Functional lasso kernel smoothing for additive regression with interaction effects

To examine the effect of the potential interaction between KIF1B variants (rs17401966 and rs3748578) and environmental factors on the risk of hepatocellular carcinoma (HCC) in a high-risk region in China. Three hundred and six patients with HCC and 306 hospital-based control participants residing in the Shunde region of Guangdong Province, China were enrolled. Clinical characteristics were collected by reviewing the complete medical histories from the patient archives, and epidemiological data were collected using a questionnaire and clinical examination. Two single nucleotide polymorphisms (SNPs) of KIF1B (rs17401966 and rs3748578) were chosen for the current study. All subjects were genotyped using a TaqMan real-time polymerase chain reaction. Multiplicative and additive logistic regression models were used to evaluate various gene-environment interactions. Smoking, frequent consumption of raw freshwater fish, hepatitis B virus (HBV) infection, and a family history of HCC were important risk factors for HCC in this population. Chronic infection with HBV was the most important environmental risk factor for HCC [odds ratio (OR) = 12.02; 95% confidence interval (95%CI): 6.02-24.00]. No significant association was found between the KIF1B variants alone and the risk of HCC. Nevertheless, a significant additive effect modification was observed between rs17401966 and alcohol consumption (P for additive interaction = 0.0382). Compared with non-drinkers carrying either the AG or GG genotype of rs17401966, individuals classified as alcohol consumers with the AA genotype of rs17401966 had a significantly increased risk of HCC (OR = 2.36; 95%CI: 1.49-3.74). The gene-environment interaction between the KIF1B rs17401966 variant and alcohol consumption may contribute to the development of HCC in Chinese individuals.

BACKGROUND AND AIM: Machine learning approaches are increasingly used in environmental mixtures epidemiology. We evaluated the operating characteristics of currently available machine learning approaches in estimating individual exposure and joint mixture effects along with interaction effects on a time-to-event outcome. METHODS: We conducted an extensive search for methods which allow for: time-to-event outcomes, multiple continuous exposures, non-linear and interaction effects on the outcome, and inferences (i.e. provide estimates and standard errors). We selected: Bayesian Additive Regression Trees (BART), Cox Proportional-Hazards model with penalized splines, Gaussian Process Regression (GPR), and Multivariate Adaptive Regression Splines (MARS). Additionally, we included the Cox Proportional-Hazards model and Cox Elastic-Net due to their popularity. We compared estimates across approaches on the association of six metals with incident cardiovascular disease in the Strong Heart Study. RESULTS:The estimates of the hazard ratio for the main metal of interest, selenium, at its 75th versus 25th percentile, holding all other metals constant, ranged from 1.29 (1.17, 1.39) to 2.00 (1.09, 3.19), estimated using Cox Elastic-Net and BART, respectively. Similar trends were found for estimates of the overall mixture effect on the hazard ratio scale when all metals are at their 75th versus 25th percentile. The estimates ranged from 2.09 (1.82, 3.29) to 4.21 (2.83, 6.93), estimated using Cox Elastic-Net and GPR, respectively. The more flexible approaches estimated higher effects with larger uncertainty. CONCLUSIONS:In this study, results across approaches tended to be the same qualitatively but different quantitatively. Increased hazards were found at higher levels of metals, but the magnitude varied. Although the overall conclusion is consistent, estimates may have different clinical impacts. The fact that the more flexible methods detected interaction and non-linear effects of metals but had higher uncertainty reveals a substantial bias-variance tradeoff. To enhance reproducibility in environmental epidemiology, it is important to show whether results are robust across different modeling approaches. KEYWORDS: Survival, Mixtures analysis, Modeling, Cardiovascular diseases

In high-dimensional data analysis, main effects and interaction effects often coexist, especially when complex nonlinear relationships are present. Effective variable selection is crucial for avoiding the curse of dimensionality and enhancing the predictive performance of a model. In this paper, we introduce a nonlinear interaction structure into the additive quantile regression model and propose an innovative penalization method. This method considers the complexity and smoothness of the additive model and incorporates heredity constraints on main effects and interaction effects through an improved regularization algorithm under marginality principle. We also establish the asymptotic properties of the penalized estimator and provide the corresponding excess risk. Our Monte Carlo simulations illustrate the proposed model and method, which are then applied to the analysis of Parkinson’s disease rating scores and further verify the effectiveness of a novel Parkinson’s disease (PD) treatment.

This article considers how functional kernel methods can be used to study α-mixing datasets. It first provides an overview of how prediction problems involving dependent functional datasets may arise from the study of time series, focusing on the standard discretized model and modelization that takes into account the functional nature of the evolution of the quantity to be studied over time. It then considers strong mixing conditions, with emphasis on the notion of α-mixing coefficients and α-mixing variables introduced by Rosenblatt (1956). It also describes some conditions for a Markov chain to be α-mixing; some useful tools that provide covariance inequalities, exponential inequalities, and Central Limit Theorem (CLT) for α-mixing sequences; the asymptotic properties of functional kernel estimators; the use of kernel smoothing methods with α-mixing datasets; and various functional kernel estimators corresponding to different prediction methods. Finally, the article highlights some interesting prospects for further research.

Modelling additive extremile regression by iteratively penalized least asymmetric weighted squares and gradient descent boosting

THIS paper examines the effect of market on the rate of return of selected firms operating in different market environments. It will be shown that the effect of on profiltability depends on the degree of concentration and rate of growth in the industries in which the firm competes, and on the absolute size of the firm. One of the most important propositions of micro-economic theory is that under competitive conditions, rates of return tend toward equality. A casual look at the data will reveal that rates of return are not equal and that differences in rates of return often persist over time. Many studies have utilized industry concentration as a measure of market power and have analyzed the effect of concentration on industry profitability (a sizeable list may be found in Weiss (1971)). Three recent studies have looked at the effect of concentration on profitability using the firm as the unit of analysis (Federal Trade Commission (FTC), Hall and Weiss (1967), and Shepherd (1972)). Although data is not generally available for most firms, the FTC study does examine the effect of relative market share (market divided by the big four firm concentration ratio) on profitability in food manufacturing firms, while the Shepherd paper examines the effect of market for a sample of large, nondiversified firms. The more recent of the above studies emphasize additive multiple regression models. While these models attempt to control for the effects of some dimensions of market structure when focusing on the effect of a particular structure variable, they do not capture the interaction effects of structure variables on profitability. Two independent variables are said to interact if the effect of one independent variable on the dependent variable depends on the level of the other independent variable. Interaction effects may be analyzed in the following three ways (1) specifying an interaction model, (2) including interaction variables in an additive model, or (3) by estimating the parameters of an additive model for subgroups of the total sample. A version of the third method is employed in this study and will be discussed in section I. To illustrate this subgrouping method, suppose we divide our sample into two subsamples (A) firms in highly concentrated industries and (B) firms in lowly concentrated industries. As will be explained below, we expect that the slope coefficient from a regression of profitability on in the high concentration subgroup will be much higher and more significant than the slope coefficient from the low concentration subsample. The primary goal of this paper is to develop and test a theory of the effect of firm on profitability under various competitive situations. We have tried to integrate, formulate, and extend some elements of oligopoly theory and to test the resulting hypotheses. The hypothesis and finding that affects rate of return is greatly strengthened by the more complex interaction hypotheses and findings.1 In carrying out this major goal we also examine the effects of both firm and industry growth on profits, develop new evidence on leverage as a measure of risk, comment on the controversy over the correct measure of profitability, and introduce the concept of market as a so;urce of product differentiation. The paper contains four major sections. The first section develops the theoretical relationship between and profitability. This discussion focuses on the interaction effects on profitability of and the market environReceived for publication September 30, 1971. Revision accepted for publication June 21, 1972. * I am indebted to Ronald G. Ehrenberg, Kenneth Gordon, Marshall C. Howard, James K. Kindahl, Thomas Muench, and George Treyz and two referees for comments and suggestions on an earlier draft of this paper and to Patricia M. Anderson for programming services and comments. ' The interaction findings, especially the growth interaction, support the case for interpreting the data in this cross-section study as representing the effect of on profitability. An examination of the dynamic process by which firms alter their market positions would require time-series data. (See Gale, 1972.)

Perceived discrimination is an important social determinant of mental and behavioral outcomes among adolescent populations. Research has found associations between perceived discrimination and increases in internalizing symptoms, such as depression and anxiety, as well as increases in a number of negative behavioral outcomes, including substance use, delinquent behavior, and HIV risk behaviors (e.g. multiple sexual partners and substance use during sex). There is a gap in the research examining how experiences of perceived discrimination impact substance use and HIV risk behaviors among more at-risk youth, such as juvenile offenders. Court Involved Non-Incarcerated (CINI) juveniles participate in substance use and sexual risk behaviors at high rates, similar to youth that are detained or incarcerated, but are less likely to have access to mental, behavioral, and health treatment options while in the community. This study aimed to assess the relationship between perceived discrimination, internalizing symptoms and substance use and HIV risk behaviors among this at-risk population. Three hundred and fifty six CINI youth were recruited from the Juvenile Intake Department of a family court system in the northeast, as a part of an ongoing, prospective cohort study. In order to assess HIV risk, 139 first-time offenders that endorsed lifetime sexual activity were examined as a part of this study. Preliminary results showed that juvenile report of moderate to high frequency of perceived discrimination was significantly related to an increase in internalizing symptoms (r =.400, p < .0001). Factorial MANCOVA analyses revealed that the interaction effect between level of perceived discrimination and internalizing symptoms was significantly associated with HIV risk behavior [Wilks’ λ = .878, F (6, 222) = 2.49, p =.024, partial eta squared = .063, power = .829]. Significant univariate main effects for the interaction effect were obtained for number of lifetime sexual partners [F (2, 123) = 5.00, p = .008, partial eta square =.081, power = .805]. For juveniles in the moderate to high discrimination/non-clinically significant internalizing symptoms group the mean number of lifetime sexual partners was 1.71, versus a mean of 9.11 lifetime sexual partners for juveniles in the moderate to high discrimination/clinically significant internalizing symptoms group. Post-hoc tests revealed that the average number of lifetime sexual partners was significantly higher for juveniles reporting moderate/high discrimination and clinically significant internalizing symptoms. Additional factorial MANCOVA and logistic regression analyses did not reveal significant associations between the discrimination by internalizing symptoms interaction effect and other HIV risk or substance use

Examining the nonparametric effect of drivers’ age in rear-end accidents through an additive logistic regression model

The aim of this paper is twofold. First, a new functional representation of accelerometer data of a distributional nature is introduced to build a complete individualized profile of each subject’s physical activity levels. Second, we extend two nonparametric functional regression models, kernel smoothing and kernel ridge regression, to handle survey data and obtain reliable conclusions about the influence of physical activity. The advantages of the proposed distributional representation are demonstrated through various analyses performed on the NHANES cohort, which possesses a complex sampling design.

SummaryWe propose a unified Bayesian approach for multivariate structured additive distributional regression analysis comprising a huge class of continuous, discrete and latent multivariate response distributions, where each parameter of these potentially complex distributions is modelled by a structured additive predictor. The latter is an additive composition of different types of covariate effects, e.g. non-linear effects of continuous covariates, random effects, spatial effects or interaction effects. Inference is realized by a generic, computationally efficient Markov chain Monte Carlo algorithm based on iteratively weighted least squares approximations and with multivariate Gaussian priors to enforce specific properties of functional effects. Applications to illustrate our approach include a joint model of risk factors for chronic and acute childhood undernutrition in India and ecological regressions studying the drivers of election results in Germany.

Semiparametric regression models offer considerable flexibility concerning the specification of additive regression predictors including effects as diverse as nonlinear effects of continuous covariates, spatial effects, random effects, or varying coefficients. Recently, such flexible model predictors have been combined with the possibility to go beyond pure mean-based analyses by specifying regression predictors on potentially all parameters of the response distribution in a distributional regression framework. In this paper, we discuss a generic concept for defining interaction effects in such semiparametric distributional regression models based on tensor products of main effects. These interactions can be assigned anisotropic penalties, i.e. different amounts of smoothness will be associated with the interacting covariates. We investigate identifiability and the decomposition of interactions into main effects and pure interaction effects (similar as in a smoothing spline analysis of variance) to facilitate a modular model building process. The decomposition is based on orthogonality in function spaces which allows for considerable flexibility in setting up the effect decomposition. Inference is based on Markov chain Monte Carlo simulations with iteratively weighted least squares proposals under constraints to ensure identifiability and effect decomposition. One important aspect is therefore to maintain sparse matrix structures of the tensor product also in identifiable, decomposed model formulations. The performance of modular regression is verified in a simulation on decomposed interaction surfaces of two continuous covariates and two applications on the construction of spatio-temporal interactions for the analysis of precipitation on the one hand and functional random effects for analysing house prices on the other hand.

Smooth backfitting has been proposed and proved as a powerful nonparametric estimation technique for additive regression models in various settings. Existing studies are restricted to cases with a moderate number of covariates and are not directly applicable to high dimensional settings. In this paper, we develop new kernel estimators based on the idea of smooth backfitting for high dimensional additive models. We introduce a novel penalization scheme, combining the idea of functional Lasso with the smooth backfitting technique. We investigate the theoretical properties of the functional Lasso smooth backfitting estimation. For the implementation of the proposed method, we devise a simple iterative algorithm where the iteration is defined by a truncated projection operator. The algorithm has only an additional thresholding operator over the projection-based iteration of the smooth backfitting algorithm. We further present a debiased version of the proposed estimator with implementation details, and investigate its theoretical properties for statistical inference. We demonstrate the finite sample performance of the methods via simulation and real data analysis.

Additive models and tree-based regression models are two main classes of statistical models used to predict the scores on a continuous response variable. It is known that additive models become very complex in the presence of higher order interaction effects, whereas some tree-based models, such as CART, have problems capturing linear main effects of continuous predictors. To overcome these drawbacks, the regression trunk model has been proposed: a multiple regression model with main effects and a parsimonious amount of higher order interaction effects. The interaction effects can be represented by a small tree: a regression trunk. This article proposes a new algorithm—Simultaneous Threshold Interaction Modeling Algorithm (STIMA)—to estimate a regression trunk model that is more general and more efficient than the initial one (RTA) and is implemented in the R-package stima. Results from a simulation study show that the performance of STIMA is satisfactory for sample sizes of 200 or higher. For sample sizes of 300 or higher, the 0.50 SE rule is the best pruning rule for a regression trunk in terms of power and Type I error. For sample sizes of 200, the 0.80 SE rule is recommended. Results from a comparative study of eight regression methods applied to ten benchmark datasets suggest that STIMA and GUIDE are the best performers in terms of cross-validated prediction error. STIMA appeared to be the best method for datasets containing many categorical variables. The characteristics of a regression trunk model are illustrated using the Boston house price dataset.Supplemental materials for this article, including the R-package stima, are available online.

Combined effect of heatwaves and residential greenness on the risk of stroke among Chinese adults: A national cohort study.

BackgroundThe Oncology Care Model (OCM) was developed as a payment model to encourage participating practices to provide better-quality care for cancer patients at a lower cost. The risk-adjustment model used in OCM is a Gamma generalized linear model (Gamma GLM) with log-link. The predicted value of expense for the episodes identified for our academic medical center (AMC), based on the model fitted to the national data, did not correlate well with our observed expense. This motivated us to fit the Gamma GLM to our AMC data and compare it with two other flexible modeling methods: Random Forest (RF) and Partially Linear Additive Quantile Regression (PLAQR). We also performed a simulation study to assess comparative performance of these methods and examined the impact of non-linearity and interaction effects, two understudied aspects in the field of cost prediction.MethodsThe simulation was designed with an outcome of cost generated from four distributions: Gamma, Weibull, Log-normal with a heteroscedastic error term, and heavy-tailed. Simulation parameters both similar to and different from OCM data were considered. The performance metrics considered were the root mean square error (RMSE), mean absolute prediction error (MAPE), and cost accuracy (CA). Bootstrap resampling was utilized to estimate the operating characteristics of the performance metrics, which were described by boxplots.ResultsRF attained the best performance with lowest RMSE, MAPE, and highest CA for most of the scenarios. When the models were misspecified, their performance was further differentiated. Model performance differed more for non-exponential than exponential outcome distributions.ConclusionsRF outperformed Gamma GLM and PLAQR in predicting overall and top decile costs. RF demonstrated improved prediction under various scenarios common in healthcare cost modeling. Additionally, RF did not require prespecification of outcome distribution, nonlinearity effect, or interaction terms. Therefore, RF appears to be the best tool to predict average cost. However, when the goal is to estimate extreme expenses, e.g., high cost episodes, the accuracy gained by RF versus its computational costs may need to be considered.