Auxiliary Covariates Research Articles

PATIENT RECRUITMENT USING ELECTRONIC HEALTH RECORDS UNDER SELECTION BIAS: A TWO-PHASE SAMPLING FRAMEWORK.

Electronic health records (EHRs) are increasingly recognized as a cost-effective resource for patient recruitment in clinical research. However, how to optimally select a cohort from millions of individuals to answer a scientific question of interest remains unclear. Consider a study to estimate the mean or mean difference of an expensive outcome. Inexpensive auxiliary covariates predictive of the outcome may often be available in patients' health records, presenting an opportunity to recruit patients selectively, which may improve efficiency in downstream analyses. In this paper we propose a two-phase sampling design that leverages available information on auxiliary covariates in EHR data. A key challenge in using EHR data for multiphase sampling is the potential selection bias, because EHR data are not necessarily representative of the target population. Extending existing literature on two-phase sampling design, we derive an optimal two-phase sampling method that improves efficiency over random sampling while accounting for the potential selection bias in EHR data. We demonstrate the efficiency gain from our sampling design via simulation studies and an application evaluating the prevalence of hypertension among U.S. adults leveraging data from the Michigan Genomics Initiative, a longitudinal biorepository in Michigan Medicine.

Precipitation data merging via machine learning: Revisiting conceptual and technical aspects

The development of accurate precipitation products of high spatio-temporal coverage is crucial for a wide range of applications. In this context, precipitation data merging (PDM), which entails the blending of satellite-based estimates with ground-based measurements, holds a prominent position, while currently there is an increasing trend in the deployment of machine learning (ML) algorithms in such endeavors. In the light of recent advances in the field, this work discusses key aspects of the PDM problem associated with: a) the conceptual formulation of the problem, that is closely related to the training of ML models and their predictive capacity, b) the selection of products fused, that is associated with the latency of final product and operational applicability of the method, c) the efficiency of single-step and two-step merging approaches, with the former one treating the problem via only regression algorithms, and the latter one via the combined use of classification and regression algorithms. By formulating PDM as a spatio-temporal prediction problem, we define and assess two different training strategies for the ML models, termed as full and per time step strategy, which entail the building of a single or several ML models, respectively. Furthermore, the performance of the full training strategy, which allows the development of predictions in both spatial and temporal dimensions, is assessed in the context of single-step and two-step merging. In each of the three scenarios, three popular ensemble tree-based ML algorithms are employed, i.e., the random forest, gradient boosting and extreme gradient boosting algorithm, resulting in nine merged products. To provide empirical evidence, we employ a datacube composed by ground-based daily precipitation observations, satellite-based and reanalysis estimates, as well as auxiliary covariates, from 1009 uniformly distributed cells (representative of a sampling area of 25 × 25 km), over four countries around the world (Australia, USA, India and Italy). The large-scale experiment indicates that: (i) full training strategy is a competitive alternative to the per time step strategy, since it enables the development of methods with improved accuracy, with respect to performance metrics and reproduction of statistics, but also with higher predictive capability and operational applicability, (ii) two-step merging enables a much better reproduction of precipitation occurrence characteristics, as reflected in the improvement of relevant categorical metrics, the reproduction of probability and autocorrelation coefficient, (iii) no significant difference was noticed in the performance of different ML algorithms.

Statistical Inference For Noisy Matrix Completion Incorporating Auxiliary Information

This 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.

Semi-parametric tensor factor analysis by iteratively projected singular value decomposition

Abstract This paper introduces a general framework of Semi-parametric TEnsor Factor Analysis (STEFA) that focuses on the methodology and theory of low-rank tensor decomposition with auxiliary covariates. Semi-parametric TEnsor Factor Analysis models extend tensor factor models by incorporating auxiliary covariates in the loading matrices. We propose an algorithm of iteratively projected singular value decomposition (IP-SVD) for the semi-parametric estimation. It iteratively projects tensor data onto the linear space spanned by the basis functions of covariates and applies singular value decomposition on matricized tensors over each mode. We establish the convergence rates of the loading matrices and the core tensor factor. The theoretical results only require a sub-exponential noise distribution, which is weaker than the assumption of sub-Gaussian tail of noise in the literature. Compared with the Tucker decomposition, IP-SVD yields more accurate estimators with a faster convergence rate. Besides estimation, we propose several prediction methods with new covariates based on the STEFA model. On both synthetic and real tensor data, we demonstrate the efficacy of the STEFA model and the IP-SVD algorithm on both the estimation and prediction tasks.

Learning conditional variational autoencoders with missing covariates

Conditional variational autoencoders (CVAEs) are versatile deep latent variable models that extend the standard VAE framework by conditioning the generative model with auxiliary covariates. The original CVAE model assumes that the data samples are independent, whereas more recent conditional VAE models, such as the Gaussian process (GP) prior VAEs, can account for complex correlation structures across all data samples. While several methods have been proposed to learn standard VAEs from partially observed datasets, these methods fall short for conditional VAEs. In this work, we propose a method to learn conditional VAEs from datasets in which auxiliary covariates can contain missing values as well. The proposed method augments the conditional VAEs with a prior distribution for the missing covariates and estimates their posterior using amortised variational inference. At training time, our method accounts for the uncertainty associated with the missing covariates while simultaneously maximising the evidence lower bound. We develop computationally efficient methods to learn CVAEs and GP prior VAEs that are compatible with mini-batching. Our experiments on simulated datasets as well as on real-world biomedical datasets show that the proposed method outperforms previous methods in learning conditional VAEs from non-temporal, temporal, and longitudinal datasets.

Smooth and Probabilistic PARAFAC Model with Auxiliary Covariates

As immunological and clinical studies become more complex, there is an increasing need to analyze temporal immunophenotypes alongside demographic and clinical covariates, where each subject receives matrix-valued time series observations for potentially high-dimensional longitudinal features, as well as other static characterizations. Researchers aim to find the low-dimensional embedding of subjects using matrix-valued time series observations and investigate relationships between static clinical responses and the embedding. However, constructing these embeddings can be challenging due to high dimensionality, sparsity, and irregularity in sample collection over time. In addition, the incorporation of static auxiliary covariates is frequently desired during such a construction. To address these issues, we propose a smoothed probabilistic PARAFAC model with covariates (SPACO) that uses auxiliary covariates of interest. We provide extensive simulations to test different aspects of SPACO and demonstrate its application to an immunological dataset from patients with SARS-CoV-2 infection. Supplementary materials for this article are available online.

A Primer on Clustering of Forest Management Units for Reliable Design-Based Direct Estimates and Model-Based Small Area Estimation

This study employs clustering analysis to group forest management units using auxiliary, satellite imagery-derived height metrics and past wall-to-wall tree census data from a natural, uneven-aged forest. Initially, we conducted an exhaustive exploration to determine the optimal number of clusters k, considering a wide range of clustering schemes, indices, and two specific k ranges. The optimal k is influenced by various factors, including the minimum k considered, the selected clustering algorithm, the clustering indices used, and the auxiliary variables. Specifically, the minimum k, the Euclidean distance metric, and the clustering index were instrumental in determining the optimal cluster numbers, with algorithms exerting minimal influence. Unlike traditional validation indices, we assessed the performance of these optimally defined clusters based on direct estimates and additional criteria. Subsequently, our research introduces a twofold methodology for Small Area Estimation (SAE). The first approach focuses on aggregating forest management units at the cluster level to increase the sample size, thereby yielding reliable design-based direct estimates for key forest attributes, including growing stock volume, basal area, tree density, and mean tree height. The second approach prepares area-level data for the future application of model-based estimators, contingent on establishing a strong correlation between target and auxiliary variables. Our methodology has the potential to enhance forest inventory practices across a wide range of forests where area-level auxiliary covariates are available.

Increasing character strength knowledge, interest, and skill: preliminary evidence for a collaborative and multimethod assessment procedure.

The study's objective was to evaluate whether a qualitative, collaborative, and multimethod assessment protocol increased reports of character strength interest, knowledge, and perceived skills. Thirty-two participants completed three phases of data collection. Participants were first screened for well-being, which was used as an auxiliary covariate to order participants into experimental conditions. Selected participants were randomly assigned to a control or collaborative and multimethod assessment (card sort × qualitative interview) condition. Participants completed pre- and post-measures of strength interest, knowledge, and perceived skill. In the final phase, second phase participants were invited to report on strength-related outcomes 24 h post-administration using an online survey. A series of 2 (Assessment Condition) × 3 (Time) mixed ANOVAs were analyzed. Results revealed a significant assessment condition by time interaction for strength knowledge and perceived skill. Participants in the collaborative and multimethod assessment condition reported higher strength knowledge and perceived skills compared to control participants. These effects were maintained for 24 h. The findings offer preliminary yet sizable support for using collaborative and multimethod assessment procedures to increase strength knowledge and perceived skill. Because of the qualitative, collaborative, and individualized nature of our assessment protocol, the findings offer a low-cost and contextually bound pathway to increase strength-based outcomes.

Estimating the average treatment effect in randomized clinical trials with all-or-none compliance

Noncompliance is a common intercurrent event in randomized clinical trials that raises important questions about analytical objectives and approaches. Motivated by the Multiple Risk Factor Intervention Trial (MRFIT), we consider how to estimate the average treatment effect (ATE) in randomized trials with all-or-none compliance. Confounding is a major challenge in estimating the ATE, and conventional methods for confounding adjustment typically require the assumption of no unmeasured confounders which may be difficult to justify. Using randomized treatment assignment as an instrumental variable, the ATE can be identified in the presence of unmeasured confounders under suitable assumptions, including an assumption that limits the effect-modifying activities of unmeasured confounders. We describe and compare several estimation methods based on different modeling assumptions. Some of these methods are able to incorporate information from auxiliary covariates for improved efficiency without introducing bias. The different methods are compared in a simulation study and applied to the MRFIT.

Nonparametric regression with responses missing at random and the scale depending on auxiliary covariates

Nonparametric regression with missing at random (MAR) responses, univariate regression component of interest, and the scale function depending on both the predictor and auxiliary covariates, is considered. The asymptotic theory suggests that both heteroscedasticity and MAR mechanism affect the sharp constant of the minimax mean integrated squared error (MISE) convergence. Our sharp minimax procedure is based on the estimation of unknown nuisance scale function, design density and availability likelihood. The estimator is adaptive to the missing mechanism and unknown smoothness of the estimated regression function. Simulation studies and real examples also justify practical feasibility of the proposed method for this complex regression setting.

ZAP:Z-Value Adaptive Procedures for False Discovery Rate Control with Side Information

AbstractAdaptive multiple testing with covariates is an important research direction that has gained major attention in recent years. It has been widely recognised that leveraging side information provided by auxiliary covariates can improve the power of false discovery rate (FDR) procedures. Currently, most such procedures are devised with p-values as their main statistics. However, for two-sided hypotheses, the usual data processing step that transforms the primary statistics, known as p-values, into p-values not only leads to a loss of information carried by the main statistics, but can also undermine the ability of the covariates to assist with the FDR inference. We develop a p-value based covariate-adaptive (ZAP) methodology that operates on the intact structural information encoded jointly by the p-values and covariates. It seeks to emulate the oracle p-value procedure via a working model, and its rejection regions significantly depart from those of the p-value adaptive testing approaches. The key strength of ZAP is that the FDR control is guaranteed with minimal assumptions, even when the working model is misspecified. We demonstrate the state-of-the-art performance of ZAP using both simulated and real data, which shows that the efficiency gain can be substantial in comparison with p-value-based methods. Our methodology is implemented in the R package zap.

Considerations for Using Multiple Imputation in Propensity Score-Weighted Analysis - A Tutorial with Applied Example.

PurposePropensity score-weighting for confounder control and multiple imputation to counter missing data are both widely used methods in epidemiological research. Combination of the two is not trivial and requires a number of decisions to produce valid inference. In this tutorial, we outline the assumptions underlying each of the methods, present our considerations in combining the two, discuss the methodological and practical implications of our choices and briefly point to alternatives. Throughout we apply the theory to a research project about post-traumatic stress disorder in Syrian refugees.Patients and MethodsWe detail how we used logistic regression-based propensity scores to produce “standardized mortality ratio”-weights and Substantive Model Compatible-Full Conditional Specification for multiple imputation of missing data to get the estimate of association. Finally, a percentile confidence interval was produced by bootstrapping.ResultsA simple propensity score model with weight truncation at 1st and 99th percentile obtained acceptable balance on all covariates and was chosen as our model. Due to computational issues in the multiple imputation, two levels of one of the substantive model covariates and two levels of one of the auxiliary covariates were collapsed. This slightly modified propensity score model was the substantive model in the SMC-FCS multiple imputation, and regression models were set up for all partially observed covariates. We set the number of imputations to 10 and number of iterations to 40. We produced 999 bootstrap estimates to compute the 95-percentile confidence interval.ConclusionCombining propensity score-weighting and multiple imputation is not a trivial task. We present considerations necessary to do so, realizing it is demanding in terms of both workload and computational time; however, we do not consider the former a drawback: it makes some of the underlying assumptions explicit and the latter may be a nuisance that will diminish with faster computers and better implementations.

Statistical analysis of spatially resolved transcriptomic data by incorporating multiomics auxiliary information.

Effective control of false discovery rate is key for multiplicity problems. Here, we consider incorporating informative covariates from external datasets in the multiple testing procedure to boost statistical power while maintaining false discovery rate control. In particular, we focus on the statistical analysis of innovative high-dimensional spatial transcriptomic data while incorporating external multiomics data that provide distinct but complementary information to the detection of spatial expression patterns. We extend OrderShapeEM, an efficient covariate-assisted multiple testing procedure that incorporates one auxiliary study, to make it permissible to incorporate multiple external omics studies, to boost statistical power of spatial expression pattern detection. Specifically, we first use a recently proposed computationally efficient statistical analysis method, spatial pattern recognition via kernels, to produce the primary test statistics for spatial transcriptomic data. Afterwards, we construct the auxiliary covariate by combining information from multiple external omics studies, such as bulk and single-cell RNA-seq data using the Cauchy combination rule. Finally, we extend and implement the integrative analysis method OrderShapeEM on the primary P-values along with auxiliary data incorporating multiomics information for efficient covariate-assisted spatial expression analysis. We conduct a series of realistic simulations to evaluate the performance of our method with known ground truth. Four case studies in mouse olfactory bulb, mouse cerebellum, human breast cancer, and human heart tissues further demonstrate the substantial power gain of our method in detecting genes with spatial expression patterns compared to existing classic approaches that do not utilize any external information.

Improving estimation efficiency for multivariate failure time data with auxiliary covariates

For the analysis of multivariate failure time data when the primary covariates are incomplete but the auxiliary covariates for them are available for the whole cohort subjects, an estimated quadratic inference function method is developed to improve the estimation efficiency under the marginal hazard model with common baseline hazard function. Both the auxiliary information and the intra-cluster correlation between the failure times are incorporated in the estimation procedure. The proposed estimator is shown to be consistent and asymptotically normal. Simulation studies demonstrate that when the intra-cluster correlation is strong or moderate, the proposed method gains noticeable efficiency compared to other existing methods.

The Proportional Mean Residual Life Regression Model with Cure Fraction and Auxiliary Covariate

The Proportional Mean Residual Life Regression Model with Cure Fraction and Auxiliary Covariate

Estimated quadratic inference function for correlated failure time data.

An estimated quadratic inference function method is proposed for correlated failure time data with auxiliary covariates. The proposed method makes efficient use of the auxiliary information for the incomplete exposure covariates and preserves the property of the quadratic inference function method that requires the covariates to be completely observed. It can improve the estimation efficiency and easily deal with the situation when the cluster size is large. The proposed estimator which minimizes the estimated quadratic inference function is shown to be consistent and asymptotically normal. A chi-squared test based on the estimated quadratic inference function is proposed to test hypotheses about the regression parameters. The small-sample performance of the proposed method is investigated through extensive simulation studies. The proposed method is then applied to analyze the Study of Left Ventricular Dysfunction (SOLVD) data as anillustration.

Synthetic Control Method: A tool for comparative case studies in economic history

AbstractThe Synthetic Control Method (SCM) has become a widely used tool in both identifying and estimating the causal impact of policies, shocks, and interventions of interest on economic and social outcomes. The technique has become particularly popular in estimating the effect of these shocks on a single treated unit. As a transparent and data‐driven statistical technique, the goal of the SCM is to construct an artificial control group for the treated unit that has similar pretreatment characteristics but has not undergone the treatment itself thus developing a plausible counterfactual against which impacts resulting from structural changes can be evaluated as part of a historical investigation. The method works well when the control group balances pre‐intervention outcomes and auxiliary covariates as much as possible. In spite of its widespread adoption, the use of the SCM in comparative economic history has lagged behind other areas of economics. In this article, we critically review the properties of the SCM and discuss the necessary conditions for a plausible application of the technique to comparative economic history in support of research designed to answer some of the long‐running historical questions and demonstrate the potential to use SCM in comparative economic history studies by estimating the impact of the oil discovery in the 1920s on Venezuela's long‐term economic growth.

Empirical analysis of current status data for additive hazards model with auxiliary covariates

Empirical analysis of current status data for additive hazards model with auxiliary covariates

Synthetic Controls with Staggered Adoption

AbstractStaggered adoption of policies by different units at different times creates promising opportunities for observational causal inference. Estimation remains challenging, however, and common regression methods can give misleading results. A promising alternative is the synthetic control method (SCM), which finds a weighted average of control units that closely balances the treated unit’s pre-treatment outcomes. In this paper, we generalize SCM, originally designed to study a single treated unit, to the staggered adoption setting. We first bound the error for the average effect and show that it depends on both the imbalance for each treated unit separately and the imbalance for the average of the treated units. We then propose ‘partially pooled’ SCM weights to minimize a weighted combination of these measures; approaches that focus only on balancing one of the two components can lead to bias. We extend this approach to incorporate unit-level intercept shifts and auxiliary covariates. We assess the performance of the proposed method via extensive simulations and apply our results to the question of whether teacher collective bargaining leads to higher school spending, finding minimal impacts. We implement the proposed method in the augsynth R package.

Bayesian clustered coefficients regression with auxiliary covariates assistant random effects

In regional economics research, a problem of interest is to detect similarities between regions, and estimate their shared coefficients in economics models. In this article, we propose a mixture of finite mixtures clustered regression model with auxiliary covariates that account for similarities in demographic or economic characteristics over a spatial domain. Our Bayesian construction provides both inference for number of clusters and clustering configurations, and estimation for parameters for each cluster. Empirical performance of the proposed model is illustrated through simulation experiments, and further applied to a study of influential factors for monthly housing cost in Georgia.