Vector Of Covariates Research Articles

Median and quantile conditional copulas

Abstract This article studies the conditional dependency between random variables, conditionally upon a covariate (vector). The conditional copula fully characterizes this conditional dependency. A way to summarize this dependence structure taking into account the impact of the covariate is via the average conditional copula, which under fairly general conditions coincides with the partial copula. A mean is just one way to summarize this conditional dependence behaviour. In this article, we introduce the notions of median conditional copula and more generally quantile conditional copula. We investigate the existence of these concepts and establish explicit expressions for calculating them. Examples are given to illustrate the concepts, and the practical use of them is demonstrated in real data examples.

Estimation of a regular conditional functional by conditional U‐statistic regression

U‐statistics constitute a large class of estimators, generalizing the empirical mean of a random variable to sums over every ‐tuple of distinct observations of . They may be used to estimate a regular functional of the law of . When a vector of covariates is available, a conditional U‐statistic describes the effect of on the conditional law of given , by estimating a regular conditional functional . We state nonasymptotic bounds of general conditional U‐statistics and study their asymptotics too. Assuming a parametric model of the conditional functional of interest, we propose a regression‐type estimator based on conditional U‐statistics. Its theoretical properties are derived, first in a nonasymptotic framework and then in two different asymptotic regimes. Some examples are given to illustrate our methods.

A Projection Approach to Local Regression with Variable-Dimension Covariates

Incomplete covariate vectors are known to be problematic for estimation and inferences on model parameters, but their impact on prediction performance is less understood. We develop an imputation-free method that builds on a random partition model admitting variable-dimension covariates. Cluster-specific response models further incorporate covariates via linear predictors, facilitating estimation of smooth prediction surfaces with relatively few clusters. We exploit marginalization techniques of Gaussian kernels to analytically project response distributions according to any pattern of missing covariates, yielding a local regression with internally consistent uncertainty propagation that uses only one set of coefficients per cluster. Aggressive shrinkage of these coefficients regulates uncertainty due to missing covariates. The method allows in- and out-of-sample prediction for any missingness pattern, even if the pattern in a new subject’s incomplete covariate vector was not seen in the training data. We develop an MCMC algorithm for posterior sampling that improves a computationally expensive update for latent cluster allocation. Finally, we demonstrate the model’s effectiveness for nonlinear point and density prediction under various circumstances by comparing with other recent methods for regression of variable dimensions on synthetic and real data. Supplemental materials for this article are available online.

Nonparametric estimation of the relative error regression for twice censored and dependent data

Let ( Y i ) 1 ≤ i ≤ n be a sequence of dependent random variables (r.v.) of interest distributed as Y and ( X i ) 1 ≤ i ≤ n be a corresponding d−dimensional vector of covariates taking values on ℝ d . The r.v. Y is twice censored and satisfies the α−mixing property. In this article, we are interested in the relative error regression estimation in the case of twice-censored data under strong mixing conditions. Under suitable assumptions, the estimator’s strong uniform almost sure consistency with rate and asymptotic normality are established. We have highlighted the covariance term, which is relatively uncommon in this context. Furthermore, we give a result about the α-mixing rate in the case of twice-censoring. As far as we know, there is no analogous result with proof in the context of twice-censoring. A simulation study is conducted in both one and two dimensions for the covariate to highlight the performance of our estimator.

Estimating the incapacitation effect among first-time incarcerated offenders

Objectives: To estimate how many offenses are averted through the incapacitation of first-time incarcerated offenders with sentences of two years or less. Methods: The counterfactual challenge of estimating criminal acts that would have been committed had the offender not been incarcerated is approached utilizing a matching design. Data comprise all offenders convicted in Sweden in 2018, matched on a vector of time-stable and time-varying covariates drawn from an extensive set of Swedish registers. Each incarcerated offender is matched to a nonincarcerated offender whose offending frequency is used to infer the incapacitation effect. Full sample estimates are provided as well as subgroup estimates for males, females, and various risk groups. Results: The annual incapacitation effect for first-time incarcerated offenders is estimated to be 0.53 when measured as the number of averted convictions and 1.14 when measured as the number of averted offenses that would have resulted in a conviction. For males, the annual number of convictions averted through incapacitation is 0.51, and for females 0.37. For the highest risk group, the annual number of averted convictions is 1.22, and the number of averted offenses resulting in conviction is 2.55. For offenders in the low-to-medium risk groups, the corresponding figures are approximately 0.31 averted convictions and approximately 0.68 averted offenses. Conclusion: For first-time incarcerated offenders, the incapacitation effect is modest and the heterogeneous effects found across different risk groups warrant considering whether the crime-preventive effect is sufficiently large for low-risk inmates and whether noncustodial sanctions might constitute an alternative that would ease overcrowding without producing any considerable risk for costs in terms of recidivism.

Efficient data integration under prior probability shift.

Conventional supervised learning usually operates under the premise that data are collected from the same underlying population. However, challenges may arise when integrating new data from different populations, resulting in a phenomenon known as dataset shift. This paper focuses on prior probability shift, where the distribution of the outcome varies across datasets but the conditional distribution of features given the outcome remains the same. To tackle the challenges posed by such shift, we propose an estimation algorithm that can efficiently combine information from multiple sources. Unlike existing methods that are restricted to discrete outcomes, the proposed approach accommodates both discrete and continuous outcomes. It also handles high-dimensional covariate vectors through variable selection using an adaptive least absolute shrinkage and selection operator penalty, producing efficient estimates that possess the oracle property. Moreover, a novel semiparametric likelihood ratio test is proposed to check the validity of prior probability shift assumptions by embedding the null conditional density function into Neyman's smooth alternatives (Neyman, 1937) and testing study-specific parameters. We demonstrate the effectiveness of our proposed method through extensive simulations and a real data example. The proposed methods serve as a useful addition to the repertoire of tools for dealing dataset shifts.

Refinements on the exact method to solve the numerical difficulties in fitting the log binomial regression model for estimating relative risk

Fitting a log binomial regression model using standard software can result in numerical difficulties because its functional form does not restrict the estimated probabilities to values not exceeding unity. The common approaches to resolve the issue are to introduce a constraint to limit the results of each iteration. However, if the ML solution lies on the boundary of the allowable parameter space, some fitted probabilities are equal to unity (named as boundary vector). The common approaches have trouble dealing with those boundary vectors and can only reach somewhere before the ML solution. Previously a remedy has been proposed, but without the details necessary to implement it. Here we provide these details, including formulae for estimating the covariances essential to implement the method, an explanation of inter-dependency between coefficient estimates, and a proof that the method can be implemented in general. Code written for R implements choice of fitting algorithms, finding appropriate starting values, identifying the covariate vector(s) with a fitted probability of unity, and strategies for covariate ordering to handle the issues caused by the common values in two distinct boundary vectors. The model-fitting results are compared with two alternative methods by simulation and example data.

Research on Microteaching Mode of College English Courses Based on Regression Network Models

Abstract This paper determines the solution vector of ELT proficiency constraint covariates using the correlation fusion approach, the proficiency prediction control objective function is constructed, and the education process’ quantitative recursive properties are discovered. The K-means algorithm is employed to obtain the predicted values of the resource limitation vector for ELT competence assessment, obtain the similarity of the distribution of teaching resources, combine linear regression grouping and integrate the ranking parameters for ELT competence assessment, obtain the characteristics of the data probability density, and finish evaluating the teaching model. The results show that the maximum utilization value reaches 99.03% by assessing English teaching ability through the K-means algorithm and linear regression, which indicates that the reasonable use of mobile Internet can enhance students’ English teaching level and ensure the efficiency of teaching resources utilization.

A modified Nadaraya–Watson procedure for variable selection and nonparametric prediction with missing data

We propose a new method for variable selection and prediction under a nonparametric regression setting, where a covariate may be missing either because its value is hidden from the observer or because it is inapplicable to the particular subject being observed. Despite its practical relevance, the problem has received little attention in the literature and its solutions are largely non-existent. Our proposal hinges on the construction of a modified Nadaraya–Watson estimator of the conditional mean regression function, with its bandwidths regularised to select variables and its weights adapted to accommodate different types of missingness. The method allows for information sharing across different missing data patterns without affecting consistency of the estimator. Unlike other conventional methods such as those based on imputations or likelihoods, our method requires only mild assumptions on the model and the missingness mechanism. For prediction we focus on finding relevant variables for predicting mean responses, conditional on covariate vectors subject to a given type of missingness. Our theoretical and numerical results show that the new method is consistent in variable selection and yields better prediction accuracy compared to existing methods.

Local prediction pools

AbstractWe propose local prediction pools as a method for combining the predictive distributions of a set of experts conditional on a set of variables believed to be related to the predictive accuracy of the experts. This is done in a two‐step process where we first estimate the conditional predictive accuracy of each expert given a vector of covariates—or pooling variables—and then combine the predictive distributions of the experts conditional on this local predictive accuracy. To estimate the local predictive accuracy of each expert, we introduce the simple, fast, and interpretable caliper method. Expert pooling weights from the local prediction pool approaches the equal weight solution whenever there is little data on local predictive performance, making the pools robust and adaptive. We also propose a local version of the widely used optimal prediction pools. Local prediction pools are shown to outperform the widely used optimal linear pools in a macroeconomic forecasting evaluation and in predicting daily bike usage for a bike rental company.

A hierarchical Bayesian analysis for bivariate Weibull distribution under left-censoring scheme

This paper presents a novel approach for analyzing bivariate positive data, taking into account a covariate vector and left-censored observations, by introducing a hierarchical Bayesian analysis. The proposed method assumes marginal Weibull distributions and employs either a usual Weibull likelihood or Weibull–Tobit likelihood approaches. A latent variable or frailty is included in the model to capture the possible correlation between the bivariate responses for the same sampling unit. The posterior summaries of interest are obtained through Markov Chain Monte Carlo methods. To demonstrate the effectiveness of the proposed methodology, we apply it to a bivariate data set from stellar astronomy that includes left-censored observations and covariates. Our results indicate that the new bivariate model approach, which incorporates the latent factor to capture the potential dependence between the two responses of interest, produces accurate inference results. We also compare the two models using the different likelihood approaches (Weibull or Weibull–Tobit likelihoods) in the application. Overall, our findings suggest that the proposed hierarchical Bayesian analysis is a promising approach for analyzing bivariate positive data with left-censored observations and covariate information.

The distribution of child physicians and early academic achievement.

To describe the distribution of pediatricians and family physicians (child physicians) across school districts and examine the association between physician supply and third-grade test scores. Data come from the January 2020 American Medical Association Physician Masterfile, the 2009-2013 and 2014-2018 waves of American Community Survey 5-Year Data, and the Stanford Education Data Archive (SEDA), which uses test scores from all U.S. public schools. We use covariate data provided by SEDA to describe student populations. This descriptive analysis constructs a physician-to-child-population ratio for every school district in the country and describes the child population served by the current distribution of physicians. We fit a set of multivariable regression models to estimate the associations between district test score outcomes and district physician supply. Our model includes state fixed effects to control for unobservable state-level factors, as well as a covariate vector of sociodemographic characteristics. Public data from three sources were matched by district ID. Physicians are highly unequally distributed across districts: nearly 3640 (29.6%) of 12,297 districts have no child physician, which includes 49% of rural districts. Rural children of color in particular have very little access to pediatric care, and this inequality is more extreme when looking exclusively at pediatricians. Districts that have higher child physician supplies tend to have higher academic test scores in early education, independent of community socioeconomic status and racial/ethnic composition. While the national data show this positive relationship (0.012 SD, 95% CI, 0.0103-0.0127), it is most pronounced for districts in the bottom tertile of physician supply (0.163 SD, 95% CI, 0.108-0.219). Our study demonstrates a highly unequal distribution of child physicians in the U.S., and that children with less access to physicians have lower academic performance in early education.

Decomposition and reproducing property of local polynomial equivalent kernels in varying coefficient models

ABSTRACT We consider local polynomial estimation for varying coefficient models and derive corresponding equivalent kernels that provide insights into the role of smoothing on the data and fill a gap in the literature. We show that the asymptotic equivalent kernels have an explicit decomposition with three parts: the inverse of the conditional moment matrix of covariates given the smoothing variable, the covariate vector, and the equivalent kernels of univariable local polynomials. We discuss finite-sample reproducing property which leads to zero bias in linear models with interactions between covariates and polynomials of the smoothing variable. By expressing the model in a centered form, equivalent kernels of estimating the intercept function are asymptotically identical to those of univariable local polynomials and estimators of slope functions are local analogues of slope estimators in linear models with weights assigned by equivalent kernels. Two examples are given to illustrate the weighting schemes and reproducing property.

Comments on: Nonparametric estimation in mixture cure models with covariates

This paper discusses the invited paper by López-Cheda, Peng and Jácome on nonparametric mixture cure models with covariates. An alternative estimation procedure is proposed in this context. The situation when the two covariate vectors (the one in the incidence and in the latency parts) share some, but not all, their covariates is also considered. Some technical aspects in the assumptions, results and proofs of the invited paper are also discussed. Comments on the simulations and the real-data application are included. Finally, possible interesting topics for further research in this field are briefly discussed.

Effects of Antidepressants on COVID-19 Outcomes: Retrospective Study on Large-Scale Electronic Health Record Data.

Antidepressants exert an anticholinergic effect in varying degrees, and various classes of antidepressants can produce a different effect on immune function. While the early use of antidepressants has a notional effect on COVID-19 outcomes, the relationship between the risk of COVID-19 severity and the use of antidepressants has not been properly investigated previously owing to the high costs involved with clinical trials. Large-scale observational data and recent advancements in statistical analysis provide ample opportunity to virtualize a clinical trial to discover the detrimental effects of the early use of antidepressants. We primarily aimed to investigate electronic health records for causal effect estimation and use the data for discovering the causal effects of early antidepressant use on COVID-19 outcomes. As a secondary aim, we developed methods for validating our causal effect estimation pipeline. We used the National COVID Cohort Collaborative (N3C), a database aggregating health history for over 12 million people in the United States, including over 5 million with a positive COVID-19 test. We selected 241,952 COVID-19-positive patients (age >13 years) with at least 1 year of medical history. The study included a 18,584-dimensional covariate vector for each person and 16 different antidepressants. We used propensity score weighting based on the logistic regression method to estimate causal effects on the entire data. Then, we used the Node2Vec embedding method to encode SNOMED-CT (Systematized Nomenclature of Medicine-Clinical Terms) medical codes and applied random forest regression to estimate causal effects. We used both methods to estimate causal effects of antidepressants on COVID-19 outcomes. We also selected few negatively effective conditions for COVID-19 outcomes and estimated their effects using our proposed methods to validate their efficacy. The average treatment effect (ATE) of using any one of the antidepressants was -0.076 (95% CI -0.082 to -0.069; P<.001) with the propensity score weighting method. For the method using SNOMED-CT medical embedding, the ATE of using any one of the antidepressants was -0.423 (95% CI -0.382 to -0.463; P<.001). We applied multiple causal inference methods with novel application of health embeddings to investigate the effects of antidepressants on COVID-19 outcomes. Additionally, we proposed a novel drug effect analysis-based evaluation technique to justify the efficacy of the proposed method. This study offers causal inference methods on large-scale electronic health record data to discover the effects of common antidepressants on COVID-19 hospitalization or a worse outcome. We found that common antidepressants may increase the risk of COVID-19 complications and uncovered a pattern where certain antidepressants were associated with a lower risk of hospitalization. While discovering the detrimental effects of these drugs on outcomes could guide preventive care, identification of beneficial effects would allow us to propose drug repurposing for COVID-19 treatment.

Validation with single-step SNPBLUP shows that evaluations can continue using a single mean of genotyped individuals, even with multiple breeds

BackgroundIn genomic prediction, it is common to centre the genotypes of single nucleotide polymorphisms based on the allele frequencies in the current population, rather than those in the base generation. The mean breeding value of non-genotyped animals is conditional on the mean performance of genotyped relatives, but can be corrected by fitting the mean performance of genotyped individuals as a fixed regression. The associated covariate vector has been referred to as a ‘J-factor’, which if fitted as a fixed effect can improve the accuracy and dispersion bias of sire genomic estimated breeding values (GEBV). To date, this has only been performed on populations with a single breed. Here, we investigated whether there was any benefit in fitting a separate J-factor for each breed in a three-way crossbred population, and in using pedigree-based expected or genome-based estimated breed fractions to define the J-factors.ResultsFor body weight at 7 days, dispersion bias decreased when fitting multiple J-factors, but only with a low proportion of genotyped individuals with selective genotyping. On average, the mean regression coefficients of validation records on those of GEBV increased with one J-factor compared to none, and further increased with multiple J-factors. However, for body weight at 35 days this was not observed. The accuracy of GEBV remained unchanged regardless of the J-factor method used. Differences between the J-factor methods were limited with correlations approaching 1 for the estimated covariate vector, the estimated coefficients of the regression on the J-factors, and the GEBV.ConclusionsBased on our results and in the particular design analysed here, i.e. all the animals with phenotype are of the same type of crossbreds, fitting a single J-factor should be sufficient, to reduce dispersion bias. Fitting multiple J-factors may reduce dispersion bias further but this depends on the trait and genotyping rate. For the crossbred population analysed, fitting multiple J-factors has no adverse consequences and if this is done, it does not matter if the breed fractions used are based on the pedigree-expectation or the genomic estimates. Finally, when GEBV are estimated from crossbred data, any observed bias can potentially be reduced by including a straightforward regression on actual breed proportions.

FUNCTIONAL SEQUENTIAL TREATMENT ALLOCATION WITH COVARIATES

We consider a sequential treatment problem with covariates. Given a realization of the covariate vector, instead of targeting the treatment with highest conditional expectation, the decision-maker targets the treatment which maximizes a general functional of the conditional potential outcome distribution, e.g., a conditional quantile, trimmed mean, or a socioeconomic functional such as an inequality, welfare, or poverty measure. We develop expected regret lower bounds for this problem and construct a near minimax optimal sequential assignment policy.

The Strong Consistency for the Estimators of Longitudinal Data in Semiparametric Regression Model with ρ ̃-Mixing Errors

Consider the following semiparametric regression model for longitudinal data with - mixing errors: , where, the response variable and the covariate vector taken from the -th subject at time , is the - mixing random variables, We establish a strong consistency for the least squares estimator of the parametric and the estimator of the non-parametric function under some mild conditions.

A Two-Sample Conditional Distribution Test Using Conformal Prediction and Weighted Rank Sum

We consider the problem of testing the equality of conditional distributions of a response variable given a vector of covariates between two populations. Such a hypothesis testing problem can be motivated from various machine learning and statistical inference scenarios, including transfer learning and causal predictive inference. We develop a nonparametric test procedure inspired from the conformal prediction framework. The construction of our test statistic combines recent developments in conformal prediction with a novel choice of conformity score, resulting in a weighted rank-sum test statistic that is valid and powerful under general settings. To our knowledge, this is the first successful attempt of using conformal prediction for testing statistical hypotheses beyond exchangeability. Our method is suitable for modern machine learning scenarios where the data has high dimensionality and large sample sizes, and can be effectively combined with existing classification algorithms to find good conformity score functions. The performance of the proposed method is demonstrated in various numerical examples.

Partial Identification of Personalized Treatment Response with Trial-reported Analyses of Binary Subgroups.

Medical journals have adhered to a reporting practice that seriously limits the usefulness of published trial findings. Medical decision makers commonly observe many patient covariates and seek to use this information to personalize treatment choices. Yet standard summaries of trial findings only partition subjects into broad subgroups, typically binary categories. Given this reporting practice, we study the problem of inference on long mean treatment outcomes E[y(t)|x], where t is a treatment, y(t) is a treatment outcome, and the covariate vector x has length K, each component being a binary variable. The available data are estimates of {E[y(t)|x k = 0], E[y(t)|x k = 1], P(x k )}, k = 1,..., K reported in journal articles. We show that reported trial findings partially identify {E[y(t)|x], P(x)}. Illustrative computations demonstrate that the summaries of trial findings in journal articles may imply only wide bounds on long mean outcomes. One can realistically tighten inferences if one can combine reported trial findings with credible assumptions having identifying power, such as bounded-variation assumptions.