Constrained Statistical Inference

在本报告年度，我们一直致力于这个项目中的几个研究问题。以下是一些成就。 越来越多的证据表明，肠道微生物群参与炎症和免疫反应，从而参与人类健康和疾病。因此，生物医学研究人员对研究人类微生物群有相当大的兴趣。由于微生物形成了一个生态系统，因此它们之间存在潜在的相互依赖关系，因此描述它们之间的联系有相当大的兴趣。皮尔逊相关等标准方法是无效的，因为观察到的数据是成分数据，即只能测量给定生态系统中各种微生物的相对丰度，如粪便样本。在这个项目中，开发了一种正式的统计方法来估计相关性。由此产生的方法是使用婴儿肠道微生物组数据进行说明的。婴儿的肠道生态在出生后一年内由于各种因素的变化而不断演变，如喂养、睡眠模式、与人的接触等。使用这一新的方法，我们首次在文献中描述了婴儿出生后一年内不同时间点的肠道微生物区系之间的关系。这篇手稿发表在《自然通讯》(Lin，Eggesbo和Peddada，《自然通讯》，2022)上。 在文献中很好地建立了一对组的微生物组差异丰度分析方法。然而，许多微生物组研究涉及多个组，有时甚至是有序的组，例如疾病的各个阶段，并且需要不同类型的比较。标准的两两比较不仅在功率和错误发现率方面效率低下，而且可能无法解决感兴趣的科学问题。在这个项目中，开发了一个通用框架，用于执行范围广泛的多组分析，并进行协变量调整和重复测量。所得到的方法使用两个真实的数据集进行了说明。第一个例子探讨了干旱对土壤微生物群的影响，第二个例子调查了外科干预对IBD患者微生物群的影响。这份手稿正在审查中。 在许多应用中，研究人员感兴趣的是组成的多变量结果，即观察到的数据之和为一个常数。例如，儿童在24小时内的活动。然而，由于各种原因，包括收集数据的方法，有时并不是所有的变量都被测量，因此我们在多变量组成向量中有遗漏的值。在假设缺失与协变量相关的情况下，本项目发展了一种简单的多重填补方法，称为成分数据多重填补(MICoDa)，用于在成分向量中填补缺失值。MICoDa使用两种非常不同的数据类型来说明，其中缺失值是由于不同的原因而出现的。第一个例子涉及幼儿的24小时体力活动数据，第二个例子涉及肠道微生物组数据。这份手稿正在印刷中，准备作为受邀的书章出版。 通常使用线性回归来执行中介分析。然而，在许多情况下，潜在的关系可能不是线性的，就像胎盘-胎儿激素和胎儿发育的情况一样。此外，这种关系的确切函数形式通常是未知的。基于这些原因，我们开发了一种新的基于形状限制推理的方法来进行中介分析。这项工作是由胎儿内分泌学的应用推动的，研究人员有兴趣了解使用杀虫剂对新生儿体重的影响，并以人绒毛膜促性腺激素(HCG)为中介。我们假设人绒毛膜促性腺激素(HCG)对出生体重的非线性影响实际上是可信的，农药暴露和hCG暴露之间存在线性关系，暴露-结局和暴露-中介模型在混杂因素中都是线性的。以人绒毛膜促性腺激素(HCG)为介体，对人群水平的产前筛查数据进行研究，我们发现，虽然自然直接效应表明农药使用与出生体重呈正相关，但天然间接效应是负相关的。

We have been working on several research problems in this project during this reporting year. Here are some accomplishments. There is growing evidence in the literature demonstrating that the (gut) microbiome is involved in inflammation and immune response, and hence human health and disease. Thus, there is considerable interest among biomedical researchers to study the human microbiome. Since microbes form an ecology, and hence are potentially inter-dependent, there is considerable interest to describe associations among them. Standard methods such as the Pearson correlation is not valid because the observed data are compositional, i.e., one gets to measure only the relative abundances of various microbes in a given ecosystem such as the stool sample. In this project a formal statistical methodology was developed to estimate correlations. The resulting methodology was illustrated using an infant gut microbiome data. An infants gut ecology continuously evolves during the first year after birth due to various factors such as changes in feeding, sleep patterns, exposure to people and so on. Using this novel methodology, for the first time in the literature, we describe associations among infant gut microbiota at different time points during the first year after birth. This manuscript was published in Nature Communications (Lin, Eggesbo and Peddada, Nature Communications, 2022). Microbiome differential abundance analysis methods for a pair of groups are well established in the literature. However, many microbiome studies involve multiple groups, sometimes even ordered groups, such as stages of a disease, and require different types of comparisons. Standard pairwise comparisons are not only inefficient in terms of power and false discovery rates, but they may not address the scientific question of interest. In this project, a general framework was developed for performing a wide range of multi-group analyses with covariate adjustments and repeated measures. The resulting methodology is illustrated using two real data sets. The first example explores the effects of aridity on the soil microbiome, and the second example investigates the effects of surgical interventions on the microbiome of IBD patients. The manuscript is under review. In many applications researchers are interested in multivariate outcomes that are compositional, i.e., the observed data sum to a constant. For example, the activities of a child in 24-hour period. However, for various reasons, including the method of collection of data, sometimes not all variables are measured and hence we have missing values in the multivariate compositional vector. Assuming that the missingness is associated with covariates, a simple multiple imputation methodology called Multiple Imputation for Compositional Data (MICoDa) is developed in this project to impute the missing values in a compositional vector. MICoDa is illustrated using two very disparate types of data where the missing values arise for different reasons. The first example relates to 24-hour physical activity data of young children and the second example relates to a gut microbiome data. This manuscript is in press for publication as an invited book chapter. Often linear regression is used to perform mediation analysis. However, in many instances, the underlying relationships may not be linear, as in the case of placental-fetal hormones and fetal development. Furthermore, the exact functional form of the relationship is generally unknown. For these reasons, we develop a novel shape-restricted inference-based methodology for conducting mediation analysis. This work is motivated by an application in fetal endocrinology where researchers are interested in understanding the effects of pesticide application on birth weight, with human chorionic gonadotropin (hCG) as the mediator. We assume a practically plausible set of nonlinear effects of the hCG on the birth weight and a linear relationship between the pesticide exposure and the hCG, with both exposure-outcome and exposure-mediator models being linear in the confounding factors. Using the proposed methodology on a population-level prenatal screening program data, with hCG as the mediator, we discovered that, while the natural direct effects suggest a positive association between pesticide application and birth weight, the natural indirect effects were negative.