可逆残差网络的归一化流的主要优点是为联合分布提供了解析表达式，可以很好地用于预期的统计和科学结论。我们的方法的关键思想是开始建模的条件分布的每个变量给定的其他变量的非线性变换的GLSL和联合收割机，他们的全球联合分布的平均随机选择的顺序因式分解，可以通过顺序减少的变量，我们的条件下的条件分布（“反向边际化”）。在推导出一种方法来拟合一个联合模型与完整的观察，我们将开发一个算法来更新模型与不完整的观察和扩展它的额外的变量。然后，将利用联合分布来获得科学上有趣的条件分布的（整体正则化）估计，从中可以导出点和区间预测。我们还将开发方法来解释整体（黑箱）模型，并调查其内部和外部的有效性。虽然联合模型已经考虑了任意的不确定性（通过建模分布），我们将制定方法来考虑认知的不确定性，即量化模型拟合的方法，并考虑预测区间内的模型不确定性。新方法将应用于IDEFICS/I.家庭队列、NAKO健康研究和GePaRD数据的数据和变量，并以这些数据和变量进行说明，这些数据和变量都是由BIPS收集和/或管理的。

Health sciences use statistical models to quantify health status and outcome as it evolves over time and is influenced by risk factors and/or treatments. Hereby the quantification of uncertainty is a crucial methodological contribution of statistics. Since trend and uncertainty are best described in terms of distributions, a model for the joint distribution of all variables and features over all time points under consideration provides the most complete statistical picture. This permits – at least formally – all conclusions statistics can provide without untestable assumptions.Such an approach is not straightforward and requires machine learning methods when the data are high dimensional. Further challenges arise in lifespan data, where the data are of different scales, are measured at individual specific time points and come from different data sources with only partial overlap or from study cohorts whose variable sets change over time. In this project, we tackle these challenges by the development of normalizing flows that utilise invertible residual neural networks and use generalised linear mixed models (GLMM) for the base distributions. The use of GLMMs is particularly attractive for health scientists because they are frequently used in applications. Normalizing flows based on invertible residual networks have the major advantage of providing analytical expressions for the joint distribution that can be well utilised for the anticipated statistical and scientific conclusions. The key idea of our method is to start modelling the conditional distribution of each variable given the other variables by nonlinear transformations of GLMMs and to combine them to an global joint distribution by an average of randomly selected sequential factorisations which can be achieved by sequentially reducing the set of variables we condition on in the conditional distributions (“reverse marginalisations”). After deriving an approach to fit a joint model with complete observations, we will develop an algorithm for updating the model with incomplete observations and extending it by additional variables. The joint distribution will then be utilised to obtain (overall regularised) estimates of scientifically interesting conditional distributions from which point and interval predications can be derived. We will also develop methods to interpret the overall (black box) model and to investigate its internal and external validity. While the joint model already accounts for aleatoric uncertainty (by modelling distributions) we will work out methods to account also for epistemic uncertainty, i.e. approaches for quantifying the model fit and to account for the model uncertainty in prediction intervals. The new methods will be applied to and illustrated with data and variables from the IDEFICS/I.Family cohort, the NAKO Health Study and GePaRD data which are all collected and/or managed by BIPS.