Anindya Bhadra

Forcing Versus Feedback: Epidemic Malaria and Monsoon Rains in Northwest India

Malaria epidemics in regions with seasonal windows of transmission can vary greatly in size from year to year. A central question has been whether these interannual cycles are driven by climate, are instead generated by the intrinsic dynamics of the disease, or result from the resonance of these two mechanisms. This corresponds to the more general inverse problem of identifying the respective roles of external forcings vs. internal feedbacks from time series for nonlinear and noisy systems. We propose here a quantitative approach to formally compare rival hypotheses on climate vs. disease dynamics, or external forcings vs. internal feedbacks, that combines dynamical models with recently developed, computational inference methods. The interannual patterns of epidemic malaria are investigated here for desert regions of northwest India, with extensive epidemiological records for Plasmodium falciparum malaria for the past two decades. We formulate a dynamical model of malaria transmission that explicitly incorporates rainfall, and we rely on recent advances on parameter estimation for nonlinear and stochastic dynamical systems based on sequential Monte Carlo methods. Results show a significant effect of rainfall in the inter-annual variability of epidemic malaria that involves a threshold in the disease response. The model exhibits high prediction skill for yearly cases in the malaria transmission season following the monsoonal rains. Consideration of a more complex model with clinical immunity demonstrates the robustness of the findings and suggests a role of infected individuals that lack clinical symptoms as a reservoir for transmission. Our results indicate that the nonlinear dynamics of the disease itself play a role at the seasonal, but not the interannual, time scales. They illustrate the feasibility of forecasting malaria epidemics in desert and semi-arid regions of India based on climate variability. This approach should be applicable to malaria in other locations, to other infectious diseases, and to other nonlinear systems under forcing.

Malaria in Northwest India: Data Analysis via Partially Observed Stochastic Differential Equation Models Driven by Lévy Noise

Many biological systems are appropriately described by partially observed Markov process (POMP) models, also known as state space models. Such models also arise throughout the physical and social sciences, in engineering, and in finance. Statistical challenges arise in carrying out inference on nonlinear, nonstationary, vector-valued POMP models. Methodologies that depend on the Markov process model only through numerical solution of sample paths are said to have the plug-and-play property. This property enables consideration of models for which the evaluation of transition densities is problematic. Our case study employs plug-and-play methodology to investigate malaria transmission in Northwest India. We address the scientific question of the respective roles of environmental factors, immunity, and nonlinear disease transmission dynamics in epidemic malaria. Previous debates on this question have been hindered by the lack of a statistical investigation that gives simultaneous consideration to the roles of human immunity and the fluctations in mosquito abundance associated with environmental or ecological covariates. We present the first time series analysis integrating these various components into a single vector-valued dynamic model. We are led to investigate a POMP involving a system of stochastic differential equations driven by Lévy noise. We find a clear role for rainfall and evidence to support models featuring the possibility of clinical immunity. An online supplement presents details of the methodology implemented and two additional figures.

Joint High-Dimensional Bayesian Variable and Covariance Selection with an Application to eQTL Analysis

We describe a Bayesian technique to (a) perform a sparse joint selection of significant predictor variables and significant inverse covariance matrix elements of the response variables in a high-dimensional linear Gaussian sparse seemingly unrelated regression (SSUR) setting and (b) perform an association analysis between the high-dimensional sets of predictors and responses in such a setting. To search the high-dimensional model space, where both the number of predictors and the number of possibly correlated responses can be larger than the sample size, we demonstrate that a marginalization-based collapsed Gibbs sampler, in combination with spike and slab type of priors, offers a computationally feasible and efficient solution. As an example, we apply our method to an expression quantitative trait loci (eQTL) analysis on publicly available single nucleotide polymorphism (SNP) and gene expression data for humans where the primary interest lies in finding the significant associations between the sets of SNPs and possibly correlated genetic transcripts. Our method also allows for inference on the sparse interaction network of the transcripts (response variables) after accounting for the effect of the SNPs (predictor variables). We exploit properties of Gaussian graphical models to make statements concerning conditional independence of the responses. Our method compares favorably to existing Bayesian approaches developed for this purpose.

Dietary Supplement Use Differs by Socioeconomic and Health-Related Characteristics among U.S. Adults, NHANES 2011–2014

The objective of this study was to estimate the prevalence of use and types of dietary supplements (DS) used by U.S. adults (≥19 years) by sociodemographic characteristics: family income-to-poverty ratio (PIR), food security status, and Supplemental Nutrition Assistance Program (SNAP) participation using NHANES 2011–2014 data (n = 11,024). DS use was ascertained via a home inventory and a retrospective 30-day questionnaire. Demographic and socioeconomic differences related to DS use were evaluated using a univariate t statistic. Half of U.S. adults (52%) took at least one DS during a 30-day period; multivitamin-mineral (MVM) products were the most commonly used (31%). DS and MVM use was significantly higher among those with a household income of ≥ 350% of the poverty level, those who were food secure, and SNAP income-ineligible nonparticipants across all sex, age, and race/ethnic groups. Among women, prevalence of use significantly differed between SNAP participants (39%) and SNAP income-eligible nonparticipants (54%). Older adults (71+ years) remained the highest consumers of DS, specifically among the highest income group (82%), while younger adults (19–30 years), predominantly in the lowest income group (28%), were the lowest consumers. Among U.S. adults, DS use and the types of products consumed varied with income, food security, and SNAP participation.

Inferring network structure in non-normal and mixed discrete-continuous genomic data

Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional independence has been studied using sparse Gaussian graphical models for continuous data and sparse Ising models for discrete data. However, there are two clear situations when these approaches are inadequate. The first occurs when the data are continuous but display non-normal marginal behavior such as heavy tails or skewness, rendering an assumption of normality inappropriate. The second occurs when a part of the data is ordinal or discrete (e.g., presence or absence of a mutation) and the other part is continuous (e.g., expression levels of genes or proteins). In this case, the existing Bayesian approaches typically employ a latent variable framework for the discrete part that precludes inferring conditional independence among the data that are actually observed. The current article overcomes these two challenges in a unified framework using Gaussian scale mixtures. Our framework is able to handle continuous data that are not normal and data that are of mixed continuous and discrete nature, while still being able to infer a sparse conditional sign independence structure among the observed data. Extensive performance comparison in simulations with alternative techniques and an analysis of a real cancer genomics data set demonstrate the effectiveness of the proposed approach.

Dietary Supplement Use among U.S. Children by Family Income, Food Security Level, and Nutrition Assistance Program Participation Status in 2011–2014

This analysis characterizes use of dietary supplements (DS) and motivations for DS use among U.S. children (≤18 years) by family income level, food security status, and federal nutrition assistance program participation using the 2011–2014 National Health and Nutrition Examination Survey data. About one-third (32%) of children used DS, mostly multivitamin-minerals (MVM; 24%). DS and MVM use were associated with higher family income and higher household food security level. DS use was lowest among children in households participating in the Supplemental Nutrition Assistance Program (SNAP; 20%) and those participating in the Special Supplemental Nutrition Assistance Program for Women, Infants, and Children (WIC; 26%) compared to both income-eligible and income-ineligible nonparticipants. Most children who used DS took only one (83%) or two (12%) products; although children in low-income families took fewer products than those in higher income families. The most common motivations for DS and MVM use were to “improve (42% or 46%)” or “maintain (34 or 38%)” health, followed by “to supplement the diet (23 or 24%)” for DS or MVM, respectively. High-income children were more likely to use DS and MVM “to supplement the diet” than middle- or low-income children. Only 18% of child DS users took DS based on a health practitioner’s recommendation. In conclusion, DS use was lower among children who were in low-income or food-insecure families, or families participating in nutrition assistance programs.

Integrative sparse Bayesian analysis of high-dimensional multi-platform genomic data in glioblastoma

While individual studies have demonstrated that mRNA expressions are affected by both copy number aberrations and microRNAs, their integrative analysis has largely been ignored. In this article, we use high-dimensional regression techniques to perform the integrative analysis of such data in the context of Glioblastoma Multiforme (GBM). It is revealed that copy numbers are more potent regulators of mRNA levels than microRNAs. We also infer the mRNA expression network after adjusting the effect of microRNAs and copy numbers. Our association analysis demonstrates the expression levels of the genes IRS1 and GRB2 are strongly associated with the underlying variations in copy numbers on chromosomal locations 17q25.1 and 3p25.2, but we fail to detect significant associations with microRNA levels.