Constrained Statistical Inference

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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.