Nested Regression Model Research Articles

Genetics of suicide ideation. A role for inflammation and neuroplasticity?

Suicide is a leading cause of death worldwide. Suicide ideation (SI) is a known risk factor for suicide behaviour (SB). The current psychobiology and genetic predisposition to SI and SB are poorly defined. Despite convincing relevance of a genetic background for SI, there is no current implementable knowledge about the genetic makeup that identifies subjects at risk for it. One of the possible reasons for the absence of a clear-cut evidence is the polygenetic nature of SI along with the very large sample sizes that are needed to observe significant genetic association result. The CATIE sample was instrumental to the analysis. SI was retrieved as measured by the Calgary test. Clinical possible covariates were identified by a nested regression model. A principal component analysis helped in defining the possible genetic stratification factors. A GWAS analysis, polygenic risk score associated with a random forest analysis and a molecular pathway analysis were undertaken to identify the genetic contribution to SI. As a result, 741 Schizophrenic individuals from the CATIE were available for the genetic analysis, including 166,325 SNPs after quality control and pruning. No GWAS significant result was found. The random forest analysis conducted by combining the polygenic risk score and several clinical variables resulted in a possibly overfitting model (OOB error rate < 1%). The molecular pathway analysis revealed several molecular pathways possibly involved in SI, of which those involved in microglia functioning were of particular interest. A medium-small sample of SKZ individuals was analyzed to shed a light on the genetic of SI. As an expected result from the underpowered sample, no GWAS positive result was retrieved, but the molecular pathway analysis indicated a possible role of microglia and neurodevelopment in SI.

Overcoming Time-Varying Confounding in Self-Controlled Case Series with Active Comparators: Application and Recommendations.

Confounding by indication is a key challenge for pharmacoepidemiologists. Although self-controlled study designs address time-invariant confounding, indications sometimes vary over time. For example, infection might act as a time-varying confounder in a study of antibiotics and uveitis, because it is time-limited and a direct cause both of receiving antibiotics and uveitis. Methods for incorporating active comparators in self-controlled studies to address such time-varying confounding by indication have only recently been developed. In this paper we formalize these methods, and provide a detailed description for how the active comparator rate ratio can be derived in a self-controlled case series (SCCS): either by explicitly comparing the regression coefficients for a drug of interest and an active comparator under certain circumstances using a simple ratio approach, or through the use of a nested regression model. The approaches are compared in two case studies, one examining the association between thiazolidinediones and fractures, and one examining the association between fluoroquinolones and uveitis using the UK Clinical Practice Research DataLink. Finally, we provide recommendations for the use of these methods, which we hope will support the design, execution and interpretation of SCCS using active comparators and thereby increase the robustness of pharmacoepidemiological studies.

Performance of copula and nested error regression models in estimating per capita expenditure of sub-district in Pidie Regency

In unit-level small area estimation (SAE), the commonly used nested error regression (NER) model assumes normality which is not always the case. To handle non-normal data, researchers in statistics have developed a novel approach using exchangeable and extendible copula called the multivariate exchangeable copula (MEC) model. This study compares the performance of parametric MEC and NER models in estimating the sub-district average of per capita expenditure (PCE) in Pidie Regency, Aceh Province. This study presents PCE, which has a skewed distribution of the three-parameter skew-normal. The parametric MEC model uses a Gaussian copula from the Elliptical family and an empirical best unbiased prediction (EBUP) estimator. Meanwhile, the NER model uses an empirical best linear unbiased prediction (EBLUP) estimator. The results reveal that at a 95% confidence level, the parametric MEC model outperforms the NER model with a smaller root of mean squared error (RMSE) and provides a more precise estimate of the sub-district average of PCE. This study highlights the importance of considering the parametric MEC model as an alternative method for skewed data in unit-level SAE. The results of this study have the potential to support the achievement of Goal 1 (to end poverty) and Goal 10 (to reduce inequality) of the sustainable development goals (SDGs) by providing average PCE estimates at the sub-district level.

Small area estimation of average compositions under multivariate nested error regression models

This paper investigates the small area estimation of population averages of unit-level compositional data. The new methodology transforms the compositions into vectors of R^m and assumes that the vectors follow a multivariate nested error regression model. Empirical best predictors of domain indicators are derived from the fitted model, and their mean squared errors are estimated by parametric bootstrap. The empirical analysis of the behavior of the introduced predictors is investigated by means of simulation experiments. An application to real data from the Spanish household budget survey is given. The target is to estimate the average of proportions of annual household expenditures on food, housing and others, by Spanish provinces.

Small area estimation under a semi‐parametric covariate measured with error

SummaryIn recent years, small area estimation has played an important role in statistics as it deals with the problem of obtaining reliable estimates for parameters of interest in areas with small or even zero sample sizes corresponding to population sizes. Nested error linear regression models are often used in small area estimation assuming that the covariates are measured without error and also the relationship between covariates and response variable is linear. Small area models have also been extended to the case in which a linear relationship may not hold, using penalised spline (P‐spline) regression, but assuming that the covariates are measured without error. Recently, a nested error regression model using a P‐spline regression model, for the fixed part of the model, has been studied assuming the presence of measurement error in covariate, in the Bayesian framework. In this paper, we propose a frequentist approach to study a semi‐parametric nested error regression model using P‐splines with a covariate measured with error. In particular, the pseudo‐empirical best predictors of small area means and their corresponding mean squared prediction error estimates are studied. Performance of the proposed approach is evaluated through a simulation and also by a real data application. We propose a frequentist approach to study a semi‐parametric nested error regression model using P‐splines with a covariate measured with error.

Multivariate Mixture Model for Small Area Estimation of Poverty Indicators

Abstract When disaggregation of national estimates in several domains or areas is required, direct survey estimators, which use only the domain-specific survey data, are usually design-unbiased even under complex survey designs (at least approximately) and require no model assumptions. Nevertheless, they are appropriate only for domains or areas with sufficiently large sample size. For example, when estimating poverty in a domain with a small sample size (small area), the volatility of a direct estimator might make that area seems like very poor in one period and very rich in the next one. Small area (or indirect) estimators have been developed in order to avoid such undesired instability. Small area estimators borrow strength from the other areas so as to improve the precision and therefore obtain much more stable estimators. However, the usual model-based assumptions, which include some kind of area homogeneity, may not hold in real applications. A more flexible model based on multivariate mixtures of normal distributions that generalises the usual nested error linear regression model is proposed for estimation of general parameters in small areas. This flexibility makes the model adaptable to more general situations, where there may be areas with a different behaviour from the other ones, making the model less restrictive (hence, more close to nonparametric) and more robust to outlying areas. An expectation-maximisation (E-M) method is designed for fitting the proposed mixture model. Under the proposed mixture model, two different new predictors of general small area indicators are proposed. A parametric bootstrap method is used to estimate the mean squared errors of the proposed predictors. Small sample properties of the new predictors and of the bootstrap procedure are analysed by simulation studies and the new methodology is illustrated with an application to poverty mapping in Palestine.

Empirical best prediction of small area bivariate parameters

AbstractThis paper introduces empirical best predictors of small area bivariate parameters, like ratios of sums or sums of ratios, by assuming that the target unit‐level vector follows a bivariate nested error regression model. The corresponding means squared errors are estimated by parametric bootstrap. Several simulation experiments empirically study the behavior of the introduced statistical methodology. An application to real data from the Spanish household budget survey gives estimators of ratios of food household expenditures by provinces.

Two-dimensional echocardiographic scoring system of the left ventricular filling pressure and clinical outcomes in heart failure with preserved ejection fraction

Abstract Funding Acknowledgements Type of funding sources: Public Institution(s). Main funding source(s): Japan Society for the Promotion of Science (JSPS) Introduction Elevated left ventricular (LV) filling pressure in non-decompensated state is a powerful indicator of worse clinical outcomes in heart failure regardless of LV ejection fraction. However, its detection is often challenging in heart failure with preserved ejection fraction (HFpEF). Purpose This study aimed to elucidate the predictive value of recently proposed echocardiographic parameter of LV filling pressure, Visually assessed time difference between the Mitral valve and Tricuspid valve opening (VMT) score in HFpEF. Methods We retrospectively analyzed 310 well-differentiated HFpEF patients in stable conditions. Using two-dimensional echocardiographic images, time sequence of opening of mitral valve and tricuspid valve was visually assessed in the apical four-chamber view and scored to 0 to 2 (0: tricuspid valve first, 1: simultaneous, 2: mitral valve first). When the inferior vena cava diameter was dilated, 1 point was added and VMT score was calculated as four grades from 0 to 3. Based on the previous study, VMT≥2 was regarded as a sign of elevated LV filling pressure (Figure 1). LV diastolic function was graded according to the guidelines. The primary endpoint was defined as a composite of cardiac death and heart failure hospitalisation during the two years after echocardiographic examination. Results During the follow-up period, 55 events (18%) occurred, including four cardiac deaths and 51 heart failure hospitalisations. Kaplan-Meier curves demonstrated that VMT≥2 (n = 54) was associated with worse outcomes compared to patients showing VMT ≤ 1 (n = 256) (log-rank test P &amp;lt;0.001). Furthermore, VMT≥2 was associated with worse outcomes when tested in 100 HFpEF patients with atrial fibrillation (log-rank test P = 0.026) (Figure 2). In the adjusted model including age, systolic blood pressure, serum albumin level, and the LV diastolic function grading, VMT≥2 was independently associated with the primary outcome (hazard ratio: 2.23; 95% confidence interval: 1.17 to 4.24, P = 0.014). Additionally, the nested regression model showed that VMT scoring provided an incremental prognostic value over clinically relevant variables (age, sex, the plasma brain natriuretic peptide level, atrial fibrillation) and LV diastolic function grading (chi-square 10.8 vs 16.3, P = 0.035). Conclusions In patients with HFpEF, the VMT score was independently and incrementally associated with adverse clinical outcomes. Moreover, it discriminated worse clinical outcome even in HFpEF patients with atrial fibrillation. Abstract Figure. VMT scoring Abstract Figure. Kaplan-Meier analysis

Prognostic Value of the Three-Dimensional Right Ventricular Ejection Fraction in Patients With Asymptomatic Aortic Stenosis.

Background: The right ventricular (RV) function is an important prognostic marker of asymptomatic aortic stenosis (AS). However, previous publications have not addressed the additive value of conventional RV parameters over left heart parameters. Whether three-dimensional echocardiography (3DE)-derived RV ejection fraction (RVEF) has prognostic utility independent of 3DE derived left heart parameters is also unknown. We investigated the prognostic utility of 3DE RVEF in patients with asymptomatic AS.Methods: We retrospectively selected 392 asymptomatic AS patients. RVEF, left ventricular ejection fraction (LVEF) and left atrial volumes (LAVs) were measured using 3DE datasets. We determined the association of those parameters, as well as of aortic valve replacement (AVR), and Charlson's comorbidity index with cardiac events. We also analyzed whether RVEF has incremental value over two-dimensional echocardiography (2DE) RV parameters.Results: During a median follow-up of 27 months, 57 patients developed cardiac events, and 68 patients received AVR. Univariate Cox proportional hazard analysis revealed that RVEF was associated with cardiac events (p < 0.001). Multivariate analysis revealed that RVEF was significantly associated with cardiac events (p < 0.001) even after adjusting for AVR, Charlson's comorbidity index, LVEF, LAV, E/e', and indexed aortic valve area (iAVA). An incremental value of RVEF over left heart parameters was also demonstrated using a nested regression model. Classification and regression-tree analysis selected RVEF first with a cut-off value of 41%. RVEF had incremental value over iAVA, LVEF, and 2DE conventional RV parameters for its association with future outcomes.Conclusions: 3DE RVEF had significant prognostic value even after adjusting for comorbidities, left heart parameters, and conventional 2DE RV parameters in asymptomatic aortic stenosis.

Domain Prediction with Grouped Income Data

Abstract One popular small area estimation method for estimating poverty and inequality indicators is the empirical best predictor under the unit-level nested error regression model with a continuous dependent variable. However, parameter estimation is more challenging when the response variable is grouped due to data confidentiality concerns or concerns about survey response burden. The work in this paper proposes methodology that enables fitting a nested error regression model when the dependent variable is grouped. Model parameters are then used for small area prediction of finite population parameters of interest. Model fitting in the case of a grouped response variable is based on the use of a stochastic expectation–maximization algorithm. Since the stochastic expectation–maximization algorithm relies on the Gaussian assumptions of the unit-level error terms, adaptive transformations are incorporated for handling departures from normality. The estimation of the mean squared error of the small area parameters is facilitated by a parametric bootstrap that captures the additional uncertainty due to the grouping mechanism and the possible use of adaptive transformations. The empirical properties of the proposed methodology are assessed by using model-based simulations and its relevance is illustrated by estimating deprivation indicators for municipalities in the Mexican state of Chiapas.

Benchmarked Estimators for a Small Area Mean Under a Onefold Nested Regression Model

SummaryIn this paper, we modify small area estimators, based on the unit‐level model, so that they add up to reliable higher‐level estimates of population totals. These modifications result in benchmarked small area estimators. We consider two benchmarking procedures. One is based on augmenting the unit‐level model with a suitable variable. The other one uses the calibrated weights of the direct estimators that are reliable at the higher levels. These weights are used in estimators that are based on the aggregation of the unit‐level model for each small area. The mean squared error estimators of the proposed benchmarked estimators are obtained by suitably modifying those associated with the corresponding non benchmarked estimators. The properties of the estimators are evaluated via simulation.

A Hierarchical Bayes Unit-Level Small Area Estimation Model for Normal Mixture Populations

National statistical agencies are regularly required to produce estimates about various subpopulations, formed by demographic and/or geographic classifications, based on a limited number of samples. Traditional direct estimates computed using only sampled data from individual subpopulations are usually unreliable due to small sample sizes. Subpopulations with small samples are termed small areas or small domains. To improve on the less reliable direct estimates, model-based estimates, which borrow information from suitable auxiliary variables, have been extensively proposed in the literature. However, standard model-based estimates rely on the normality assumptions of the error terms. In this research we propose a hierarchical Bayesian (HB) method for the unit-level nested error regression model based on a normal mixture for the unit-level error distribution. Our method proposed here is applicable to model cases with unit-level error outliers as well as cases where each small area population is comprised of two subgroups, neither of which can be treated as an outlier. Our proposed method is more robust than the normality based standard HB method (Datta and Ghosh, Annals Stat. 19, 1748–1770, 1991) to handle outliers or multiple subgroups in the population. Our proposal assumes two subgroups and the two-component mixture model that has been recently proposed by Chakraborty et al. (Int. Stat. Rev. 87, 158–176, 2019) to address outliers. To implement our proposal we use a uniform prior for the regression parameters, random effects variance parameter, and the mixing proportion, and we use a partially proper non-informative prior distribution for the two unit-level error variance components in the mixture. We apply our method to two examples to predict summary characteristics of farm products at the small area level. One of the examples is prediction of twelve county-level crop areas cultivated for corn in some Iowa counties. The other example involves total cash associated in farm operations in twenty-seven farming regions in Australia. We compare predictions of small area characteristics based on the proposed method with those obtained by applying the Datta and Ghosh (Annals Stat. 19, 1748–1770, 1991) and the Chakraborty et al. (Int. Stat. Rev. 87, 158–176, 2019) HB methods. Our simulation study comparing these three Bayesian methods, when the unit-level error distribution is normal, or t, or two-component normal mixture, showed the superiority of our proposed method, measured by prediction mean squared error, coverage probabilities and lengths of credible intervals for the small area means.

Empirical best linear unbiased predictors in multivariate nested-error regression models

For analyzing unit-level multivariate data in small area estimation, we consider the multivariate nested error regression model (MNER) and provide the empirical best linear unbiased predictor (EBLUP) of a small area characteristic based on second-order unbiased and consistent estimators of the ‘within’ and ‘between’ multivariate components of variance. The second-order approximation of the mean squared error (MSE) matrix of the EBLUP and its unbiased estimator are derived in closed forms. The confidence interval with second-order accuracy is also provided analytically.

Small area mean estimation after effect clustering

ABSTRACTProviding reliable estimates of subpopulation/area parameters has attracted increased attention due to their importance in applications such as policymaking. Due to low or even no samples from some areas, we must adopt indirect model approaches. Existing indirect small area estimation methods often assume that a single nested error regression model is suitable for all the small areas. In particular, the effects of the auxiliary variables are either fixed or have a single attraction center. In some applications, it can be more appropriate to cluster the small areas so that the effects of the auxiliary variables are fixed but have multiple centers in the nested error regression model. In this paper, we examine an extended nested error regression model in which the auxiliary variables have mixed effects with multiple centers. We use a penalty approach to identify these centers and estimate the model parameters simultaneously. We then propose two new small area mean estimators and construct estimators of their mean square errors. Simulations based on artificial and realistic finite populations show that the new estimators can be efficient. Furthermore, the confidence intervals based on the new methods have accurate coverage probabilities. We illustrate the proposed methods with the Survey of Labour and Income Dynamics conducted in Canada.

Small Area Quantile Estimation

SummarySample surveys are widely used to obtain information about totals, means, medians and other parameters of finite populations. In many applications, similar information is desired for subpopulations such as individuals in specific geographic areas and socio‐demographic groups. When the surveys are conducted at national or similarly high levels, a probability sampling can result in just a few sampling units from many unplanned subpopulations at the design stage. Cost considerations may also lead to low sample sizes from individual small areas. Estimating the parameters of these subpopulations with satisfactory precision and evaluating their accuracy are serious challenges for statisticians. To overcome the difficulties, statisticians resort to pooling information across the small areas via suitable model assumptions, administrative archives and census data. In this paper, we develop an array of small area quantile estimators. The novelty is the introduction of a semiparametric density ratio model for the error distribution in the unit‐level nested error regression model. In contrast, the existing methods are usually most effective when the response values are jointly normal. We also propose a resampling procedure for estimating the mean square errors of these estimators. Simulation results indicate that the new methods have superior performance when the population distributions are skewed and remain competitive otherwise.

Resource-based view on safety culture's influence on hospital performance: The moderating role of electronic health record implementation.

Patient safety and safety culture have received increasing attention from agencies such as the Agency of Healthcare Research and Quality and the Institute of Medicine. Safety culture refers to the fundamental values, attitudes, and perceptions that provide a unique source of competitive advantage to improve performance. This study contributes to the literature and expands understanding of safety culture and hospital performance outcomes when considering electronic health record (EHR) usage. Based on the resource-based view of the firm, this study examined the association between safety culture and hospital quality and financial performance in the presence of EHR. Data consist of the 2016 Hospital Survey on Patient Safety, Hospital Compare, American Hospital Association's annual survey, and the American Hospital Association's Information Technology supplement. Our final analytic sample consisted of 154 hospitals. We used a two-part nested regression model approach. Safety culture has a direct positive relationship with financial performance (operating margin). Furthermore, having basic EHR as compared to not having EHR further enhances this positive relationship. On the other hand, safety culture does not have a direct association with quality performance (readmissions) in most cases. However, safety culture coupled with basic EHR functionalities, compared to not having EHR, is associated with lower readmissions. Hospitals should strive to improve patient safety culture as part of their strategic plan for quality improvement. In addition, hospital managers should consider implementing EHR as a resource that can support safety culture's effect on outcomes such as financial and quality performance indicators. Future studies can examine the differences between basic and advanced EHR presence in relation to safety culture.

Interval Estimation for Mean Response in a Simple Nested Error Regression Model in Gauge R &amp; R Study

In a measurement system monitoring manufacturing processes, one often uses gauge repeatability and reproducibility (R & R) experiment to determine the amount of variability due to parts, final products, operators, or gauge. A measurement system that employs operators randomly chosen to conduct measurements on randomly selected parts can be statistically modelled. When a measurement is assumed to be linearly related to a predictor variable and a simple nested error regression model is applied for the measurement system, one might be interested in making inferences concerning the variability for the mean response in the model. In general, confidence intervals are uniformly more informative than hypothesis tests in making inferences to parametric values in statistical models. Confidence intervals for the mean response in a simple nested error regression model can be useful tools to determine whether the variability is appropriately managed in a manufacturing process. Several confidence intervals for the mean response in the model are proposed. The confidence intervals proposed in this article are based on a moderate large sample method. Computer simulation is performed to see if the proposed intervals maintain the stated confidence level and a numerical example is provided to explain the proposed intervals by calculating confidence intervals for the mean response in the model.

The spatial empirical Bayes predictor of the small area mean for a lognormal variable of interest and spatially correlated random effects

The standard small area estimator, the empirical best linear unbiased predictor (EBLUP), estimates small area parameters by way of linear mixed models. The EBLUP assumes normal and independent random small area effects as well as normal and independent random sampling errors. Under these assumptions, the variable of interest also follows a normal distribution. In practice, however, the above assumptions are often violated. The variable of interest is often non-normal and highly skewed, and the small areas are frequently spatially dependent. In this paper, we propose the spatial empirical Bayes predictor (SEBP) of the small area mean of a positively skewed variable of interest in the presence of spatial dependence among the random small area effects. We assume that the variable of interest follows a normal distribution after a log transformation and that its log transform is linked to some auxiliary variables by a nested error regression model. The SEBP is derived under the log-transformed nested error regression model. By way of simulation, we show that compared to its alternatives, i.e., the direct estimator which is solely based on the survey data for the small area under study, the EBLUP which does not take into account spatial dependence and skewness, the empirical Bayes predictor which takes into account skewness but not spatial dependence among the small areas, the SEBP has the smallest average relative bias and average relative root-mean-squared error for various combinations—though not all—of skewness and spatial correlation.

Small area estimation with multiple covariates measured with errors: A nested error linear regression approach of combining multiple surveys

Small area estimation has become a very active area of research in statistics. Many models studied in small area estimation focus on one or more variables of interest from a single survey without paying close attention to the nature of the covariates. It is useful to utilize the idea of borrowing strength from covariates to build a model which combines two (or multiple) surveys. In many real applications, there are also covariates measured with errors. In this paper, we study a nested error linear regression model which has multiple unit- or area-level error-free covariates, possibly coming from administrative records, and multiple area-level covariates subject to structural measurement error where the data on the latter covariates are obtained from multiple surveys. In particular, we derive empirical best predictors of small area means and estimators of mean squared prediction error of the empirical best predictors of small area means. Performance of the proposed approach is studied through a simulation study and also by a real application.

Heteroscedastic nested error regression models with variance functions

The article considers a nested error regression model with heteroscedastic variance functions for analyzing clustered data, where the normality for the underlying distributions is not assumed. Classical methods in normal nested error regression models with homogenous variances are extended in the two directions: heterogeneous variance functions for error terms and non-normal distributions for random effects and error terms. Consistent estimators for model parameters are suggested, and second-order approximations of their biases and variances are derived. The mean squared errors of the empirical best linear unbiased predictors are expressed explicitly to second-order. Second-order unbiased estimators of the mean squared errors are provided analytically in closed forms. The proposed model and the resulting procedures are numerically investigated through simulation and empirical studies.