Measurement error models with interactions.
Ontology highlight
ABSTRACT:
SUBMITTER: Midthune D
PROVIDER: S-EPMC4834948 | biostudies-literature |
REPOSITORIES: biostudies-literature
Similar Datasets
Project description:Predicting the value of a variable Y corresponding to a future value of an explanatory variable X, based on a sample of previously observed independent data pairs (X(1), Y(1)), …, (X(n), Y(n)) distributed like (X, Y), is very important in statistics. In the error-free case, where X is observed accurately, this problem is strongly related to that of standard regression estimation, since prediction of Y can be achieved via estimation of the regression curve E(Y|X). When the observed X(i)s and the future observation of X are measured with error, prediction is of a quite different nature. Here, if T denotes the future (contaminated) available version of X, prediction of Y can be achieved via estimation of E(Y|T). In practice, estimating E(Y|T) can be quite challenging, as data may be collected under different conditions, making the measurement errors on X(i) and X non-identically distributed. We take up this problem in the nonparametric setting and introduce estimators which allow a highly adaptive approach to smoothing. Reflecting the complexity of the problem, optimal rates of convergence of estimators can vary from the semiparametric n(-1/2) rate to much slower rates that are characteristic of nonparametric problems. Nevertheless, we are able to develop highly adaptive, data-driven methods that achieve very good performance in practice.
| S-EPMC2864536 | biostudies-literature
Project description:This paper is dedicated to the memory of Peter G. Hall. It concerns a deceptively simple question: if one observes variables corrupted with measurement error of possibly very complex form, can one recreate asymptotically the clusters that would have been found had there been no measurement error? We show that the answer is yes, and that the solution is surprisingly simple and general. The method itself is to simulate, by computer, realizations with the same distribution as that of the true variables, and then to apply clustering to these realizations. Technically, we show that if one uses K-means clustering or any other risk minimizing clustering, and a multivariate deconvolution device with certain smoothness and convergence properties, then, in the limit, the cluster means based on our method converge to the same cluster means as if there is no measurement error. Along with the method and its technical justification, we analyze two important nutrition data sets, finding patterns that make sense nutritionally.
| S-EPMC6329467 | biostudies-literature
Project description:Objective measures of oxygen consumption and carbon dioxide production by mammals are used to predict their energy expenditure. Since energy expenditure is not directly observable, it can be viewed as a latent construct with multiple physical indirect measures such as respiratory quotient, volumetric oxygen consumption, and volumetric carbon dioxide production. Metabolic rate is defined as the rate at which metabolism occurs in the body. Metabolic rate is also not directly observable. However, heat is produced as a result of metabolic processes within the body. Therefore, metabolic rate can be approximated by heat production plus some errors. While energy expenditure and metabolic rates are correlated, they are not equivalent. Energy expenditure results from physical function, while metabolism can occur within the body without the occurrence of physical activities. In this manuscript, we present a novel approach for studying the relationship between metabolic rate and indicators of energy expenditure. We do so by extending our previous work on MIMIC ME models to allow responses that are sparsely observed functional data, defining the sparse functional multiple indicators, multiple cause measurement error (FMIMIC ME) models. The mean curves in our proposed methodology are modeled using basis splines. A novel approach for estimating the variance of the classical measurement error based on functional principal components is presented. The model parameters are estimated using the EM algorithm and a discussion of the model's identifiability is provided. We show that the defined model is not a trivial extension of longitudinal or functional data methods, due to the presence of the latent construct. Results from its application to data collected on Zucker diabetic fatty rats are provided. Simulation results investigating the properties of our approach are also presented.
| S-EPMC5677589 | biostudies-literature
Project description:We develop model averaging estimation in the linear regression model where some covariates are subject to measurement error. The absence of the true covariates in this framework makes the calculation of the standard residual-based loss function impossible. We take advantage of the explicit form of the parameter estimators and construct a weight choice criterion. It is asymptotically equivalent to the unknown model average estimator minimizing the loss function. When the true model is not included in the set of candidate models, the method achieves optimality in terms of minimizing the relative loss, whereas, when the true model is included, the method estimates the model parameter with root n rate. Simulation results in comparison with existing Bayesian information criterion and Akaike information criterion model selection and model averaging methods strongly favour our model averaging method. The method is applied to a study on health.
| S-EPMC7450939 | biostudies-literature
Project description:Studies of clinical characteristics frequently measure covariates with a single observation. This may be a mismeasured version of the "true" phenomenon due to sources of variability like biological fluctuations and device error. Descriptive analyses and outcome models that are based on mismeasured data generally will not reflect the corresponding analyses based on the "true" covariate. Many statistical methods are available to adjust for measurement error. Imputation methods like regression calibration and moment reconstruction are easily implemented but are not always adequate. Sophisticated methods have been proposed for specific applications like density estimation, logistic regression, and survival analysis. However, it is frequently infeasible for an analyst to adjust each analysis separately, especially in preliminary studies where resources are limited. We propose an imputation approach called moment-adjusted imputation that is flexible and relatively automatic. Like other imputation methods, it can be used to adjust a variety of analyses quickly, and it performs well under a broad range of circumstances. We illustrate the method via simulation and apply it to a study of systolic blood pressure and health outcomes in patients hospitalized with acute heart failure.
| S-EPMC3208089 | biostudies-literature
Project description:Spatial data are often aggregated from a finer (smaller) to a coarser (larger) geographical level. The process of data aggregation induces a scaling effect which smoothes the variation in the data. To address the scaling problem, multiscale models that link the convolution models at different scale levels via the shared random effect have been proposed. One of the main goals in aggregated health data is to investigate the relationship between predictors and an outcome at different geographical levels. In this paper, we extend multiscale models to examine whether a predictor effect at a finer level hold true at a coarser level. To adjust for predictor uncertainty due to aggregation, we applied measurement error models in the framework of multiscale approach. To assess the benefit of using multiscale measurement error models, we compare the performance of multiscale models with and without measurement error in both real and simulated data. We found that ignoring the measurement error in multiscale models underestimates the regression coefficient, while it overestimates the variance of the spatially structured random effect. On the other hand, accounting for the measurement error in multiscale models provides a better model fit and unbiased parameter estimates.
| S-EPMC5437596 | biostudies-literature
Project description:Data from many scientific areas often come with measurement error. Density or distribution function estimation from contaminated data and nonparametric regression with errors-in-variables are two important topics in measurement error models. In this paper, we present a new software package decon for R, which contains a collection of functions that use the deconvolution kernel methods to deal with the measurement error problems. The functions allow the errors to be either homoscedastic or heteroscedastic. To make the deconvolution estimators computationally more efficient in R, we adapt the fast Fourier transform algorithm for density estimation with error-free data to the deconvolution kernel estimation. We discuss the practical selection of the smoothing parameter in deconvolution methods and illustrate the use of the package through both simulated and real examples.
| S-EPMC3100171 | biostudies-literature
Project description:We consider measurement error problem in the Cox model, where the underlying association between the true exposure and its surrogate is unknown, but can be estimated from a validation study. Under this framework, one can accommodate general distributional structures for the error-prone covariates, not restricted to a linear additive measurement error model or Gaussian measurement error. The proposed copula-based approach enables us to fit flexible measurement error models, and to be applicable with an internal or external validation study. Large sample properties are derived and finite sample properties are investigated through extensive simulation studies. The methods are applied to a study of physical activity in relation to breast cancer mortality in the Nurses' Health Study.
| S-EPMC4466084 | biostudies-literature
Project description:We propose a new class of semiparametric estimators for proportional hazards models in the presence of measurement error in the covariates, where the baseline hazard function, the hazard function for the censoring time, and the distribution of the true covariates are considered as unknown infinite dimensional parameters. We estimate the model components by solving estimating equations based on the semiparametric efficient scores under a sequence of restricted models where the logarithm of the hazard functions are approximated by reduced rank regression splines. The proposed estimators are locally efficient in the sense that the estimators are semiparametrically efficient if the distribution of the error-prone covariates is specified correctly, and are still consistent and asymptotically normal if the distribution is misspecified. Our simulation studies show that the proposed estimators have smaller biases and variances than competing methods. We further illustrate the new method with a real application in an HIV clinical trial.
| S-EPMC4955637 | biostudies-literature
Project description:Network psychometric models are often estimated using a single indicator for each node in the network, thus failing to consider potential measurement error. In this study, we investigate the impact of measurement error on cross-sectional network models. First, we conduct a simulation study to evaluate the performance of models based on single indicators as well as models that utilize information from multiple indicators per node, including average scores, factor scores, and latent variables. Our results demonstrate that measurement error impairs the reliability and performance of network models, especially when using single indicators. The reliability and performance of network models improves substantially with increasing sample size and when using methods that combine information from multiple indicators per node. Second, we use empirical data from the STAR*D trial (n = 3,731) to further evaluate the impact of measurement error. In the STAR*D trial, depression symptoms were assessed via three questionnaires, providing multiple indicators per symptom. Consistent with our simulation results, we find that when using sub-samples of this dataset, the discrepancy between the three single-indicator networks (one network per questionnaire) diminishes with increasing sample size. Together, our simulated and empirical findings provide evidence that measurement error can hinder network estimation when working with smaller samples and offers guidance on methods to mitigate measurement error.
| S-EPMC10786122 | biostudies-literature