Constrained Statistical Inference

National Institute Of Environmental Health Sciences

Investigators

Linked publications, trials & patents

Abstract

We have been working on several research problems in this project during this reporting year. Here are a sample of accomplishments. Comparison of two or more experimental groups on the basis of high dimensional features is a common and well-studied problem in the literature. Methods such as Benjamini-Hochberg (1995)and others are widely used in the literature for testing hypotheses regarding thousands of features (e.g., genes). Most methods make assumptions regarding the underlying correlation structure regarding these features and often those conditions are either not true or difficult to verify. In a manuscript we recently published (Peng et al., 2025), we developed methodology that is robust to the underlying dependence structure, under some modeling assumptions. The resulting methodology provides a better control of the false discovery rates while providing higher power than population methodology such as the Benjamini-Hochberg (1995) procedure. The National Toxicology Program’s (NTP’s) quantitative high throughput screening (qHTS) assays involve studying the dose response patterns of thousands of chemicals to determine if a chemical is potentially an active compound or not. Often the qHTS assays consist of 15 dose groups and multiple independent replicates at each dose. Typically, an active compound is expected to have a monotonic pattern (increasing or decreasing) which are modeled using the Hill function. In reality, however, the shapes are not always strictly monotonic, and even if they are monotonic, they may not follow a Hill function. Intrinsically, the Hill function has an upper and a lower asymptote, but some dose-response curves observed in qHTS data may not display this feature. Furthermore, due to cell death and other factors, at high (or low) doses the response may depart from the expected Hill function resulting in concave or convex shapes. Hence, Hill function may not be always appropriate to model qHTS data, and hence the AC_50estimates reported from Hill models may not be valid. Since thousands of chemicals are processed using qHTS assays, it is necessary to have an automated procedure that would describe the correct shape of the dose-response curve and estimate suitable estimates of toxicity. In this project we are developing nonparametric, I-splines and C-splines based methods for describing dose-response relationships that would be helpful to screen thousands of compounds without restricting to the functional form of a curve. This work is in progress. In many applications, relationships between a pair of variables is not always linear and may not even be monotonic. In such cases, standard measures of association such as the Pearson correlation and the Spearman correlation are not appropriate. To make matters more complicated, unknown to the researchers, there may be clusters within data. To deal with such complex data, in this project (Bera et al., 2025) we developed an automated procedure called CLuster based Association Measure (CLAM) that first discovers clusters in a data driven manner and then derives cluster specific as well as overall aggregated measure of dependence between two variables. The measure of dependence is flexible to accommodate linear as well as well nonlinear relationships between a pair of variables. By its construction, CLAM is designed to detect influential observations and outliers in the data and provides estimates that are robust to such observations. Since CLAM provides cluster specific dependence measure, it provides deeper insights into the relationships between variables at a cluster level. Furthermore, the framework of the methodology is very general and not limited to bivariate data, but also can be applied to describe correlations in high dimensional genomic data as well as correlations between large matrices of images. Researchers are often interested in performing inferences on two or more ordered experimental groups, such as disease status or ordered exposure groups etc. In addition to the mean expression of a feature, one is often interested in testing hypotheses regarding trends in correlation coefficients among features, as they are important to understand how the networks among features evolve over multiple ordered groups. For example, in the case of gut microbiome, one may be interested in discovering differences in interactions among commensal bacteria over stages of infection. To answer such questions, we are developing general methods for estimating multiple correlation matrices where the elements of the matrices are subject to inequality constraints over ordered groups. The methodology is designed to discover patterns among correlation coefficients over ordered groups. This work is in progress. There is a growing concern regarding the increase in preterm birth rates (<37 weeks of gestation) and early term birth rates (37 to 39 weeks) in the US. According to a recent U.S. Centers for Disease Control and Prevention (CDC) report, between 2014 and 2022, birth rates shifted towards shorter gestational ages, with preterm and early term rates rising by 12% and 20%, respectively. There are numerous factors associated with preterm births, among them is exposures to high temperatures during pregnancy. We are investigating the association between extreme ambient temperatures during pregnancy and early delivery using data collected from NICHD’s Consortium on Safe Labor (CSL) study. The CSL was a retrospective observational study designed to collect comprehensive information on contemporary labor and delivery practices. We have access to data from electronic medical records on 203,691 pregnant women with singleton births from 19 hospitals representing 12 clinical centers from 15 non-overlapping hospital referral regions in California, Chicago, Delaware, Florida, Indiana, Maryland, Massachusetts, New York, Ohio, Texas, Utah, and Washington D.C. Thus, we have a broad representation of temperatures and environmental exposures across the United States between 2002 and 2008. All births at 23 weeks of gestation or later at these institutions were included in the study. This work is in progress.