Vector Of Covariates Research Articles

Traditional and Rank-Based Tests for Ordered Alternatives in a Cluster Correlated Model.

Methods for the analysis of one-factor randomized groups designs with ordered treatments are well established, but they do not apply in the case of more complex experiments. This article describes ordered treatment methods based on maximum-likelihood and robust estimation that apply to designs with clustered data, including those with a vector of covariates. The contrast coefficients proposed for the ordered treatment estimates yield higher power than those advocated by Abelson and Tukey; the proposed robust estimation method is shown (using theory and simulation) to yield both high power and robustness to outliers. Extensions for nonmonotonic alternatives are easily obtained.

Targeted estimation of heterogeneous treatment effect in observational survival analysis.

The aim of clinical effectiveness research using repositories of electronic health records is to identify what health interventions 'work best' in real-world settings. Since there are several reasons why the net benefit of intervention may differ across patients, current comparative effectiveness literature focuses on investigating heterogeneous treatment effect and predicting whether an individual might benefit from an intervention. The majority of this literature has concentrated on the estimation of the effect of treatment on binary outcomes. However, many medical interventions are evaluated in terms of their effect on future events, which are subject to loss to follow-up. In this study, we describe a framework for the estimation of heterogeneous treatment effect in terms of differences in time-to-event (survival) probabilities. We divide the problem into three phases: (1) estimation of treatment effect conditioned on unique sets of the covariate vector; (2) identification of features important for heterogeneity using non-parametric variable importance methods; and (3) estimation of treatment effect on the reference classes defined by the previously selected features, using one-step Targeted Maximum Likelihood Estimation. We conducted a series of simulation studies and found that this method performs well when either sample size or event rate is high enough and the number of covariates contributing to the effect heterogeneity is moderate. An application of this method to a clinical case study was conducted by estimating the effect of oral anticoagulants on newly diagnosed non-valvular atrial fibrillation patients using data from the UK Clinical Practice Research Datalink.

Instrument search in pseudo-likelihood approach for nonignorable nonresponse

With nonignorable nonresponse, an effective method to construct valid estimators of population parameters is to use a covariate vector called instrument that can be excluded from the nonresponse propensity, but are associated with the response even when other covariates are conditioned. The existing work in this approach assumes such an instrument is given, which is frequently not the case in applications. In this paper, we investigate how to search for an instrument from a given set of covariates, based on a pseudo likelihood approach assuming a parametric distribution of response conditioned on covariates and a totally unspecified nonresponse propensity. We propose a method and show that it produces a consistent instrument selection as the sample size tends to infinity, under some regularity conditions. The proposed method is examined in a simulation study and illustrated in a real data example.

Variable screening for survival data in the presence of heterogeneous censoring

AbstractVariable screening for censored survival data is most challenging when both survival and censoring times are correlated with an ultrahigh‐dimensional vector of covariates. Existing approaches to handling censoring often make use of inverse probability weighting by assuming independent censoring with both survival time and covariates. This is a convenient but rather restrictive assumption which may be unmet in real applications, especially when the censoring mechanism is complex and the number of covariates is large. To accommodate heterogeneous (covariate‐dependent) censoring that is often present in high‐dimensional survival data, we propose a Gehan‐type rank screening method to select features that are relevant to the survival time. The method is invariant to monotone transformations of the response and of the predictors, and works robustly for a general class of survival models. We establish the sure screening property of the proposed methodology. Simulation studies and a lymphoma data analysis demonstrate its favorable performance and practical utility.

Industrial equipment reliability estimation: A Bayesian Weibull regression model with covariate selection

A three-state continuous-time semi-Markov process is used to model the degradation of an industrial equipment. The transition times are assumed Weibull-distributed and influenced by a set of covariates. A Weibull Regression Model is developed within the Bayesian probability framework, to account for the influence of these covariates and estimate the model parameters with the related uncertainty, on the basis of few data and expert judgment. The number of covariates is reduced by a two-step selection procedure derived from the condition monitoring engineering practice. The developed model enables estimating reliability and time-dependent state probabilities for a component degrading in given operational and ambient conditions, represented by a vector of covariates. The model is illustrated by way of a real case study concerning the degradation process affecting diaphragm valves used in the biopharmaceutical industry.

Nonparametric Estimation of Conditional Expectation with Auxiliary Information and Dimension Reduction

Nonparametric estimation of the conditional expectation of an outcome Y given a covariate vector U is of primary importance in many statistical applications such as prediction and personalized medicine. In some problems, there is an additional auxiliary variable Z in the training dataset used to construct estimators, but Z is not available for future prediction or selecting patient treatment in personalized medicine. For example, in the training dataset longitudinal outcomes are observed, but only the last outcome Y is concerned in the future prediction or analysis. The longitudinal outcomes other than the last point is then the variable Z that is observed and related with both Y and U. Previous work on how to make use of Z in the estimation of mainly focused on using Z in the construction of a linear function of U to reduce covariate dimension for better estimation. Using , we propose a two-step estimation of inner and outer expectations, respectively, with sufficient dimension reduction for kernel estimation in both steps. The information from Z is utilized not only in dimension reduction, but also directly in the estimation. Because of the existence of different ways for dimension reduction, we construct two estimators that may improve the estimator without using Z. The improvements are shown in the convergence rate of estimators as the sample size increases to infinity as well as in the finite sample simulation performance. A real data analysis about the selection of mammography intervention is presented for illustration.

Estimation in the Cox survival regression model with covariate measurement error and a changepoint.

The Cox regression model is a popular model for analyzing the relationship between a covariate vector and a survival endpoint. The standard Cox model assumes a constant covariate effect across the entire covariate domain. However, in many epidemiological and other applications, the covariate of main interest is subject to a threshold effect: a change in the slope at a certain point within the covariate domain. Often, the covariate of interest is subject to some degree of measurement error. In this paper, we study measurement error correction in the case where the threshold is known. Several bias correction methods are examined: two versions of regression calibration (RC1 and RC2, the latter of which is new), two methods based on the induced relative risk under a rare event assumption (RR1 and RR2, the latter of which is new), a maximum pseudo-partial likelihood estimator (MPPLE), and simulation-extrapolation (SIMEX). We develop the theory, present simulations comparing the methods, and illustrate their use on data concerning the relationship between chronic air pollution exposure to particulate matter PM10 and fatal myocardial infarction (Nurses Health Study (NHS)), and on data concerning the effect of a subject's long-term underlying systolic blood pressure level on the risk of cardiovascular disease death (Framingham Heart Study (FHS)). The simulations indicate that the best methods are RR2 andMPPLE.

Prediction in polynomial errors-in-variables models

A multivariate errors-in-variables (EIV) model with an intercept term, and a polynomial EIV model are considered. Focus is made on a structural homoskedastic case, where vectors of covariates are i.i.d. and measurement errors are i.i.d. as well. The covariates contaminated with errors are normally distributed and the corresponding classical errors are also assumed normal. In both models, it is shown that (inconsistent) ordinary least squares estimators of regression parameters yield an a.s. approximation to the best prediction of response given the values of observable covariates. Thus, not only in the linear EIV, but in the polynomial EIV models as well, consistent estimators of regression parameters are useless in the prediction problem, provided the size and covariance structure of observation errors for the predicted subject do not differ from those in the data used for the model fitting.

Smoothing Quantile Regressions

We propose to smooth the objective function, rather than only the indicator on the check function, in a linear quantile regression context. Not only does the resulting smoothed quantile regression estimator yield a lower mean squared error and a more accurate Bahadur–Kiefer representation than the standard estimator, but it is also asymptotically differentiable. We exploit the latter to propose a quantile density estimator that does not suffer from the curse of dimensionality. This means estimating the conditional density function without worrying about the dimension of the covariate vector. It also allows for two-stage efficient quantile regression estimation. Our asymptotic theory holds uniformly with respect to the bandwidth and quantile level. Finally, we propose a rule of thumb for choosing the smoothing bandwidth that should approximate well the optimal bandwidth. Simulations confirm that our smoothed quantile regression estimator indeed performs very well in finite samples. Supplementary materials for this article are available online.

Semi-supervised inference: General theory and estimation of means

We propose a general semi-supervised inference framework focused on the estimation of the population mean. As usual in semi-supervised settings, there exists an unlabeled sample of covariate vectors and a labeled sample consisting of covariate vectors along with real-valued responses (“labels”). Otherwise, the formulation is “assumption-lean” in that no major conditions are imposed on the statistical or functional form of the data. We consider both the ideal semi-supervised setting where infinitely many unlabeled samples are available, as well as the ordinary semi-supervised setting in which only a finite number of unlabeled samples is available. Estimators are proposed along with corresponding confidence intervals for the population mean. Theoretical analysis on both the asymptotic distribution and $\ell_{2}$-risk for the proposed procedures are given. Surprisingly, the proposed estimators, based on a simple form of the least squares method, outperform the ordinary sample mean. The simple, transparent form of the estimator lends confidence to the perception that its asymptotic improvement over the ordinary sample mean also nearly holds even for moderate size samples. The method is further extended to a nonparametric setting, in which the oracle rate can be achieved asymptotically. The proposed estimators are further illustrated by simulation studies and a real data example involving estimation of the homeless population.

An omnibus approach to assess covariate balance in observational studies using the distance covariance.

Adequate baseline covariate balance among groups is critical in observational studies designed to estimate causal effects. Propensity score-based methods are popular ways to achieve covariate balance among groups. Existing methods are not easily generalizable to situations in which covariates of mixed type are collected nor do they provide a convenient way to compare the overall covariate vector distributions. Instead, covariate balance is assessed at the individual covariate level, thus the potential for increased overall type I error. We propose the use of the distance covariance, developed by Székely and colleagues, as an omnibus test of independence between covariate vectors and study group. We illustrate the advantages of this methodology in simulated data and in a cardiac surgery study designed to assess the impact of preoperative statin therapy on outcomes.

A single-index model with multiple-links

In a regression model for treatment outcome in a randomized clinical trial, a treatment effect modifier is a covariate that has an interaction with the treatment variable, implying that the treatment efficacies vary across values of such a covariate. In this paper, we present a method for determining a composite variable from a set of baseline covariates, that can have a nonlinear association with the treatment outcome, and acts as a composite treatment effect modifier. We introduce a parsimonious generalization of the single-index models that targets the effect of the interaction between the treatment conditions and the vector of covariates on the outcome, a single-index model with multiple-links (SIMML) that estimates a single linear combination of the covariates(i.e., a single-index), with treatment-specific nonparametric link functions. The approach emphasizes a focus on the treatment-by-covariates interaction effects on the treatment outcome that are relevant for making optimal treatment decisions. Asymptotic results for estimator are obtained under possible model misspecification. A treatment decision rule based on the derived single-index is defined, and it is compared to other methods for estimating optimal treatment decision rules. An application to a clinical trial for the treatment of depression is presented.

Nonparametric independence testing via mutual information

SummaryWe propose a test of independence of two multivariate random vectors, given a sample from the underlying population. Our approach is based on the estimation of mutual information, whose decomposition into joint and marginal entropies facilitates the use of recently developed efficient entropy estimators derived from nearest neighbour distances. The proposed critical values may be obtained by simulation in the case where an approximation to one marginal is available or by permuting the data otherwise. This facilitates size guarantees, and we provide local power analyses, uniformly over classes of densities whose mutual information satisfies a lower bound. Our ideas may be extended to provide new goodness-of-fit tests for normal linear models based on assessing the independence of our vector of covariates and an appropriately defined notion of an error vector. The theory is supported by numerical studies on both simulated and real data.

Multivariate Missing Data Handling with Iterative Bayesian Additive Lasso (IBAL) Multiple Imputation in Multicore Environment on Cloud

Dealing with high dimensional data of the form p>n for multivariate analysis of missingness is very complicated. It arises in many fields mainly in social science, economics and medical study; genome is an example for that where is to mention that samples are very less compared to study elements nothing but variables. The analysis is a combination of large covariate vectors with response and non-response effects of unknown functional form related to response variable of interest. Thus, there is a need for regularized regression models, with effect of smoothing parametric method to do this in this work combine regularization by incorporating different types of covariates. Although regularization approaches fits to framework but the computation high demands in high dimensional analysis they also rely on penalized estimation. The solution is to implement regularization in iteration based smoothing approaches to fit such analysis. The proposed algorithm called Iterative Bayesian Additive Lasso (IBAL) is compared with standard methods in medical analysis and produced unbiased results. The overall work done in multi core environment offered by Cloud Service called Microsoft Azure. The performance is estimated with benchmarks like Standard Error (SE), Mean Square Error (MSE), and Confidence Interval (CI).

L2RM: Low-Rank Linear Regression Models for High-Dimensional Matrix Responses

The aim of this article is to develop a low-rank linear regression model to correlate a high-dimensional response matrix with a high-dimensional vector of covariates when coefficient matrices have low-rank structures. We propose a fast and efficient screening procedure based on the spectral norm of each coefficient matrix to deal with the case when the number of covariates is extremely large. We develop an efficient estimation procedure based on the trace norm regularization, which explicitly imposes the low rank structure of coefficient matrices. When both the dimension of response matrix and that of covariate vector diverge at the exponential order of the sample size, we investigate the sure independence screening property under some mild conditions. We also systematically investigate some theoretical properties of our estimation procedure including estimation consistency, rank consistency, and nonasymptotic error bound under some mild conditions. We further establish a theoretical guarantee for the overall solution of our two-step screening and estimation procedure. We examine the finite-sample performance of our screening and estimation methods using simulations and a large-scale imaging genetic dataset collected by the Philadelphia Neurodevelopmental Cohort study. Supplementary materials for this article are available online.

Specification tests for the propensity score

This paper proposes new nonparametric diagnostic tools to assess the asymptotic validity of different treatment effects estimators that rely on the correct specification of the propensity score. We derive a particular restriction relating the propensity score distribution of treated and control groups, and develop specification tests based upon it. The resulting tests do not suffer from the “curse of dimensionality” when the vector of covariates is high-dimensional, are fully data-driven, do not require tuning parameters such as bandwidths, and are able to detect a broad class of local alternatives converging to the null at the parametric rate n−1∕2, with n the sample size. We show that the use of an orthogonal projection on the tangent space of nuisance parameters facilitates the simulation of critical values by means of a multiplier bootstrap procedure, and can lead to power gains. The finite sample performance of the tests is examined by means of a Monte Carlo experiment and an empirical application. Open-source software is available for implementing the proposed tests.

3459 Modeling Emergency Department Length of Stay of Patients With Substance Use Disorder Using an Accelerated Failure Time Model

OBJECTIVES/SPECIFIC AIMS: Emergency department (ED) length of stay (LOS) is one of the important indicators of quality and efficiency of ED service delivery and is reported to be both cause and result of ED crowding. Increased ED LOS is associated with ED crowding, increases service cost and sometimes poor patient outcome. Substance abuse is one of the major determinants of morbidity, mortality and healthcare needs. Substance abuse may confound the healthcare and service needs of patients in the ED irrespective of primary purpose of their ED visit and may lengthen the ED LOS. The aim of this study was to evaluate the effect of patients’ demographic and clinical characteristics and of different patient-related activities such as screening brief intervention and referral to treatment (SBIRT) on the ED LOS of patients discharged from the ED with a diagnosis of substance abuse. METHODS/STUDY POPULATION: We conducted a retrospective data analysis of electronic health records. The study population included 26971 patients who visited our hospital ED between 2013 and 2017, had a history of substance abuse and were discharged from the ED. An accelerated failure time (AFT) model was used to analyze the influence of covariates on patient ED LOS. The predictor factors in the model included age, gender, ED arrival shift and weekday, diagnosis history of mental health and drug use, acuity triage level from 1 to 5, with 1 being worse severity, and whether any lab tests were ordered, SBIRT intervention and whether patient was homeless. The AFT model is an alternative to the Cox Proportional Hazard Ratio model, which directly models the log of ED LOS as a function of a vector of covariates. The model defines the increase or decrease in LOS with the changes in the covariate levels as an acceleration factor or time ratio (TR). RESULTS/ANTICIPATED RESULTS: The overall median ED LOS was 4 hours with IQR of 4.2 hours. The average age of the study population was 39.3 years, 58.6% of the patients were male and 57% where White; 63.4% had a history of drug use; 43% had a history of mental health issue, and 0.4% were homeless. In the analysis using the AFT model, increased age (a year increase, TR =1.01, p =0.008), female sex (TR=1.044, P<0.001), SBIRT (TR=1.525, P <0.001), history of mental health issue (TR=1.117, P<0.00), evening arrival (evening vs night, TR=1.04, p=0.006), history of drug use (drug vs alcohol only, TR=1.04, p=0.001), higher acuity (triage level 1 vs 5, TR=2.795, p <0.001) and homelessness (TR=1.073, P = 0.021) lengthened the ED LOS. In contrast, weekend arrival (TR=0.956, p=0.004) and day shift arrival (day vs night, TR=0.958, p=0.004) shortened the ED LOS. DISCUSSION/SIGNIFICANCE OF IMPACT: We identified gender, age, SBIRT, arrival shift, weekend arrival, mental health status, substance abuse, acuity level and homelessness to be significant predictor of ED LOS. The fact that SBIRT increased the LOS should be balanced with the advantages of engaging patients into substance use disorder treatment. Understanding the determinants of ED LOS in this population may provide useful information for physicians or patients to better anticipate an individual’s LOS and to help administrators plan the ED staffing and other resources mobilization.

An Adaptive-to-Model Test for Parametric Single-Index Errors-in-Variables Models

This paper provides some useful tests for fitting a parametric single-index regression model when covariates are measured with error and validation data is available. We propose two tests whose consistency rates do not depend on the dimension of the covariate vector when an adaptive-to-model strategy is applied. One of these tests has a bias term that becomes arbitrarily large with increasing sample size but its asymptotic variance is smaller, and the other is asymptotically unbiased with larger asymptotic variance. Compared with the existing local smoothing tests, the new tests behave like a classical local smoothing test with only one covariate, and still are omnibus against general alternatives. This avoids the difficulty associated with the curse of dimensionality. Further, a systematic study is conducted to give an insight on the effect of the values of the ratio between the sample size and the size of validation data on the asymptotic behavior of these tests. Simulations are conducted to examine the performance in several finite sample scenarios.

Marginal distribution test for checking proportional hazards model assumption

Let Z be the covariate vector and Y be the response variable with the joint cumulative distribution function FY,Z. Given a random sample from FY,Z, in order to analyze the data based on a certain proportional hazards (PH) model, say Θ0, one needs to test the null hypothesis H0: FY,Z∈Θ0 first. The existing tests to achieve this task make use of the residuals and are invalid in certain situations, such as when FY,Z is not from any PH model. To overcome this disadvantage, we propose a valid model checking test of H0. It is based on the weighted average of the difference between two estimators of the marginal distribution of the response variable: its non-parametric maximum likelihood estimator and its estimator under Θ0. This test is called the marginal distribution (MD) test. We give the theoretical justification of the MD test. The simulation study suggests that the MD test is always valid, whereas the existing tests may be invalid and they are often unlikely to reject the wrong PH model assumption when they are not valid.

Strong uniform consistency of a kernel conditional quantile estimator for censored and associated data

In survival or reliability studies, it is common to deal with data which are not only incomplete but weakly dependent too. Random right-censoring and random left-truncation are two common forms of such data when they are neither independent nor strongly mixing but rather associated. In this paper, we focus on kernel estimation of the conditional quantile function of a strictly stationary associated random variable $T$ given a $d$-dimensional vector of covariates $X$, under random right-censoring. As main results, we establish a strong uniform consistency rate for the estimator. Then the finite sample performance of the estimator is illustrated on a simulation study.