arXiv subjects

Somnath Datta

Publications and source records attributed to Somnath Datta.

14 recordsLinked to original sources

arXiv2026

Estimating Association Between Paired Outcomes in Clustered Data with Informative Subgroup Size

Informative cluster size (ICS) and informative subgroup size (ISS) can distort marginal association estimates when the number of observed units, or their distribution across outcome-defined categories, is related to the outcomes under study. This issue is especially relevant for paired outcomes, where the observed association can depend on cluster size, paired-category composition, and the process by which units become available for analysis. We propose three weighted estimating approaches for marginal association between paired outcomes in clustered data. The weights are derived from within-cluster resampling arguments and extend inverse cluster-size and subgroup-size weighting to paired outcome categories. We also modify an existing ISS testing procedure by utilizing Stouffer's method to reduce computational burden. To evaluate the methods, we develop a simulator for clustered paired outcomes that separates unit-level association, latent cluster-level association, and outcome-dependent retention. Simulations show that pair-based weighting can reduce bias when association arises through unit-level dependence and subgroup composition is informative, but can attenuate association carried by latent cluster-level structure. Typical inverse-cluster weighting remains more stable when the association is primarily cluster-level. Application to NHANES oral-health data shows small positive periodontal and caries associations overall, with filled-surface outcomes showing stronger ISS evidence and greater sensitivity to pair-based weighting than decayed-surface outcomes. These results indicate that marginal association under ICS and ISS should be interpreted in relation to the source of association, observed-unit structure, and assumptions used to choose the weighting scheme.

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arXiv2026

Linked-Tucker Factorized Individualized Regression for Paired Multivariate Categorical Outcomes

We propose a joint individualized hurdle-ordinal regression model for paired zero-inflated ordinal outcomes with subject-specific, spatially varying, and time-varying covariate effects, motivated by the Iowa Fluoride Study (IFS). The two outcomes, dental caries and dental fluorosis, are measured repeatedly across ages at fine spatial resolution, yielding nested longitudinal data with substantial zero inflation, ordinality, and heterogeneity across individuals and locations. For each outcome, a hurdle component models disease presence, while a proportional-odds component models severity among positive observations. To parsimoniously represent the high-dimensional coefficient arrays, we introduce a linked Tucker tensor factorization. Shared subject-mode factors induce dependence between the caries and fluorosis coefficient tensors, while separate spatial factors accommodate the distinct measurement grids of tooth surfaces and tooth zones. A horseshoe prior on the core tensor elements encourages sparsity, and posterior computation is performed using the No-U-Turn Sampler in NumPyro. Population-level effect summaries are obtained by projecting individualized posterior linear predictors onto the design space, and Wasserstein barycenters aggregate these summaries across tooth locations and anatomical classes. Applied to the IFS, the model reveals spatially heterogeneous associations between early-life fluoride and dietary exposures and both outcomes. Fluoride exposure is associated with increased odds and severity of fluorosis, while soda intake consistently increases caries risk. These associations differ between presence and severity components and vary across tooth locations, ages, and subpopulations defined by prior caries status, highlighting the importance of the joint hurdle-ordinal framework for disentangling disease occurrence from disease progression in multilevel dental data.

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arXiv2025

Analyzing zero-inflated clustered longitudinal ordinal outcomes using GEE-type models with an application to dental fluorosis studies

Motivated by the Iowa Fluoride Study (IFS), which tracked fluoride intake and dental outcomes from childhood to young adulthood (ages 9, 13, 17, and 23), we analyze dental fluorosis - a condition caused by excessive fluoride exposure during enamel formation. In this context, fluorosis scores across tooth surfaces present as zero-inflated, clustered, and longitudinal ordinal outcomes, prompting the development of a unified modeling framework. Leveraging generalized estimating equations (GEEs), we construct separate models for the presence and severity of fluorosis and propose a combined model that links these components though shared covariates. To improve estimation efficiency and borrowing strength across timepoints, we incorporate James-Stein shrinkage estimators. We compare several working correlation structures, including a data-driven jackknifed structure, and perform model selection via rank aggregation. Simulation studies validate the finite-sample performance of the proposed models, and a bootstrap-based power analysis further confirms the validity of the testing procedure. In our analysis of the IFS data, early-life total daily fluoride intake, average home water fluoride concentration, and specific teeth and zones emerge as significant risk factors for dental fluorosis. Maxillary lateral incisors and zones closer to the gum show protective effects across different ages. These findings reveal novel age-specific associations between early-life exposures and the progression of dental fluorosis through early adulthood.

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arXiv2025

Conditional-Marginal Nonparametric Estimation for Stage Waiting Times from Multi-Stage Models under Dependent Right Censoring

We investigate two population-level quantities (corresponding to complete data) related to uncensored stage waiting times in a progressive multi-stage model, conditional on a prior stage visit. We show how to estimate these quantities consistently using right-censored data. The first quantity is the stage waiting time distribution (survival function), representing the proportion of individuals who remain in stage j within time t after entering stage j. The second quantity is the cumulative incidence function, representing the proportion of individuals who transition from stage j to stage j' within time t after entering stage j. To estimate these quantities, we present two nonparametric approaches. The first uses an inverse probability of censoring weighting (IPCW) method, which reweights the counting processes and the number of individuals at risk (the at-risk set) to address dependent right censoring. The second method utilizes the notion of fractional observations (FRE) that modifies the at-risk set by incorporating probabilities of individuals (who might have been censored in a prior stage) eventually entering the stage of interest in the uncensored or full data experiment. Neither approach is limited to the assumption of independent censoring or Markovian multi-stage frameworks. Simulation studies demonstrate satisfactory performance for both sets of estimators, though the IPCW estimator generally outperforms the FRE estimator in the setups considered in our simulations. These estimations are further illustrated through applications to two real-world datasets: one from patients undergoing bone marrow transplants and the other from patients diagnosed with breast cancer.

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arXiv2024

Modeling Zero-Inflated Correlated Dental Data through Gaussian Copulas and Approximate Bayesian Computation

We develop a new longitudinal count data regression model that accounts for zero-inflation and spatio-temporal correlation across responses. This project is motivated by an analysis of Iowa Fluoride Study (IFS) data, a longitudinal cohort study with data on caries (cavity) experience scores measured for each tooth across five time points. To that end, we use a hurdle model for zero-inflation with two parts: the presence model indicating whether a count is non-zero through logistic regression and the severity model that considers the non-zero counts through a shifted Negative Binomial distribution allowing overdispersion. To incorporate dependence across measurement occasion and teeth, these marginal models are embedded within a Gaussian copula that introduces spatio-temporal correlations. A distinct advantage of this formulation is that it allows us to determine covariate effects with population-level (marginal) interpretations in contrast to mixed model choices. Standard Bayesian sampling from such a model is infeasible, so we use approximate Bayesian computing for inference. This approach is applied to the IFS data to gain insight into the risk factors for dental caries and the correlation structure across teeth and time.

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arXiv2024

Selection of single cell clustering methodologies through rank aggregation of multiple performance measures

As single-cell gene expression data analysis continues to grow, the need for reliable clustering methods has become increasingly important. The prevalence of heuristic means for method choice could lead to inaccurate reports if comprehensive evaluation of the methods is omitted. Typical comparisons of methods fail to address the complexity presented by the data, transformations, or internal parameters. Previous work in the field of microarray data provided measures to evaluate the stability characteristic of clustering algorithms. Additional work on aggregation in the same era presented a way to compare multiple methodologies using several performance measures. In this paper, we provide adaptations to these measures and employ two aggregation schemes to create ranked lists of method and parameter choices for six unique datasets. Our findings demonstrate that an ensemble of validation measures, combined with ranking based on measures' dataset specific preferences, provides an objective way to select clustering methodologies, taking into account characteristic evaluation from each measure.

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arXiv2024

Nonparametric estimation of a state entry time distribution conditional on a "past" state occupation in a progressive multistate model with current status data

Case-I interval-censored (current status) data from multistate systems are often encountered in biomedical and epidemiological studies. In this article, we focus on the problem of estimating state entry distribution and occupation probabilities, contingent on a preceding state occupation. This endeavor is particularly complex owing to the inherent challenge of the unavailability of directly observed counts of individuals at risk of transitioning from a state, due to severe interval censoring. We propose two nonparametric approaches, one using the fractional at-risk set approach recently adopted in the right-censoring framework and the other a new estimator based on the ratio of marginal state occupation probabilities. Both estimation approaches utilize innovative applications of concepts from the competing risks paradigm. The finite-sample behavior of the proposed estimators is studied via extensive simulation studies where we show that the estimators based on severely censored current status data have good performance when compared with those based on complete data. We demonstrate the application of the two methods to analyze data from patients diagnosed with breast cancer.

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arXiv2023

A Bayesian Nonparametric Approach for Identifying Differentially Abundant Taxa in Multigroup Microbiome Data with Covariates

Scientific studies in the last two decades have established the central role of the microbiome in disease and health. Differential abundance analysis seeks to identify microbial taxa associated with sample groups defined by a factor such as disease subtype, geographical region, or environmental condition. The results, in turn, help clinical practitioners and researchers diagnose disease and develop treatments more effectively. However, microbiome data analysis is uniquely challenging due to high-dimensionality, sparsity, compositionally, and collinearity. There is a critical need for unified statistical approaches for differential analysis in the presence of covariates. We develop a zero-inflated Bayesian nonparametric (ZIBNP) methodology that meets these multipronged challenges. The proposed technique flexibly adapts to the unique data characteristics, casts the high proportion of zeros in a censoring framework, and mitigates high-dimensionality and collinearity by utilizing the dimension-reducing property of the semiparametric Chinese restaurant process. Additionally, the ZIBNP approach relates the microbiome sampling depths to inferential precision while accommodating the compositional nature of microbiome data. Through simulation studies and analyses of the CAnine Microbiome during Parasitism (CAMP) and Global Gut microbiome datasets, we demonstrate the accuracy of ZIBNP compared to established methods for differential abundance analysis in the presence of covariates.

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arXiv2023

Pseudo-value regression of clustered multistate current status data with informative cluster sizes

Multistate current status (CS) data presents a more severe form of censoring due to the single observation of study participants transitioning through a sequence of well-defined disease states at random inspection times. Moreover, these data may be clustered within specified groups, and informativeness of the cluster sizes may arise due to the existing latent relationship between the transition outcomes and the cluster sizes. Failure to adjust for this informativeness may lead to a biased inference. Motivated by a clinical study of periodontal disease (PD), we propose an extension of the pseudo-value approach to estimate covariate effects on the state occupation probabilities (SOP) for these clustered multistate CS data with informative cluster or intra-cluster group sizes. In our approach, the proposed pseudo-value technique initially computes marginal estimators of the SOP utilizing nonparametric regression. Next, the estimating equations based on the corresponding pseudo-values are reweighted by functions of the cluster sizes to adjust for informativeness. We perform a variety of simulation studies to study the properties of our pseudo-value regression based on the nonparametric marginal estimators under different scenarios of informativeness. For illustration, the method is applied to the motivating PD dataset, which encapsulates the complex data-generation mechanism.

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arXiv2023

Adjusting for informative cluster size in pseudo-value based regression approaches with clustered time to event data

Informative cluster size (ICS) arises in situations with clustered data where a latent relationship exists between the number of participants in a cluster and the outcome measures. Although this phenomenon has been sporadically reported in statistical literature for nearly two decades now, further exploration is needed in certain statistical methodologies to avoid potentially misleading inferences. For inference about population quantities without covariates, inverse cluster size reweightings are often employed to adjust for ICS. Further, to study the effect of covariates on disease progression described by a multistate model, the pseudo-value regression technique has gained popularity in time-to-event data analysis. We seek to answer the question: "How to apply pseudo-value regression to clustered time-to-event data when cluster size is informative?" ICS adjustment by the reweighting method can be performed in two steps; estimation of marginal functions of the multistate model and fitting the estimating equations based on pseudo-value responses, leading to four possible strategies. We present theoretical arguments and thorough simulation experiments to ascertain the correct strategy for adjusting for ICS. A further extension of our methodology is implemented to include informativeness induced by the intra-cluster group size. We demonstrate the methods in two real-world applications: (i) to determine predictors of tooth survival in a periodontal study, and (ii) to identify indicators of ambulatory recovery in spinal cord injury patients who participated in locomotor-training rehabilitation.

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arXiv2023

Differential Co-Abundance Network Analyses for Microbiome Data Adjusted for Clinical Covariates Using Jackknife Pseudo-Values

A recent breakthrough in differential network (DN) analysis of microbiome data has been realized with the advent of next-generation sequencing technologies. The DN analysis disentangles the microbial co-abundance among taxa by comparing the network properties between two or more graphs under different biological conditions. However, the existing methods to the DN analysis for microbiome data do not adjust for other clinical differences between subjects. We propose a Statistical Approach via Pseudo-value Information and Estimation for Differential Network Analysis (SOHPIE-DNA) that incorporates additional covariates such as continuous age and categorical BMI. SOHPIE-DNA is a regression technique adopting jackknife pseudo-values that can be implemented readily for the analysis. We demonstrate through simulations that SOHPIE-DNA consistently reaches higher recall and F1-score, while maintaining similar precision and accuracy to existing methods (NetCoMi and MDiNE). Lastly, we apply SOHPIE-DNA on two real datasets from the American Gut Project and the Diet Exchange Study to showcase the utility. The analysis of the Diet Exchange Study is to showcase that SOHPIE-DNA can also be used to incorporate the temporal change of connectivity of taxa with the inclusion of additional covariates. As a result, our method has found taxa that are related to the prevention of intestinal inflammation and severity of fatigue in advanced metastatic cancer patients.

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arXiv2022

A Pseudo-Value Regression Approach for Differential Network Analysis of Co-Expression Data

The differential network (DN) analysis identifies changes in measures of association among genes under two or more experimental conditions. In this article, we introduce a Pseudo-value Regression Approach for Network Analysis (PRANA). This is a novel method of differential network analysis that also adjusts for additional clinical covariates. We start from mutual information (MI) criteria, followed by pseudo-value calculations, which are then entered into a robust regression model. This article assesses the model performances of PRANA in a multivariable setting, followed by a comparison to dnapath and DINGO in both univariable and multivariable settings through variety of simulations. Performance in terms of precision, recall, and F1 score of differentially connected (DC) genes is assessed. By and large, PRANA outperformed dnapath and DINGO, neither of which is equipped to adjust for available covariates such as patient-age. Lastly, we employ PRANA in a real data application from the Gene Expression Omnibus (GEO) database to identify DC genes that are associated with chronic obstructive pulmonary disease (COPD) to demonstrate its utility. To the best of our knowledge, this is the first attempt of utilizing a regression modeling for DN analysis by collective gene expression levels between two or more groups with the inclusion of additional clinical covariates. By and large, adjusting for available covariates improves accuracy of a DN analysis.

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arXiv2022

Selection of the Optimal Personalized Treatment from Multiple Treatments with Right-censored Multivariate Outcome Measures

We propose a novel personalized concept for the optimal treatment selection for a situation where the response is a multivariate vector, that could contain right-censored variables such as survival time. The proposed method can be applied with any number of treatments and outcome variables, under a broad set of models. Following a working semiparametric Single Index Model that relates covariates and responses, we first define a patient-specific composite score, constructed from individual covariates. We then estimate conditional means of each response, given the patient score, correspond to each treatment, using a nonparametric smooth estimator. Next, a rank aggregation technique is applied to estimate an ordering of treatments based on ranked lists of treatment performance measures given by conditional means. We handle the right-censored data by incorporating the inverse probability of censoring weighting to the corresponding estimators. An empirical study illustrates the performance of the proposed method in finite sample problems. To show the applicability of the proposed procedure for real data, we also present a data analysis using HIV clinical trial data, that contained a right-censored survival event as one of the endpoints.

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arXiv2018

Inference on the marginal distribution of clustered data with informative cluster size

In spite of recent contributions to the literature, informative cluster size settings are not well known and understood. In this paper, we give a formal definition of the problem and describe it from different viewpoints. Data generating mechanisms, parametric and nonparametric models are considered in light of examples. Our emphasis is on nonparametric and robust approaches to the inference on the marginal distribution. Descriptive statistics and parameters of interest are defined as functionals and they are accompanied with a generally applicable testing procedure. The theory is illustrated with an example on patients with incomplete spinal cord injuries.

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