arXiv subjects

Raymond J. Carroll

Publications and source records attributed to Raymond J. Carroll.

At least 19 recordsLinked to original sources

arXiv2025

PDA in Action: Ten Principles for High-Quality Multi-Site Clinical Evidence Generation

Background: Distributed Research Networks (DRNs) offer significant opportunities for collaborative multi-site research and have significantly advanced healthcare research based on clinical observational data. However, generating high-quality real-world evidence using fit-for-use data from multi-site studies faces important challenges, including biases associated with various types of heterogeneity within and across sites and data sharing difficulties. Over the last ten years, Privacy-Preserving Distributed Algorithms (PDA) have been developed and utilized in numerous national and international real-world studies spanning diverse domains, from comparative effectiveness research, target trial emulation, to healthcare delivery, policy evaluation, and system performance assessment. Despite these advances, there remains a lack of comprehensive and clear guiding principles for generating high-quality real-world evidence through collaborative studies leveraging the methods under PDA. Objective: The paper aims to establish ten principles of best practice for conducting high-quality multi-site studies using PDA. These principles cover all phases of research, including study preparation, protocol development, analysis, and final reporting. Discussion: The ten principles for conducting a PDA study outline a principled, efficient, and transparent framework for employing distributed learning algorithms within DRNs to generate reliable and reproducible real-world evidence.

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arXiv2025

A Communication-Efficient Distributed Algorithm for Learning with Heterogeneous and Structurally Incomplete Multi-Site Data

In multicenter biomedical research, integrating data from multiple decentralized sites provides more robust and generalizable findings due to its larger sample size and the ability to account for the between-site heterogeneity. However, sharing individual-level data across sites is often difficult due to patient privacy concerns and regulatory restrictions. To overcome this challenge, many distributed algorithms, that fit a global model by only communicating aggregated information across sites, have been proposed. A major challenge in applying existing distributed algorithms to real-world data is that their validity often relies on the assumption that data across sites are independently and identically distributed, which is frequently violated in practice. In biomedical applications, data distributions across clinical sites can be heterogeneous. Additionally, the set of covariates available at each site may vary due to different data collection protocols. We propose a distributed inference framework for data integration in the presence of both distribution heterogeneity and data structural heterogeneity. By modeling heterogeneous and structurally missing data using density-tilted generalized method of moments, we developed a general aggregated data-based distributed algorithm that is communication-efficient and heterogeneity-aware. We establish the asymptotic properties of our estimator and demonstrate the validity of our method via simulation studies.

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arXiv2025

Distributed inference for heterogeneous mixture models using multi-site data

Mixture models postulate the overall population as a mixture of finite subpopulations with unobserved membership. Fitting mixture models usually requires large sample sizes and combining data from multiple sites can be beneficial. However, sharing individual participant data across sites is often less feasible due to various types of practical constraints, such as data privacy concerns. Moreover, substantial heterogeneity may exist across sites, and locally identified latent classes may not be comparable across sites. We propose a unified modeling framework where a common definition of the latent classes is shared across sites and heterogeneous mixing proportions of latent classes are allowed to account for between-site heterogeneity. To fit the heterogeneous mixture model on multi-site data, we propose a novel distributed Expectation-Maximization (EM) algorithm where at each iteration a density ratio tilted surrogate Q function is constructed to approximate the standard Q function of the EM algorithm as if the data from multiple sites could be pooled together. Theoretical analysis shows that our estimator achieves the same contraction property as the estimators derived from the EM algorithm based on the pooled data.

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arXiv2024

Semi-Supervised Quantile Estimation: Robust and Efficient Inference in High Dimensional Settings

We consider quantile estimation in a semi-supervised setting, characterized by two available data sets: (i) a small or moderate sized labeled data set containing observations for a response and a set of possibly high dimensional covariates, and (ii) a much larger unlabeled data set where only the covariates are observed. We propose a family of semi-supervised estimators for the response quantile(s) based on the two data sets, to improve the estimation accuracy compared to the supervised estimator, i.e., the sample quantile from the labeled data. These estimators use a flexible imputation strategy applied to the estimating equation along with a debiasing step that allows for full robustness against misspecification of the imputation model. Further, a one-step update strategy is adopted to enable easy implementation of our method and handle the complexity from the non-linear nature of the quantile estimating equation. Under mild assumptions, our estimators are fully robust to the choice of the nuisance imputation model, in the sense of always maintaining root-n consistency and asymptotic normality, while having improved efficiency relative to the supervised estimator. They also attain semi-parametric optimality if the relation between the response and the covariates is correctly specified via the imputation model. As an illustration of estimating the nuisance imputation function, we consider kernel smoothing type estimators on lower dimensional and possibly estimated transformations of the high dimensional covariates, and we establish novel results on their uniform convergence rates in high dimensions, involving responses indexed by a function class and usage of dimension reduction techniques. These results may be of independent interest. Numerical results on both simulated and real data confirm our semi-supervised approach's improved performance, in terms of both estimation and inference.

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arXiv2023

Gaussian Processes with Errors in Variables: Theory and Computation

Covariate measurement error in nonparametric regression is a common problem in nutritional epidemiology and geostatistics, and other fields. Over the last two decades, this problem has received substantial attention in the frequentist literature. Bayesian approaches for handling measurement error have only been explored recently and are surprisingly successful, although the lack of a proper theoretical justification regarding the asymptotic performance of the estimators. By specifying a Gaussian process prior on the regression function and a Dirichlet process Gaussian mixture prior on the unknown distribution of the unobserved covariates, we show that the posterior distribution of the regression function and the unknown covariates density attain optimal rates of contraction adaptively over a range of Hölder classes, up to logarithmic terms. This improves upon the existing classical frequentist results which require knowledge of the smoothness of the underlying function to deliver optimal risk bounds. We also develop a novel surrogate prior for approximating the Gaussian process prior that leads to efficient computation and preserves the covariance structure, thereby facilitating easy prior elicitation. We demonstrate the empirical performance of our approach and compare it with competitors in a wide range of simulation experiments and a real data example.

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arXiv2021

Nonparametric, tuning-free estimation of S-shaped functions

We consider the nonparametric estimation of an S-shaped regression function. The least squares estimator provides a very natural, tuning-free approach, but results in a non-convex optimisation problem, since the inflection point is unknown. We show that the estimator may nevertheless be regarded as a projection onto a finite union of convex cones, which allows us to propose a mixed primal-dual bases algorithm for its efficient, sequential computation. After developing a projection framework that demonstrates the consistency and robustness to misspecification of the estimator, our main theoretical results provide sharp oracle inequalities that yield worst-case and adaptive risk bounds for the estimation of the regression function, as well as a rate of convergence for the estimation of the inflection point. These results reveal not only that the estimator achieves the minimax optimal rate of convergence for both the estimation of the regression function and its inflection point (up to a logarithmic factor in the latter case), but also that it is able to achieve an almost-parametric rate when the true regression function is piecewise affine with not too many affine pieces. Simulations and a real data application to air pollution modelling also confirm the desirable finite-sample properties of the estimator, and our algorithm is implemented in the R package Sshaped.

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arXiv2020

Data integration in high dimension with multiple quantiles

This article deals with the analysis of high dimensional data that come from multiple sources (experiments) and thus have different possibly correlated responses, but share the same set of predictors. The measurements of the predictors may be different across experiments. We introduce a new regression approach with multiple quantiles to select those predictors that affect any of the responses at any quantile level and estimate the nonzero parameters. Our estimator is a minimizer of a penalized objective function, which aggregates the data from the different experiments. We establish model selection consistency and asymptotic normality of the estimator. In addition we present an information criterion, which can also be used for consistent model selection. Simulations and two data applications illustrate the advantages of our method, which takes the group structure induced by the predictors across experiments and quantile levels into account.

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arXiv2020

Nonparametric Bayesian Deconvolution of a Symmetric Unimodal Density

We consider nonparametric measurement error density deconvolution subject to heteroscedastic measurement errors as well as symmetry about zero and shape constraints, in particular unimodality. The problem is motivated by applications where the observed data are estimated effect sizes from regressions on multiple factors, where the target is the distribution of the true effect sizes. We exploit the fact that any symmetric and unimodal density can be expressed as a mixture of symmetric uniform densities, and model the mixing density in a new way using a Dirichlet process location-mixture of Gamma distributions. We do the computations within a Bayesian context, describe a simple scalable implementation that is linear in the sample size, and show that the estimate of the unknown target density is consistent. Within our application context of regression effect sizes, the target density is likely to have a large probability near zero (the near null effects) coupled with a heavy-tailed distribution (the actual effects). Simulations show that unlike standard deconvolution methods, our Constrained Bayesian Deconvolution method does a much better job of reconstruction of the target density. Applications to a genome-wise association study (GWAS) and microarray data reveal similar results.

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arXiv2019

Bayesian Copula Density Deconvolution for Zero-Inflated Data in Nutritional Epidemiology

Estimating the marginal and joint densities of the long-term average intakes of different dietary components is an important problem in nutritional epidemiology. Since these variables cannot be directly measured, data are usually collected in the form of 24-hour recalls of the intakes, which show marked patterns of conditional heteroscedasticity. Significantly compounding the challenges, the recalls for episodically consumed dietary components also include exact zeros. The problem of estimating the density of the latent long-time intakes from their observed measurement error contaminated proxies is then a problem of deconvolution of densities with zero-inflated data. We propose a Bayesian semiparametric solution to the problem, building on a novel hierarchical latent variable framework that translates the problem to one involving continuous surrogates only. Crucial to accommodating important aspects of the problem, we then design a copula-based approach to model the involved joint distributions, adopting different modeling strategies for the marginals of the different dietary components. We design efficient Markov chain Monte Carlo algorithms for posterior inference and illustrate the efficacy of the proposed method through simulation experiments. Applied to our motivating nutritional epidemiology problems, compared to other approaches, our method provides more realistic estimates of the consumption patterns of episodically consumed dietary components.

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arXiv2019

Sparse semiparametric canonical correlation analysis for data of mixed types

Canonical correlation analysis investigates linear relationships between two sets of variables, but often works poorly on modern data sets due to high-dimensionality and mixed data types such as continuous, binary and zero-inflated. To overcome these challenges, we propose a semiparametric approach for sparse canonical correlation analysis based on Gaussian copula. Our main contribution is a truncated latent Gaussian copula model for data with excess zeros, which allows us to derive a rank-based estimator of the latent correlation matrix for mixed variable types without the estimation of marginal transformation functions. The resulting canonical correlation analysis method works well in high-dimensional settings as demonstrated via numerical studies, as well as in application to the analysis of association between gene expression and micro RNA data of breast cancer patients.

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arXiv2019

A spline-assisted semiparametric approach to non-parametric measurement error models

It is well known that the minimax rates of convergence of nonparametric density and regression function estimation of a random variable measured with error is much slower than the rate in the error free case. Surprisingly, we show that if one is willing to impose a relatively mild assumption in requiring that the error-prone variable has a compact support, then the results can be greatly improved. We describe new and constructive methods to take full advantage of the compact support assumption via spline-assisted semiparametric methods. We further prove that the new estimator achieves the usual nonparametric rate in estimating both the density and regression functions as if there were no measurement error. The proof involves linear and bilinear operator theories, semiparametric theory, asymptotic analysis regarding Bsplines, as well as integral equation treatments. The performance of the new methods is demonstrated through several simulations and a data example.

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arXiv2019

Sample Splitting as an M-Estimator with Application to Physical Activity Scoring

Sample splitting is widely used in statistical applications, including classically in classification and more recently for inference post model selection. Motivating by problems in the study of diet, physical activity, and health, we consider a new application of sample splitting. Physical activity researchers wanted to create a scoring system to quickly assess physical activity levels. A score is created using a large cohort study. Then, using the same data, this score serves as a covariate in a model for the risk of disease or mortality. Since the data are used twice in this way, standard errors and confidence intervals from fitting the second model are not valid. To allow for proper inference, sample splitting can be used. One builds the score with a random half of the data and then uses the score when fitting a model to the other half of the data. We derive the limiting distribution of the estimators. An obvious question is what happens if multiple sample splits are performed. We show that as the number of sample splits increases, the combination of multiple sample splits is effectively equivalent to solving a set of estimating equations.

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arXiv2019

Finite Sample Hypothesis Tests for Stacked Estimating Equations

Suppose there are two unknown parameters, each parameter is the solution to an estimating equation, and the estimating equation of one parameter depends on the other parameter. The parameters can be jointly estimated by "stacking" their estimating equations and solving for both parameters simultaneously. Asymptotic confidence intervals are readily available for stacked estimating equations. We introduce a bootstrap-based hypothesis test for stacked estimating equations which does not rely on asymptotic approximations. Test statistics are constructed by splitting the sample in two, estimating the first parameter on a portion of the sample then plugging the result into the second estimating equation to solve for the next parameter using the remaining sample. To reduce simulation variability from a single split, we repeatedly split the sample and take the sample mean of all the estimates. For parametric models, we derive the limiting distribution of sample splitting estimator and show they are equivalent to stacked estimating equations.

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arXiv2016

Additive Function-on-Function Regression

We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology based on a novel combination of spline bases with an eigenbasis to represent the trivariate kernel function. We discuss prediction of a new response trajectory, propose an inference procedure that accounts for total variability in the predicted response curves, and construct pointwise prediction intervals. The estimation/inferential procedure accommodates realistic scenarios such as correlated error structure as well as sparse and/or irregular designs. We investigate our methodology in finite sample size through simulations and two real data applications.

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arXiv2016

Bayesian Semiparametric Multivariate Density Deconvolution

We consider the problem of multivariate density deconvolution when the interest lies in estimating the distribution of a vector-valued random variable but precise measurements of the variable of interest are not available, observations being contaminated with additive measurement errors. The existing sparse literature on the problem assumes the density of the measurement errors to be completely known. We propose robust Bayesian semiparametric multivariate deconvolution approaches when the measurement error density is not known but replicated proxies are available for each unobserved value of the random vector. Additionally, we allow the variability of the measurement errors to depend on the associated unobserved value of the vector of interest through unknown relationships which also automatically includes the case of multivariate multiplicative measurement errors. Basic properties of finite mixture models, multivariate normal kernels and exchangeable priors are exploited in many novel ways to meet the modeling and computational challenges. Theoretical results that show the flexibility of the proposed methods are provided. We illustrate the efficiency of the proposed methods in recovering the true density of interest through simulation experiments. The methodology is applied to estimate the joint consumption pattern of different dietary components from contaminated 24 hour recalls.

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arXiv2016

Data Integration with High Dimensionality

We consider a problem of data integration. Consider determining which genes affect a disease. The genes, which we call predictor objects, can be measured in different experiments on the same individual. We address the question of finding which genes are predictors of disease by any of the experiments. Our formulation is more general. In a given data set, there are a fixed number of responses for each individual, which may include a mix of discrete, binary and continuous variables. There is also a class of predictor objects, which may differ within a subject depending on how the predictor object is measured, i.e., depend on the experiment. The goal is to select which predictor objects affect any of the responses, where the number of such informative predictor objects or features tends to infinity as sample size increases. There are marginal likelihoods for each way the predictor object is measured, i.e., for each experiment. We specify a pseudolikelihood combining the marginal likelihoods, and propose a pseudolikelihood information criterion. Under regularity conditions, we establish selection consistency for the pseudolikelihood information criterion with unbounded true model size, which includes a Bayesian information criterion with appropriate penalty term as a special case. Simulations indicate that data integration improves upon, sometimes dramatically, using only one of the data sources.

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arXiv2015

Estimation and inference in generalized additive coefficient models for nonlinear interactions with high-dimensional covariates

In the low-dimensional case, the generalized additive coefficient model (GACM) proposed by Xue and Yang [Statist. Sinica 16 (2006) 1423-1446] has been demonstrated to be a powerful tool for studying nonlinear interaction effects of variables. In this paper, we propose estimation and inference procedures for the GACM when the dimension of the variables is high. Specifically, we propose a groupwise penalization based procedure to distinguish significant covariates for the "large $p$ small $n$" setting. The procedure is shown to be consistent for model structure identification. Further, we construct simultaneous confidence bands for the coefficient functions in the selected model based on a refined two-step spline estimator. We also discuss how to choose the tuning parameters. To estimate the standard deviation of the functional estimator, we adopt the smoothed bootstrap method. We conduct simulation experiments to evaluate the numerical performance of the proposed methods and analyze an obesity data set from a genome-wide association study as an illustration.

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arXiv2014

Bayesian Regression Analysis of Data with Random Effects Covariates from Nonlinear Longitudinal Measurements

Joint models for a wide class of response variables and longitudinal measurements consist on a mixed-effects model to fit longitudinal trajectories whose random effects enter as covariates in a generalized linear model for the primary response. They provide a useful way to asses association between these two kinds of data, which in clinical studies are often collected jointly on a series of individuals and may help understanding, for instance, the mechanisms of recovery of a certain disease or the efficacy of a given therapy. The most common joint model in this framework is based on a linear mixed model for the longitudinal data. However, for complex datasets the linearity assumption may be too restrictive. Some works have considered generalizing this setting with the use of a nonlinear mixed-effects model for the longitudinal trajectories but the proposed estimation procedures based on likelihood approximations have been shown De la Cruz et al. (2011) to exhibit some computational efficiency problems. In this article we propose an MCMC-based estimation procedure in the joint model with a nonlinear mixed-effects model for the longitudinal data and a generalized linear model for the primary response. Moreover, we consider that the errors in the longitudinal model may be correlated. We apply our method to the analysis of hormone levels measured at the early stages of pregnancy that can be used to predict normal versus abnormal pregnancy outcomes. We also conduct a simulation study to asses the importance of modelling correlated errors and quantify the consequences of model misspecification.

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