Search

In this article, we investigate the Gaussian graphical model inference problem in a novel setting that we call erose measurements, referring to irregularly measured or observed data. For graphs, this results in different node pairs having vastly different sample sizes which frequently arises in data integration, genomics, neuroscience, and sensor networks. Existing works characterize the graph selection performance using the minimum pairwise sample size, which provides little insights for erosely measured data, and no existing inference method is applicable. We aim to fill in this gap by proposing the first inference method that characterizes the different uncertainty levels over the graph caused by the erose measurements, named GI-JOE (Graph Inference when Joint Observations are Erose). Specifically, we develop an edge-wise inference method and an affiliated FDR control procedure, where the variance of each edge depends on the sample sizes associated with corresponding neighbors. We prove statistical validity under erose measurements, thanks to careful localized edge-wise analysis and disentangling the dependencies across the graph. Finally, through simulation studies and a real neuroscience data example, we demonstrate the advantages of our inference methods for graph selection from erosely measured data. for this article are available online. [ABSTRACT FROM AUTHOR]

AbstractThis article investigates statistical inference for noisy matrix completion in a semi-supervised model when auxiliary covariates are available. The model consists of two parts. One part is a low-rank matrix induced by unobserved latent factors; the other part models the effects of the observed covariates through a coefficient matrix which is composed of high-dimensional column vectors. We model the observational pattern of the responses through a logistic regression of the covariates, and allow its probability to go to zero as the sample size increases. We apply an iterative least squares (LS) estimation approach in our considered context. The iterative LS methods in general enjoy a low computational cost, but deriving the statistical properties of the resulting estimators is a challenging task. We show that our method only needs a few iterations, and the resulting entry-wise estimators of the low-rank matrix and the coefficient matrix are guaranteed to have asymptotic normal distributions. As a result, individual inference can be conducted for each entry of the unknown matrices. We also propose a simultaneous testing procedure with multiplier bootstrap for the high-dimensional coefficient matrix. This simultaneous inferential tool can help us further investigate the effects of covariates for the prediction of missing entries. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. [ABSTRACT FROM AUTHOR]

The last two decades have seen considerable progress in foundational aspects of statistical network analysis, but the path from theory to application is not straightforward. Two large, heterogeneous samples of small networks of within-household contacts in Belgium were collected using two different but complementary sampling designs: one smaller but with all contacts in each household observed, the other larger and more representative but recording contacts of only one person per household. We wish to combine their strengths to learn the social forces that shape household contact formation and facilitate simulation for prediction of disease spread, while generalising to the population of households in the region. To accomplish this, we describe a flexible framework for specifying multi-network models in the exponential family class and identify the requirements for inference and prediction under this framework to be consistent, identifiable, and generalisable, even when data are incomplete; explore how these requirements may be violated in practice; and develop a suite of quantitative and graphical diagnostics for detecting violations and suggesting improvements to candidate models. We report on the effects of network size, geography, and household roles on household contact patterns (activity, heterogeneity in activity, and triadic closure). for this article are available online. [ABSTRACT FROM AUTHOR]

Comparative biologists are often interested in inferring covariation between multiple biological traits sampled across numerous related taxa. To properly study these relationships, we must control for the shared evolutionary history of the taxa to avoid spurious inference. An additional challenge arises as obtaining a full suite of measurements becomes increasingly difficult with increasing taxa. This generally necessitates data imputation or integration, and existing control techniques typically scale poorly as the number of taxa increases. We propose an inference technique that integrates out missing measurements analytically and scales linearly with the number of taxa by using a post-order traversal algorithm under a multivariate Brownian diffusion (MBD) model to characterize trait evolution. We further exploit this technique to extend the MBD model to account for sampling error or non-heritable residual variance. We test these methods to examine mammalian life history traits, prokaryotic genomic and phenotypic traits, and HIV infection traits. We find computational efficiency increases that top two orders-of-magnitude over current best practices. While we focus on the utility of this algorithm in phylogenetic comparative methods, our approach generalizes to solve long-standing challenges in computing the likelihood for matrix-normal and multivariate normal distributions with missing data at scale.

We study the identification and estimation of statistical functionals of multivariate data missing nonmonotonically and not-at-random, taking a semiparametric approach. Specifically, we assume that the missingness mechanism satisfies what has been previously called "no self-censoring" or "itemwise conditionally independent nonresponse," which roughly corresponds to the assumption that no partially observed variable directly determines its own missingness status. We show that this assumption, combined with an odds ratio parameterization of the joint density, enables identification of functionals of interest, and we establish the semiparametric efficiency bound for the nonparametric model satisfying this assumption. We propose a practical augmented inverse probability weighted estimator, and in the setting with a (possibly high-dimensional) always-observed subset of covariates, our proposed estimator enjoys a certain double-robustness property. We explore the performance of our estimator with simulation experiments and on a previously studied dataset of HIV-positive mothers in Botswana. for this article are available online. [ABSTRACT FROM AUTHOR]

Frontal power asymmetry (FA), a measure of brain function derived from electroencephalography, is a potential biomarker for major depressive disorder (MDD). Though FA is functional in nature, it is typically reduced to a scalar value prior to analysis, possibly obscuring its relationship with MDD and leading to a number of studies that have provided contradictory results. To overcome this issue, we sought to fit a functional regression model to characterize the association between FA and MDD status, adjusting for age, sex, cognitive ability, and handedness using data from a large clinical study that included both MDD and healthy control (HC) subjects. Since nearly 40% of the observations are missing data on either FA or cognitive ability, we propose an extension of multiple imputation (MI) by chained equations that allows for the imputation of both scalar and functional data. We also propose an extension of Rubin's Rules for conducting valid inference in this setting. The proposed methods are evaluated in a simulation and applied to our FA data. For our FA data, a pooled analysis from the imputed datasets yielded similar results to those of the complete case analysis. We found that, among young females, HCs tended to have higher FA over the θ, α, and β frequency bands, but that the difference between HC and MDD subjects diminishes and ultimately reverses with age. For males, HCs tended to have higher FA in the β frequency band, regardless of age. Young male HCs had higher FA in the θ and α bands, but this difference diminishes with increasing age in the α band and ultimately reverses with increasing age in the θ band. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement. [ABSTRACT FROM AUTHOR]

Modeling infectious disease dynamics has been critical throughout the COVID-19 pandemic. Of particular interest are the incidence, prevalence, and effective reproductive number (Rt). Estimating these quantities is challenging due to under-ascertainment, unreliable reporting, and time lags between infection, onset, and testing. We propose a Multilevel Epidemic Regression Model to Account for Incomplete Data (MERMAID) to jointly estimate Rt, ascertainment rates, incidence, and prevalence over time in one or multiple regions. Specifically, MERMAID allows for a flexible regression model of Rt that can incorporate geographic and time-varying covariates. To account for under-ascertainment, we (a) model the ascertainment probability over time as a function of testing metrics and (b) jointly model data on confirmed infections and population-based serological surveys. To account for delays between infection, onset, and reporting, we model stochastic lag times as missing data, and develop an EM algorithm to estimate the model parameters. We evaluate the performance of MERMAID in simulation studies, and assess its robustness by conducting sensitivity analyses in a range of scenarios of model misspecifications. We apply the proposed method to analyze COVID-19 daily confirmed infection counts, PCR testing data, and serological survey data across the United States. Based on our model, we estimate an overall COVID-19 prevalence of 12.5% (ranging from 2.4% in Maine to 20.2% in New York) and an overall ascertainment rate of 45.5% (ranging from 22.5% in New York to 81.3% in Rhode Island) in the United States from March to December 2020. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement. [ABSTRACT FROM AUTHOR]

Noncompliance with assigned treatments is a common challenge in analyzing and interpreting randomized clinical trials (RCTs). One way to handle noncompliance is to estimate the complier-average causal effect (CACE), the intervention's efficacy in the subpopulation that complies with assigned treatment. In a two-step meta-analysis, one could first estimate CACE for each study, then combine them to estimate the population-averaged CACE. However, when some trials do not report noncompliance data, the two-step meta-analysis can be less efficient and potentially biased by excluding these trials. This article proposes a flexible Bayesian hierarchical CACE framework to simultaneously account for heterogeneous and incomplete noncompliance data in a meta-analysis of RCTs. The models are motivated by and used for a meta-analysis estimating the CACE of epidural analgesia on cesarean section, in which only 10 of 27 trials reported complete noncompliance data. The new analysis includes all 27 studies and the results present new insights on the causal effect after accounting for noncompliance. Compared to the estimated risk difference of 0.8% (95% CI: –0.3%, 1.9%) given by the two-step intention-to-treat meta-analysis, the estimated CACE is 4.1% (95% CrI: –0.3%, 10.5%). We also report simulation studies to evaluate the performance of the proposed method. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement. [ABSTRACT FROM AUTHOR]

This article reviews recent advances in missing data research using graphical models to represent multivariate dependencies. We first examine the limitations of traditional frameworks from three different perspectives: transparency, estimability, and testability. We then show how procedures based on graphical models can overcome these limitations and provide meaningful performance guarantees even when data are missing not at random (MNAR). In particular, we identify conditions that guarantee consistent estimation in broad categories of missing data problems, and derive procedures for implementing this estimation. Finally, we derive testable implications for missing data models in both missing at random and MNAR categories. [ABSTRACT FROM AUTHOR]

We describe the Bedside Patient Rescue (BPR) project, the goal of which is risk prediction of adverse events for non-intensive care unit patients using ∼100 variables (vitals, lab results, assessments, etc.). There are several missing predictor values for most patients, which in the health sciences is the norm, rather than the exception. A Bayesian approach is presented that addresses many of the shortcomings to standard approaches to missing predictors: (i) treatment of the uncertainty due to imputation is straight-forward in the Bayesian paradigm, (ii) the predictor distribution is flexibly modeled as an infinite normal mixture with latent variables to explicitly account for discrete predictors (i.e., as in multivariate probit regression models), and (iii) certain missing not at random situations can be handled effectively by allowing the indicator of missingness into the predictor distribution only to inform the distribution of the missing variables. The proposed approach also has the benefit of providing a distribution for the prediction, including the uncertainty inherent in the imputation. Therefore, we can ask questions such as: is it possible this individual is at high risk but we are missing too much information to know for sure? How much would we reduce the uncertainty in our risk prediction by obtaining a particular missing value? This approach is applied to the BPR problem resulting in excellent predictive capability to identify deteriorating patients. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement. [ABSTRACT FROM AUTHOR]

This article deals with nonobserved dyads during the sampling of a network and consecutive issues in the inference of the stochastic block model (SBM). We review sampling designs and recover missing at random (MAR) and not missing at random (NMAR) conditions for the SBM. We introduce variants of the variational EM algorithm for inferring the SBM under various sampling designs (MAR and NMAR) all available as an R package. Model selection criteria based on integrated classification likelihood are derived for selecting both the number of blocks and the sampling design. We investigate the accuracy and the range of applicability of these algorithms with simulations. We explore two real-world networks from ethnology (seed circulation network) and biology (protein–protein interaction network), where the interpretations considerably depend on the sampling designs considered. for this article are available online. [ABSTRACT FROM AUTHOR]

Many surveillance systems of infectious diseases are syndrome-based, capturing patients by clinical manifestation. Only a fraction of patients, mostly severe cases, undergo laboratory validation to identify the underlying pathogen. Motivated by the need to understand transmission dynamics and associate risk factors of enteroviruses causing the hand, foot, and mouth disease (HFMD) in China, we developed a Bayesian spatio-temporal modeling framework for surveillance data of infectious diseases with small validation sets. A novel approach was proposed to sample unobserved pathogen-specific patient counts over space and time and was compared to an existing sampling approach. The practical utility of this framework in identifying key parameters was assessed in simulations for a range of realistic sizes of the validation set. Several designs of sampling patients for laboratory validation were compared with and without aggregation of sparse validation data. The methodology was applied to the 2009 HFMD epidemic in southern China to evaluate transmissibility and the effects of climatic conditions for the leading pathogens of the disease, enterovirus 71, and Coxsackie A16. for this article are available online. [ABSTRACT FROM AUTHOR]

In studies evaluating the accuracy of diagnostic tests, three designs are commonly used, crossover, randomized, and noncomparative. Existing methods for meta-analysis of diagnostic tests mainly consider the simple cases in which the reference test in all or none of the studies can be considered a gold standard test, and in which all studies use either a randomized or noncomparative design. The proliferation of diagnostic instruments and the diversity of study designs create a need for more general methods to combine studies that include or do not include a gold standard test and that use various designs. This article extends the Bayesian hierarchical summary receiver operating characteristic model to network meta-analysis of diagnostic tests to simultaneously compare multiple tests within a missing data framework. The method accounts for correlations between multiple tests and for heterogeneity between studies. It also allows different studies to include different subsets of diagnostic tests and provides flexibility in the choice of summary statistics. The model is evaluated using simulations and illustrated using real data on tests for deep vein thrombosis, with sensitivity analyses. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

This article investigates the problem of matrix completion from the corrupted data, when the additional covariates are available. Despite being seldomly considered in the matrix completion literature, these covariates often provide valuable information for completing the unobserved entries of the high-dimensional target matrix A0. Given a covariate matrix X with its rows representing the row covariates of A0, we consider a column-space-decomposition model A0 = Xβ0 + B0, where β0 is a coefficient matrix and B0 is a low-rank matrix orthogonal to X in terms of column space. This model facilitates a clear separation between the interpretable covariate effects (Xβ0) and the flexible hidden factor effects (B0). Besides, our work allows the probabilities of observation to depend on the covariate matrix, and hence a missing-at-random mechanism is permitted. We propose a novel penalized estimator for A0 by utilizing both Frobenius-norm and nuclear-norm regularizations with an efficient and scalable algorithm. Asymptotic convergence rates of the proposed estimators are studied. The empirical performance of the proposed methodology is illustrated via both numerical experiments and a real data application. [ABSTRACT FROM AUTHOR]

In survey interviews, “Don’t know” (DK) responses are commonly treated as missing data. One way to reduce the rate of such responses is to probe initial DK answers with a follow-up question designed to encourage respondents to give substantive, non-DK responses. However, such probing can also reduce data quality by introducing additional or differential measurement error. We propose a latent variable model for analyzing the effects of probing on responses to survey questions. The model makes it possible to separate measurement effects of probing from true differences between respondents who do and do not require probing. We analyze new data from an experiment, which compared responses to two multi-item batteries of questions with and without probing. In this study, probing reduced the rate of DK responses by around a half. However, it also had substantial measurement effects, in that probed answers were often weaker measures of constructs of interest than were unprobed answers. These effects were larger for questions on attitudes than for pseudo-knowledge questions on perceptions of external facts. The results provide evidence against the use of probing of “Don’t know” responses, at least for the kinds of items and respondents considered in this study. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

In the absence of a unique identifier, combining information from multiple files relies on partially identifying variables (e.g., gender, initials). With a record linkage procedure, these variables are used to distinguish record pairs that belong together (matches) from record pairs that do not belong together (nonmatches). Generally, the combined strength of the partially identifying variables is too low causing imperfect linkage; some true nonmatches are identified as match and, on the other hand, some truematches as nonmatch. To avoid bias in further analyses, it is necessary to correct for imperfect linkage. In this article, pregnancy data fromthe Perinatal Registry of theNetherlandswere used to estimate the associations between the (baseline) characteristics from the first delivery and the time to a second delivery. Because of privacy regulations, no unique identifier was available to determine which pregnancies belonged to the samewoman. To deal with imperfect linkage in a time-to-event setting, wherewe have a file with baseline characteristics and a file with event times, we developed a jointmodel in which the record linkage procedure and the time-to-event analysis are performed simultaneously. R code and example data are available as online supplementalmaterial. [ABSTRACT FROM AUTHOR]

We present a nonparametric Bayesian joint model for multivariate continuous and categorical variables, with the intention of developing a flexible engine for multiple imputation of missing values. The model fuses Dirichlet process mixtures of multinomial distributions for categorical variables with Dirichlet process mixtures of multivariate normal distributions for continuous variables. We incorporate dependence between the continuous and categorical variables by (1) modeling the means of the normal distributions as component-specific functions of the categorical variables and (2) forming distinct mixture components for the categorical and continuous data with probabilities that are linked via a hierarchical model. This structure allows the model to capture complex dependencies between the categorical and continuous data with minimal tuning by the analyst. We apply the model to impute missing values due to item nonresponse in an evaluation of the redesign of the Survey of Income and Program Participation (SIPP). The goal is to compare estimates from a field test with the new design to estimates from selected individuals from a panel collected under the old design. We show that accounting for the missing data changes some conclusions about the comparability of the distributions in the two datasets. We also perform an extensive repeated sampling simulation using similar data from complete cases in an existing SIPP panel, comparing our proposed model to a default application of multiple imputation by chained equations. Imputations based on the proposed model tend to have better repeated sampling properties than the default application of chained equations in this realistic setting. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Our work is motivated by a prostate cancer study aimed at identifying mRNA and miRNA biomarkers that are predictive of cancer recurrence after prostatectomy. It has been shown in the literature that incorporating known biological information on pathway memberships and interactions among biomarkers improves feature selection of high-dimensional biomarkers in relation to disease risk. Biological information is often represented by graphs or networks, in which biomarkers are represented by nodes and interactions among them are represented by edges; however, biological information is often not fully known. For example, the role of microRNAs (miRNAs) in regulating gene expression is not fully understood and the miRNA regulatory network is not fully established, in which case new strategies are needed for feature selection. To this end, we treat unknown biological information as missing data (i.e., missing edges in graphs), different from commonly encountered missing data problems where variable values are missing. We propose a new concept of imputing unknown biological information based on observed data and define the imputed information as the novel biological information. In addition, we propose a hierarchical group penalty to encourage sparsity and feature selection at both the pathway level and the within-pathway level, which, combined with the imputation step, allows for incorporation of known and novel biological information. While it is applicable to general regression settings, we develop and investigate the proposed approach in the context of semiparametric accelerated failure time models motivated by our data example. Data application and simulation studies show that incorporation of novel biological information improves performance in risk prediction and feature selection and the proposed penalty outperforms the extensions of several existing penalties. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

An important practical problem for statistical agencies and central banks that publish economic data is the seasonal adjustment of mixed frequency stock and flow time series. This may arise in practice due to changes in funding of a particular survey. Mathematically, the problem can be reduced to the need to compute imputations, forecasts, and backcasts from a given model of the highest available frequency data. The nonstationarity of the economic time series coupled with the alteration of sampling frequency makes the problem of model estimation and imputation challenging. For flow data the analysis cannot be recast as a missing value problem, so that time series imputation methods are ineffective. We provide explicit formulas and algorithms that allow one to compute the log Gaussian likelihood of the mixed sample, as well as any imputations and forecasts. Formulas for the relevant mean squared error are also derived. We evaluate the methodology through simulations, and illustrate the techniques on some economic time series. [ABSTRACT FROM PUBLISHER]

Over the past decade, doubly robust estimators have been proposed for a variety of target parameters in causal inference and missing data models. These are asymptotically unbiased when at least one of two nuisance working models is correctly specified, regardless of which. While their asymptotic distribution is not affected by the choice of root-nconsistent estimators of the nuisance parameters indexing these working models when all working models are correctly specified, this choice of estimators can have a dramatic impact under misspecification of at least one working model. In this article, we will therefore propose a simple and generic estimation principle for the nuisance parameters indexing each of the working models, which is designed to improve the performance of the doubly robust estimator of interest, relative to the default use of maximum likelihood estimators for the nuisance parameters. The proposed approach locally minimizes the squared first-order asymptotic bias of the doubly robust estimator under misspecification of both working models and results in doubly robust estimators with easy-to-calculate asymptotic variance. It moreover improves the stability of the weights in those doubly robust estimators which invoke inverse probability weighting. Simulation studies confirm the desirable finite-sample performance of the proposed estimators. Supplementary materials for this article are available online. [ABSTRACT FROM PUBLISHER]

Undernutrition, resulting in restricted growth, and quantified here using height-for-agez-scores, is an important contributor to childhood morbidity and mortality. Since all levels of mild, moderate, and severe undernutrition are of clinical and public health importance, it is of interest to estimate the shape of thez-scores’ distributions. We present a finite normal mixture model that uses data on 4.3 million children to make annual country-specific estimates of these distributions for under-5-year-old children in the world’s 141 low- and middle-income countries between 1985 and 2011. We incorporate both individual-level data when available, as well as aggregated summary statistics from studies whose individual-level data could not be obtained. We place a hierarchical Bayesian probit stick-breaking model on the mixture weights. The model allows for nonlinear changes in time, and it borrows strength in time, in covariates, and within and across regional country clusters to make estimates where data are uncertain, sparse, or missing. This work addresses three important problems that often arise in the fields of public health surveillance and global health monitoring. First, data are always incomplete. Second, different data sources commonly use different reporting metrics. Last, distributions, and especially their tails, are often of substantive interest. [ABSTRACT FROM PUBLISHER]

We analyze an incomplete marked point pattern of heat-related 911 calls between the years 2006–2010 in Houston, TX, to primarily investigate conditions that are associated with increased vulnerability to heat-related morbidity and, secondarily, build a statistical model that can be used as a public health tool to predict the volume of 911 calls given a time frame and heat exposure. We model the calls as arising from a nonhomogenous Cox process with unknown intensity measure. By using the kernel convolution construction of a Gaussian process, the intensity surface is modeled using a low-dimensional representation and properly adheres to circular domain constraints. We account for the incomplete observations by marginalizing the joint intensity measure over the domain of the missing marks and also demonstrate model based imputation. We find that spatial regions of high risk for heat-related 911 calls are temporally dynamic with the highest risk occurring in urban areas during the day. We also find that elderly populations have an increased probability of calling 911 with heat-related issues than younger populations. Finally, the age of individuals and hour of the day with the highest intensity of heat-related 911 calls varies by race/ethnicity. Supplementary materials are included with this article. [ABSTRACT FROM AUTHOR]

A practical impediment in adaptive clinical trials is that outcomes must be observed soon enough to apply decision rules to choose treatments for new patients. For example, if outcomes take up to six weeks to evaluate and the accrual rate is one patient per week, on average three new patients will be accrued while waiting to evaluate the outcomes of the previous three patients. The question is how to treat the new patients. This logistical problem persists throughout the trial. Various ad hoc practical solutions are used, none entirely satisfactory. We focus on this problem in phase I–II clinical trials that use binary toxicity and efficacy, defined in terms of event times, to choose doses adaptively for successive cohorts. We propose a general approach to this problem that treats late-onset outcomes as missing data, uses data augmentation to impute missing outcomes from posterior predictive distributions computed from partial follow-up times and complete outcome data, and applies the design’s decision rules using the completed data. We illustrate the method with two cancer trials conducted using a phase I–II design based on efficacy–toxicity trade-offs, including a computer stimulation study. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Ronald Fisher was by all accounts a first-rate mathematician, but he saw himself as a scientist, not a mathematician, and he railed against what George Box called (in his Fisher lecture) “mathematistry.” Mathematics is the indispensable foundation of statistics, but for me the real excitement and value of our subject lies in its application to other disciplines. We should not view statistics as another branch of mathematics and favor mathematical complexity over clarifying, formulating, and solving real-world problems. Valuing simplicity, I describe 10 simple and powerful ideas that have influenced my thinking about statistics, in my areas of research interest: missing data, causal inference, survey sampling, and statistical modeling in general. The overarching theme is that statistics is a missing data problem and the goal is to predict unknowns with appropriate measures of uncertainty. [ABSTRACT FROM PUBLISHER]

Constructing classification rules for accurate diagnosis of a disorder is an important goal in medical practice. In many clinical applications, there is no clinically significant anatomical or physiological deviation that exists to identify the gold standard disease status to inform development of classification algorithms. Despite the absence of perfect disease class identifiers, there are usually one or more disease-informative auxiliary markers along with feature variables that comprise known symptoms. Existing statistical learning approaches do not effectively draw information from auxiliary prognostic markers. We propose a large margin classification method, with particular emphasis on the support vector machine, assisted by available informative markers to classify disease without knowing a subject's true disease status. We view this task as statistical learning in the presence of missing data, and introduce a pseudo-Expectation-Maximization (EM) algorithm to the classification. A major difference between a regular EM algorithm and the algorithm proposed here is that we do not model the distribution of missing data given the observed feature variables either parametrically or semiparametrically. We also propose a sparse variable selection method embedded in the pseudo-EM algorithm. Theoretical examination shows that the proposed classification rule is Fisher consistent, and that under a linear rule, the proposed selection has an oracle variable selection property and the estimated coefficients are asymptotically normal. We apply the methods to build decision rules for including subjects in clinical trials of a new psychiatric disorder and present four applications to data available at the University of California, Irvine Machine Learning Repository. [ABSTRACT FROM AUTHOR]

End-of-life medical expenses are a significant proportion of all health care expenditures. These costs were studied using costs of services from Medicare claims and cause of death (CoD) from death certificates. In the absence of a unique identifier linking the two datasets, common variables identified unique matches for only 33% of deaths. The remaining cases formed cells with multiple cases (32% in cells with an equal number of cases from each file and 35% in cells with an unequal number). We sampled from the joint posterior distribution of model parameters and the permutations that link cases from the two files within each cell. The linking models included the regression of location of death on CoD and other parameters, and the regression of cost measures with a monotone missing data pattern on CoD and other demographic characteristics. Permutations were sampled by enumerating the exact distribution for small cells and by the Metropolis algorithm for large cells. Sparse matrix data structures enabled efficient calculations despite the large dataset (≈1.7 million cases). The procedure generatesmdatasets in which the matches between the two files are imputed. Themdatasets can be analyzed independently and results can be combined using Rubin’s multiple imputation rules. Our approach can be applied in other file-linking applications. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

In this article, we consider imputation in the USDA’s Agricultural Resource Management Survey (ARMS) data, which is a complex, high-dimensional economic dataset. We develop a robust joint model for ARMS data, which requires that variables are transformed using a suitable class of marginal densities (e.g., skew normal family). We assume that the transformed variables may be linked through a Gaussian copula, which enables construction of the joint model via a sequence of conditional linear models. We also discuss the criteria used to select the predictors for each conditional model. For the purpose of developing an imputation method that is conducive to these model assumptions, we propose a regression-based technique that allows for flexibility in the selection of conditional models while providing a valid joint distribution. In this procedure, labeled as iterative sequential regression (ISR), parameter estimates and imputations are obtained using a Markov chain Monte Carlo sampling method. Finally, we apply the proposed method to the full ARMS data, and we present a thorough data analysis that serves to gauge the appropriateness of the resulting imputations. Our results demonstrate the effectiveness of the proposed algorithm and illustrate the specific deficiencies of existing methods. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Diffusion process models are widely used in science, engineering, and finance. Most diffusion processes are described by stochastic differential equations in continuous time. In practice, however, data are typically observed only at discrete time points. Except for a few very special cases, no analytic form exists for the likelihood of such discretely observed data. For this reason, parametric inference is often achieved by using discrete-time approximations, with accuracy controlled through the introduction of missing data. We present a new multiresolution Bayesian framework to address the inference difficulty. The methodology relies on the use of multiple approximations and extrapolation and is significantly faster and more accurate than known strategies based on Gibbs sampling. We apply the multiresolution approach to three data-driven inference problems, one of which features a multivariate diffusion model with an entirely unobserved component. [ABSTRACT FROM PUBLISHER]

The current goal of initial antiretroviral (ARV) therapy is suppression of plasma human immunodeficiency virus (HIV)-1 RNA levels to below 200 copies per milliliter. A proportion of HIV-infected patients who initiate antiretroviral therapy in clinical practice or antiretroviral clinical trials either fail to suppress HIV-1 RNA or have HIV-1 RNA levels rebound on therapy. Frequently, these patients have sustained CD4 cell counts responses and limited or no clinical symptoms and, therefore, have potentially limited indications for altering therapy which they may be tolerating well despite increased viral replication. On the other hand, increased viral replication on therapy leads to selection of resistance mutations to the antiretroviral agents comprising their therapy and potentially cross-resistance to other agents in the same class decreasing the likelihood of response to subsequent antiretroviral therapy. The optimal time to switch antiretroviral therapy to ensure sustained virologic suppression and prevent clinical events in patients who have rebound in their HIV-1 RNA, yet are stable, is not known. Randomized clinical trials to compare early versus delayed switching have been difficult to design and more difficult to enroll. In some clinical trials, such as the AIDS Clinical Trials Group (ACTG) Study A5095, patients randomized to initial antiretroviral treatment combinations, who fail to suppress HIV-1 RNA or have a rebound of HIV-1 RNA on therapy are allowed to switch from the initial ARV regimen to a new regimen, based on clinician and patient decisions. We delineate a statistical framework to estimate the effect of early versus late regimen change using data from ACTG A5095 in the context of two-stage designs. In causal inference, a large class of doubly robust estimators are derived through semiparametric theory with applications to missing data problems. This class of estimators is motivated through geometric arguments and relies on large samples for good performance. By now, several authors have noted that a doubly robust estimator may be suboptimal when the outcome model is misspecified even if it is semiparametric efficient when the outcome regression model is correctly specified. Through auxiliary variables, two-stage designs, and within the contextual backdrop of our scientific problem and clinical study, we propose improved doubly robust, locally efficient estimators of a population mean and average causal effect for early versus delayed switching to second-line ARV treatment regimens. Our analysis of the ACTG A5095 data further demonstrates how methods that use auxiliary variables can improve over methods that ignore them. Using the methods developed here, we conclude that patients who switch within 8 weeks of virologic failure have better clinical outcomes, on average, than patients who delay switching to a new second-line ARV regimen after failing on the initial regimen. Ordinary statistical methods fail to find such differences. This article has online supplementary material. [ABSTRACT FROM AUTHOR]

Choosing the subset of covariates to use in regression or generalized linear models is a ubiquitous problem. The Bayesian paradigm addresses the problem of model uncertainty by considering models corresponding to all possible subsets of the covariates, where the posterior distribution over models is used to select models or combine them via Bayesian model averaging (BMA). Although conceptually straightforward, BMA is often difficult to implement in practice, since either the number of covariates is too large for enumeration of all subsets, calculations cannot be done analytically, or both. For orthogonal designs with the appropriate choice of prior, the posterior probability of any model can be calculated without having to enumerate the entire model space and scales linearly with the number of predictors, p. In this article we extend this idea to a much broader class of nonorthogonal design matrices. We propose a novel method which augments the observed nonorthogonal design by at most p new rows to obtain a design matrix with orthogonal columns and generate the 'missing' response variables in a data augmentation algorithm. We show that our data augmentation approach keeps the original posterior distribution of interest unaltered, and develop methods to construct Rao-Blackwellized estimates of several quantities of interest, including posterior model probabilities of any model, which may not be available from an ordinary Gibbs sampler. Our method can be used for BMA in linear regression and binary regression with nonorthogonal design matrices in conjunction with independent 'spike and slab' priors with a continuous prior component that is a Cauchy or other heavy tailed distribution that may be represented as a scale mixture of normals. We provide simulated and real examples to illustrate the methodology. Supplemental materials for the manuscript are available online. [ABSTRACT FROM AUTHOR]

The continual reassessment method (CRM) is a commonly used dose-finding design for phase I clinical trials. Practical applications of this method have been restricted by two limitations: (1) the requirement that the toxicity outcome needs to be observed shortly after the initiation of the treatment; and (2) the potential sensitivity to the prespecified toxicity probability at each dose. To overcome these limitations, we naturally treat the unobserved toxicity outcomes as missing data, and use the expectation-maximization (EM) algorithm to estimate the dose toxicity probabilities based on the incomplete data to direct dose assignment. To enhance the robustness of the design, we propose prespecifying multiple sets of toxicity probabilities, each set corresponding to an individual CRM model. We carry out these multiple CRMs in parallel, across which model selection and model averaging procedures are used to make more robust inference. We evaluate the operating characteristics of the proposed robust EM-CRM designs through simulation studies and show that the proposed methods satisfactorily resolve both limitations of the CRM. Besides improving the MTD selection percentage, the new designs dramatically shorten the duration of the trial, and are robust to the prespecification of the toxicity probabilities. [ABSTRACT FROM AUTHOR]

In seasonal influenza epidemics, pathogens such as respiratory syncytial virus (RSV) often cocirculate with influenza and cause influenza-like illness (ILI) in human hosts. However, it is often impractical to test for each potential pathogen or to collect specimens for each observed ILI episode, making inference about influenza transmission difficult. In the setting of infectious diseases, missing outcomes impose a particular challenge because of the dependence among individuals. We propose a Bayesian competing-risk model for multiple cocirculating pathogens for inference on transmissibility and intervention efficacies under the assumption that missingness in the biological confirmation of the pathogen is ignorable. Simulation studies indicate a reasonable performance of the proposed model even if the number of potential pathogens is misspecified. They also show that a moderate amount of missing laboratory test results has only a small impact on inference about key parameters in the setting of close contact groups. Using the proposed model, we found that a nonpharmaceutical intervention is marginally protective against transmission of influenza A in a study conducted in elementary schools. [ABSTRACT FROM AUTHOR]

Many scientific, sociological, and economic applications present data that are collected on multiple scales of resolution. One particular form of multiscale data arises when data are aggregated across different scales both longitudinally and by economic sector. Frequently, such datasets experience missing observations in a manner that they can be accurately imputed, while respecting the constraints imposed by the multiscale nature of the data, using the method we propose known as Bayesian multiscale multiple imputation. Our approach couples dynamic linear models with a novel imputation step based on singular normal distribution theory. Although our method is of independent interest, one important implication of such methodology is its potential effect on confidential databases protected by means of cell suppression. In order to demonstrate the proposed methodology and to assess the effectiveness of disclosure practices in longitudinal databases, we conduct a large-scale empirical study using the U.S. Bureau of Labor Statistics Quarterly Census of Employment and Wages (QCEW). During the course of our empirical investigation it is determined that several of the predicted cells are within 1% accuracy, thus causing potential concerns for data confidentiality. [ABSTRACT FROM AUTHOR]

Missing data is a ubiquitous problem in medical and social sciences. It is well known that inferences based only on the complete data may not only lose efficiency, but may also lead to biased results if the data is not missing completely at random (MCAR). The inverse-probability weighting method proposed by Horvitz and Thompson (1952) is a popular alternative when the data is not MCAR. The Horvitz-Thompson method, however, is sensitive to the inverse weights and may suffer from loss of efficiency. In this paper, we propose a unified empirical likelihood approach to missing data problems and explore the use of empirical likelihood to effectively combine unbiased estimating equations when the number of estimating equations is greater than the number of unknown parameters. One important feature of this approach is the separation of the complete data unbiased estimating equations from the incomplete data unbiased estimating equations. The proposed method can achieve semiparametric efficiency if the probability of missingness is correctly specified. Simulation results show that the proposed method has better finite sample performance than its competitors. Supplemental materials for this paper, including proofs of the main theoretical results and the R code used for the NHANES example, are available online on the journal website. [ABSTRACT FROM AUTHOR]

Incomplete longitudinal data often are analyzed with estimating equations for inference on a parameter from a marginal mean regression model. Generalized estimating equations, although commonly used for incomplete longitudinal data, are invalid for data that are not missing completely at random. There exists a class of inverse probability weighted estimating equations that are valid under dropouts missing at random, including an easy-to-implement but inefficient member. A relatively computationally complex semiparametric efficient estimator in this class has been applied to continuous data. A specific form of this estimator is developed for binary data and used as a benchmark for assessing the efficiency of the simpler estimator in a simulation study. Both are applied in the estimation of 15-year cigarette smoking trends in the United States from a cohort of 5077 young adults. The results suggest that declines in smoking from previous reports have been exaggerated. [ABSTRACT FROM AUTHOR]

We propose an incomplete-data, quasi-likelihood framework for estimation and score tests that accommodates both dependent and partially observed data. The motivation comes from genetic association studies, where we address the problems of estimating haplotype frequencies and testing association between a disease and haplotypes of multiple, tightly linked genetic markers, using case-control samples containing related individuals. We consider a more general setting in which the complete data are dependent with marginal distributions following a generalized linear model. We form a vector, Z, whose elements are conditional expectations of the elements of the complete-data vector, given selected functions of the incomplete data. Assuming that the covariance matrix of Z is available, we create an optimal linear estimating function based on Z, which we solve by an iterative method. This approach addresses key difficulties in haplotype frequency estimation and testing problems in related individuals: (a) dependence that is known but can be complicated; (b) data that are incomplete for structural reasons, as well as possibly missing, with different amounts of information for different observations; (c) the need for computational speed to analyze large numbers of markers; and (d) a well-established null model but an alternative model that is unknown and is difficult to specify fully in related individuals. For haplotype analysis, we give sufficient conditions for consistency and asymptotic normality of the estimator and asymptotic x2 null distribution of the score test. We apply the method to test for association of haplotypes with alcoholism in the GAW 14 COGA data set. [ABSTRACT FROM AUTHOR]

In studies of the accuracy of diagnostic tests, it is common that both the diagnostic test itself and the reference test are imperfect. This is the case for the microsatellite instability test, which is routinely used as a prescreening procedure to identify individuals with Lynch syndrome, the most common hereditary colorectal cancer syndrome. The microsatellite instability test is known to have imperfect sensitivity and specificity. Meanwhile, the reference test, mutation analysis, is also imperfect. We evaluate this test via a random effects meta-analysis of 17 studies. Study-specific random effects account for between-study heterogeneity in mutation prevalence, test Sensitivities and specificities under a nonlinear mixed effects model and a Bayesian hierarchical model. Using model selection techniques, we explore a range of random effects models to identify a best-fitting model. We also evaluate sensitivity to the conditional independence assumption between the microsatellite instability test and the mutation analysis by allowing for correlation between them. Finally, we use simulations to illustrate the importance of including appropriate random effects and the impact of overfitting, underfitting, and misfitting on model performance. Our approach can be used to estimate the accuracy of two imperfect diagnostic tests from a meta-analysis of multiple studies or a multicenter study when the prevalence of disease, test sensitivities and/or specificities may be heterogeneous among studies or centers. [ABSTRACT FROM AUTHOR]

We consider novel methods for the computation of model selection criteria in missing-data problems based on the output of the EM algorithm. The methodology is very general and can be applied to numerous situations involving incomplete data within an EM framework, from covariates missing at random in arbitrary regression models to nonignorably missing longitudinal responses and/or covariates. Toward this goal, we develop a class of information criteria for missing-data problems, called ICH, Q, which yields the Akaike information criterion and the Bayesian information criterion as special cases. The computation of ICH, Q requires an analytic approximation to a complicated function, called the H-function, along with output from the EM algorithm used in obtaining maximum likelihood estimates. The approximation to the H-function leads to a large class of information criteria, called ICH͂(k), Q. Theoretical properties of ICH͂(k), Q, including consistency, are investigated in detail. To eliminate the analytic approximation to the H-function, a computationally simpler approximation to ICH, Q, called ICQ, is proposed, the computation of which depends solely on the Q-function of the EM algorithm. Advantages and disadvantages of ICH͂(k), Q and ICQ are discussed and examined in detail in the context of missing-data problems. Extensive simulations are given to demonstrate the methodology and examine the small-sample and large-sample performance of UCH͂(k), Q and ICQ in missing-data problems. An AIDS data set also is presented to illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

We propose a general strategy for variable selection in semiparametric regression models by penalizing appropriate estimating functions. Important applications include semiparametric linear regression with censored responses and semiparametric regression with missing predictors. Unlike the existing penalized maximum likelihood estimators, the proposed penalized estimating functions may not pertain to the derivatives of any objective functions and may be discrete in the regression coefficients. We establish a general asymptotic theory for penalized estimating functions and present suitable numerical algorithms to implement the proposed estimators. In addition, we develop a resampling technique to estimate the variances of the estimated regression coefficients when the asymptotic variances cannot be evaluated directly. Simulation studies demonstrate that the proposed methods perform well in variable selection and variance estimation. We illustrate our methods using data from the Paul Coverdell Stroke Registry. [ABSTRACT FROM AUTHOR]

Many double-blind placebo-controlled randomized experiments with active drugs suffer from complications beyond simple noncompliance. First, the compliance with assigned dose is often partial, with patients taking only part of the assigned dose, whether active or placebo. Second, the blinding may be imperfect in the sense that there may be detectable positive or negative side effects of the active drug, and consequently, simple compliance has to be extended to allow different compliances to active drug and placebo. Efron and Feldman presented an analysis of such a situation and discussed inference for dose-response from the nonrandomized data in the active treatment arm, which stimulated active discussion, including on the role of the intention-to-treat principle in such studies. Here, we formulate the problem within the principal stratification framework of Frangakis and Rubin, which adheres to the intention-to-treat principle, and we present a new analysis of the Efron-Feldman data within this framework. Moreover, we describe precise assumptions under which dose-response can be inferred from such nonrandomized data, which seem debatable in the setting of this example. Although this article only deals in detail with the specific Efron-Feldman data, the same framework can be applied to various circumstances in both natural science and social science. [ABSTRACT FROM AUTHOR]

Multiple imputation was first conceived as a tool that statistical agencies could use to handle nonresponse in large-sample public use surveys. In the last two decades, the multiple-imputation framework has been adapted for other statistical contexts. For example, individual researchers use multiple imputation to handle missing data in small samples, statistical agencies disseminate multiply-imputed data sets for purposes of protecting data confidentiality, and survey methodologists and epidemiologists use multiple imputation to correct for measurement errors. In some of these settings, Rubin's original rules for combining the point and variance estimates from the multiply-imputed data sets are not appropriate, because what is known—and thus the conditional expectations and variances used to derive inferential methods—differs from that in the missing-data context. These applications require new combining rules and methods of inference. In fact, more than 10 combining rules exist in the published literature. This article describes some of the main adaptations of the multiple-imputation framework, including missing data in large and small samples, data confidentiality, and measurement error. It reviews the combining rules for each setting and explains why they differ. Finally, it highlights research topics in extending the multiple-imputation framework. [ABSTRACT FROM AUTHOR]