Real-Time Regression Analysis of Streaming Clustered Data With Possible Abnormal Data Batches

A popular approach, generalized estimating equations (GEE), has been applied to the multivariate accelerated failure time (AFT) model of the clustered and censored data. However, this method needs to estimate the correlation parameters and calculate the inverse of the correlation matrix. Meanwhile, the efficiency of the parameter estimators is low when the correlation structure is misspecified and/or the marginal distribution is heavy-tailed. This paper proposes using the quadratic inference functions (QIF) with a mixture correlation structure to estimate the coefficients in the multivariate AFT model, which can avoid estimating the correlation parameters and computing the inverse matrix of the correlation matrix. Moreover, the estimator derived from the QIF is consistent and asymptotically normal. Simulation studies indicate that the proposed method outperforms the method based on GEE when the marginal distribution has a heavy tail. Finally, the proposed method is used to analyze a real dataset for illustration.

A National Automotive Sampling System–Crashworthiness Data System (NASS–CDS) based Similarity Scoring Methodology (SSM) is presented for the quantitative comparison of real-world crashes to crash tests. Using NASS–CDS 2000–2008, five categorical and five continuous crash, vehicle and occupant parameters were utilised for frontal and side impacts. Mahalanobis metric results revealed that 1% of frontal and 23% of side NASS–CDS cases scored received similarity scores of <0.14 demonstrating greater similarity to standard crash tests. These included 20,334 frontal and 442,511 side impact case occupants (weighted). On average, the best scores occurred for NASS–CDS cases compared to FMVSS 214 side crash tests. The majority of real-world crashes had lower delta-Vs and maximum crush than associated crash tests. The results will aid in the study of occupant safety and vehicle crashworthiness by helping researchers identify population groups to study real-world injuries versus the injury risk predicted by anthropomorphic test devices.

Background: Injury is the fifth leading cause of death in the US, and a large proportion of injury deaths result from Motor Vehicle Crashes (MVCs). Side impact collisions pose high risks of death and serious injury compared to other crash types, both for crashes with other vehicles and single-vehicle crashes with fixed objects, such as utility poles. However, few studies have appropriately compared the propensity for injury of these two types of side impact. Methods: The present study used 10 years of data abstracted from the National Automotive Sampling System Crashworthiness Data System (NASS-CDS) to analyze the risks of polytrauma in side impact crashes for two types of side impacts: pole-like fixed objects and other vehicles. Additionally, ratios comparing the relative risk of nearversus far-side occupants in the two types of crashes were calculated. These risk ratios were developed using a multi-variable general estimating equations (GEE) log-binomial model, with injury severity characterized using the injury severity score (ISS), a measure of the extent of polytrauma. Results & Conclusion: Relative to side impacts with other vehicles, pole-type side impacts are highly associated (RR = 1.53 [95% CI: 1.15, 2.03]) with ISS ≥ 16. After adjusting for other crash characteristics, near-side seating position relative to the side of the vehicle receiving the impact was also associated with a significant increase in risk of polytrauma (RR = 1.82 [95% CI: 1.36, 2.44]). The results of the present study inform vehicle and road design from the perspective of injury prevention. Apostolos Alexandridis! !

BackgroundLongitudinal ordinal data are commonly analyzed using a marginal proportional odds model for relating ordinal outcomes to covariates in the biomedical and health sciences. The generalized estimating equation (GEE) consistently estimates the regression parameters of marginal models even if the working covariance structure is misspecified. For small-sample longitudinal binary data, recent studies have shown that the bias of regression parameters may result from the GEE and have addressed the issue by applying Firth’s adjustment for the likelihood score equation to the GEE as if generalized estimating functions were likelihood score functions. In this manuscript, for the proportional odds model for longitudinal ordinal data, the small-sample properties of the GEE were investigated, and a bias-reduced GEE (BR-GEE) was derived.MethodsBy applying the adjusted function originally derived for the likelihood score function of the proportional odds model to the GEE, we produced the BR-GEE. We investigated the small-sample properties of both GEE and BR-GEE through simulation and applied them to a clinical study dataset.ResultsIn simulation studies, the BR-GEE had a bias closer to zero, smaller root mean square error than the GEE with coverage probability of confidence interval near or above the nominal level. The simulation also showed that BR-GEE maintained a type I error rate near or below the nominal level.ConclusionsFor the analysis of longitudinal ordinal data involving a small number of subjects, the BR-GEE is advantageous for obtaining estimates of the regression parameters of marginal proportional odds models.

This article is concerned with estimations for longitudinal partial linear models with covariate that is measured with error. We propose a generalized empirical likelihood method by combining correction attenuation and quadratic inference functions. The method takes into account the within-subject correlation without involving direct estimation of nuisance parameters in the correlation matrix. We de fine a generalized empirical likelihood-based statistic for the regression coe fficients and residual adjusted empirical likelihood for the baseline function. The empirical log-likelihood ratios are proven to be asymptotically chi-squared, and the corresponding confi dence regions are then constructed. Compared with methods based on normal approximations, the generalized empirical likelihood does not require consistent estimators for the asymptotic variance and bias. Furthermore, a simulation study is conducted to evaluate the performance of the proposed method.

Abstract.In this paper, we consider improved estimating equations for semiparametric partial linear models (PLM) for longitudinal data, or clustered data in general. We approximate the non‐parametric function in the PLM by a regression spline, and utilize quadratic inference functions (QIF) in the estimating equations to achieve a more efficient estimation of the parametric part in the model, even when the correlation structure is misspecified. Moreover, we construct a test which is an analogue to the likelihood ratio inference function for inferring the parametric component in the model. The proposed methods perform well in simulation studies and real data analysis conducted in this paper.

The generalized estimating equation (GEE) has been a popular tool for marginal regression analysis with longitudinal data, and its extension, the weighted GEE approach, can further accommodate data that are missing at random (MAR). Model selection methodologies for GEE, however, have not been systematically developed to allow for missing data. We propose the missing longitudinal information criterion (MLIC) for selection of the mean model, and the MLIC for correlation (MLICC) for selection of the correlation structure in GEE when the outcome data are subject to dropout/monotone missingness and are MAR. Our simulation results reveal that the MLIC and MLICC are effective for variable selection in the mean model and selecting the correlation structure, respectively. We also demonstrate the remarkable drawbacks of naively treating incomplete data as if they were complete and applying the existing GEE model selection method. The utility of proposed method is further illustrated by two real applications involving missing longitudinal outcome data.

In this paper, we investigate the variable selection for varying coefficient errors-in-variables (EV) models with longitudinal data when some covariates are measured with additive errors. A variable selection method based on bias-corrected penalized quadratic inference function (pQIF) is proposed by combining the basis function approximation to coefficient functions and bias-corrected quadratic inference function (QIF) with shrinkage estimations. The proposed method can handle the measurement errors of covariates and within-subject correlation, estimate and select non-zero nonparametric coefficient functions. With appropriate selection of the tuning parameters, we establish the consistency of the variable selection method and the sparsity properties of the regularized estimators. The finite sample performance of the proposed method is assessed by simulation studies. The utility of the method is further demonstrated via a real data analysis.

Proportion data with support lying in the interval [0,1] are a commonplace in various domains of medicine and public health. When these data are available as clusters, it is important to correctly incorporate the within-cluster correlation to improve the estimation efficiency while conducting regression-based risk evaluation. Furthermore, covariates may exhibit a nonlinear relationship with the (proportion) responses while quantifying disease status. As an alternative to various existing classical methods for modeling proportion data (such as augmented Beta regression) that uses maximum likelihood, or generalized estimating equations, we develop a partially linear additive model based on the quadratic inference function. Relying on quasi-likelihood estimation techniques and polynomial spline approximation for unknown nonparametric functions, we obtain the estimators for both parametric part and nonparametric part of our model and study their large-sample theoretical properties. We illustrate the advantages and usefulness of our proposition over other alternatives via extensive simulation studies, and application to a real dataset from a clinical periodontal study.

Quasi-least squares (QLS) is an alternative computational approach for estimation of the correlation parameter in the framework of generalized estimating equations (GEE). QLS overcomes some limitations of GEE that were discussed in Crowder (1995). In addition, it allows for easier implementation of some correlation structures that are not available for GEE. We describe a user written SAS macro called %QLS, and demonstrate application of our macro using a clinical trial example for the comparison of two treatments for a common toenail infection. %QLS also computes the lower and upper boundaries of the correlation parameter for analysis of longitudinal binary data that were described by Prentice (1988). Furthermore, it displays a warning message if the Prentice constraints are violated. This warning is not provided in existing GEE software packages and other packages that were recently developed for application of QLS (in Stata, MATLAB, and R). %QLS allows for analysis of continuous, binary, or count data with one of the following working correlation structures: the first-order autoregressive, equicorrelated, Markov, or tri-diagonal structures.

Statistical modeling (regression analyses) have been growing rapidly into various directions to accommodate various data conditions. For longitudinal or repeated measures data, one of the suitable models is GEE (Generalized Estimating Equation). In practice, to do complex modeling such as GEE, the use of statistical software is necessary and it is available on free open source software R. However, GEE modeling on R can only be access through command line interface (CLI), and most practical researchers very much rely on Graphical User Interface (GUI) based statistics software. To make access to GEE (both order 1 and 2) much easier, we developed, using Shiny toolkit, two types of web-based GUI, standard pull down menu type and e-module type (with narrative theories) that can be utilized for learning and fitting GEE. This paper discusses the features of the interfaces and illustrates the use of them.&#x0D; Keywords: longitudinal data, Generalized Estimating Equation (GEE), exponential families, statistical modeling, correlated response, nonparametric, natural splines, shiny toolkit

Investigating the association between school substance programs and student substance use: accounting for informative cluster size.

Misclassifications in binary responses have long been a common problem in medical and health surveys. One way to handle misclassifications in clustered or longitudinal data is to incorporate the misclassification model through the generalized estimating equation (GEE) approach. However, existing methods are developed under a non‐survey setting and cannot be used directly for complex survey data. We propose a pseudo‐GEE method for the analysis of binary survey responses with misclassifications. We focus on cluster sampling and develop analysis strategies for analyzing binary survey responses with different forms of additional information for the misclassification process. The proposed methodology has several attractive features, including simultaneous inferences for both the response model and the association parameters. Finite sample performance of the proposed estimators is evaluated through simulation studies and an application using a real dataset from the Canadian Longitudinal Study on Aging.

Modern longitudinal data from wearable devices consist of biological signals at high‐frequency time points. Distributed statistical methods have emerged as a powerful tool to overcome the computational burden of estimation and inference with large data, but methodology for distributed functional regression remains limited. We propose a distributed estimation and inference procedure that efficiently estimates both functional and scalar parameters with intensively measured longitudinal outcomes. The procedure overcomes computational difficulties through a scalable divide‐and‐conquer algorithm that partitions the outcomes into smaller sets. We circumvent traditional basis selection problems by analyzing data using quadratic inference functions in smaller subsets such that the basis functions have a low dimension. To address the challenges of combining estimates from dependent subsets, we propose a statistically efficient one‐step estimator derived from a constrained generalized method of moments objective function with a smoothing penalty. We show theoretically and numerically that the proposed estimator is as statistically efficient as non‐distributed alternative approaches and more efficient computationally. We demonstrate the practicality of our approach with the analysis of accelerometer data from the National Health and Nutrition Examination Survey.

Questionnaires are widely used in clinical research and mental health studies, but their responses are usually more subjective than clinical biomarkers. Researchers may use latent variable models such as the item response theory (IRT) model to characterize individual ability, but response instability and small sample sizes can lead to increased uncertainty in estimation. Historical data from similar questionnaires may help reduce variation, but they must be incorporated adaptively. The challenge is further compounded by the need to ensure computational efficiency in IRT models with a large number of parameters. In this work, we develop a Bayesian framework for adaptive borrowing in IRT models based on an approximated normalized power prior (NPP) that treats the borrowing weight as a random parameter. The proposed method makes NPP feasible for general IRT models and is coupled with a full Bayesian data augmentation strategy that enables joint estimation of ability and item parameters through an efficient Gibbs sampler. In simulations, the approach adaptively increases borrowing when historical and current data are compatible and automatically downweights conflicting information. Relative to analyzes without borrowing, the method reduces variance and mean squared error while maintaining coverage across a range of test lengths, item discrimination profiles, and historical-current concordance scenarios. We illustrate the method by integrating historical mental health surveys into current assessments, yielding more precise ability estimates with preserved calibration. An efficient implementation is provided in our updated package NPP available on the Comprehensive R Archive Network.