Semiparametric Regression Model Research Articles

Semiparametric distribution regression with instruments and monotonicity

This paper proposes IV-based estimators for the semiparametric distribution regression model in the presence of an endogenous regressor, which are based on an extension of IV probit estimators and the idea of control functions. We discuss the causal interpretation of the estimators and two methods (monotone rearrangement and isotonic regression) to ensure a monotonically increasing distribution function. Asymptotic properties and simulation evidence are provided. An application to income equations with German SOEP data reveals statistically significant and heterogeneous differences to the inconsistent non-IV-based estimator.

Semiparametric Probit Regression Model with General Interval-Censored Failure Time Data

Interval-censored data frequently arise in various biomedical areas involving periodical follow-ups where the failure or event time of interest cannot be observed exactly but is only known to fall into a time interval. This article considers a semiparametric probit regression model, a valuable alternative to other commonly used semiparametric models in survival analysis, to investigate potential risk factors for the interval-censored failure time of interest. We develop an expectation-maximization (EM) algorithm to conduct the pseudo maximum likelihood estimation (MLE) using the working independence strategy for general or mixed-case interval-censored data. The resulting estimators of regression parameters are shown to be consistent and asymptotically normal with the empirical process techniques. In addition, we propose a novel penalized EM algorithm for simultaneously achieving variable selection and parameter estimation in the case of high-dimensional covariates. The proposed variable selection method can be readily implemented with some existing software and considerably reduces the estimation error of the proposed pseudo-MLE approach. Simulation studies demonstrate the satisfactory performance of the proposed methods. An application to a set of interval-censored data on prostate cancer further confirms the utility of the methodology. Supplementary materials for this article are available online.

Public Health Evaluation of COVID-19 Vaccine Acceptability and Health Behaviors in South Africa: Past, Current, and Future Implications (2020–2022)

South Africa is facing a high burden of COVID-19 pandemic with low-vaccine coverage in the African Region. We aimed to investigate the temporal changes and impacts in health behaviors on vaccine acceptability in pre-, during-, and post-vaccine roll-out periods. In this cross-sectional study, we used the combined data from the nationally conducted “COVID-19 Vaccine Surveys (CVACS)” (May 2020–February/March 2022). Semiparametric regression models were used to capture the nonlinear association between the vaccine acceptability and health behaviors. Our study provided compelling evidence for a substantial decline in COVID-19 vaccine trust which shifted from 62%–70% to 26%–42% overtime. Participants younger than 40 years of age were less likely to receive the vaccine before it became available. However, this association changed in the postvaccine period with significant uptake in vaccine acceptance in younger groups. South Africans who identified themselves as black were more likely to intend to receive (aORs ranged: 1.93−3.60) and to trust the vaccine’s safety and efficacy (aORs ranged:1.79−1.23) in all time periods. “Mask wearing” and “frequent hand washing” were the most commonly reported behaviors. Given the lower rates of vaccine acceptability and a reduction in preventative health behaviors, monitoring the spread of infections is crucial and may have significant clinical and epidemiological implications.

Robust Analysis of the Influencing Factors for Hospitalization Costs of Senile Cataracts Patients in Chengdu Considering Different Types of Insurance

Chengdu is one of the earliest pilot cities for urban-rural basic medical insurance integration in China. This study aimed to analyze the influencing factors of hospitalization costs of senile cataract in a tertiary hospital in Chengdu by robust method, especially considering the influence of medical insurance type. A total of 1310 discharged patients from a tertiary hospital from January 2020 to June 2021 who were mainly diagnosed with senile cataracts were selected as the research subjects. Kruskal-Wallis H test and Spearman correlation analysis are used to conduct univariate statistical analysis. The robust multivariate linear regression model and a semi-parametric multivariate regression model are established to obtain the influencing factors for their hospitalization costs. The robust multivariate regression model results show that reimbursement ratio, number of surgeries, type of medical insurance, hospitalization days, number of additional diagnoses and material proportion have significant correlations with the response variable, i.e. total hospitalization costs of the senile cataract patients. In the robust multivariate regression analysis, the type of insurance is significantly associated with the hospitalization costs. Fixing other variables, the hospitalization costs of patients with UEBMI insurance were 7.6% higher than those with URRBMI insurance. Generalized additive model (GAM) can express the nonlinear relationship between explanatory variables and response variable. Because of the nonlinear part of the GAM, the interpretation and description of the model can provide more knowledge than the linear models. In the GAM model, the type of insurance is also significantly related to the total costs. According to the regression effects of reimbursement ratio, number of surgeries, type of medical insurance, hospitalization days, number of additional diagnoses and material proportion on total costs, the paper aims to provide some references for promoting the reform of the local medical system and improving the eye health status and quality of life of middle-aged and elderly groups.

Variational inference: uncertainty quantification in additive models

AbstractMarkov chain Monte Carlo (MCMC)-based simulation approaches are by far the most common method in Bayesian inference to access the posterior distribution. Recently, motivated by successes in machine learning, variational inference (VI) has gained in interest in statistics since it promises a computationally efficient alternative to MCMC enabling approximate access to the posterior. Classical approaches such as mean-field VI (MFVI), however, are based on the strong mean-field assumption for the approximate posterior where parameters or parameter blocks are assumed to be mutually independent. As a consequence, parameter uncertainties are often underestimated and alternatives such as semi-implicit VI (SIVI) have been suggested to avoid the mean-field assumption and to improve uncertainty estimates. SIVI uses a hierarchical construction of the variational parameters to restore parameter dependencies and relies on a highly flexible implicit mixing distribution whose probability density function is not analytic but samples can be taken via a stochastic procedure. With this paper, we investigate how different forms of VI perform in semiparametric additive regression models as one of the most important fields of application of Bayesian inference in statistics. A particular focus is on the ability of the rivalling approaches to quantify uncertainty, especially with correlated covariates that are likely to aggravate the difficulties of simplifying VI assumptions. Moreover, we propose a method, where we combine both advantages of MFVI and SIVI and compare its performance. The different VI approaches are studied in comparison with MCMC in simulations and an application to tree height models of douglas fir based on a large-scale forestry data set.

Estimation and convergence rates in the distributional single index model

The distributional single index model is a semiparametric regression model in which the conditional distribution functions of a real‐valued outcome variable depend on ‐dimensional covariates through a univariate, parametric index function , and increase stochastically as increases. We propose least squares approaches for the joint estimation of and in the important case where and obtain convergence rates of , thereby improving an existing result that gives a rate of . A simulation study indicates that the convergence rate for the estimation of might be faster. Furthermore, we illustrate our methods in an application on house price data that demonstrates the advantages of shape restrictions in single index models.

The consistency of the estimators in semiparametric regression model based on m-asymptotic negatively associated errors

In this article, we analyze the strong consistency and r-th (r > 1) mean consistency for the estimators β u, n and g u, n of β and g, respectively, based on m-asymptotic negatively associated errors. Furthermore, the convergence rate for the strong consistency of the estimators is also considered. The results obtained in this article extend the corresponding ones for ρ ∗-mixing random variables and other dependent sequences.

Health and growth in China: Greater investment in both soft- and hard-ware are needed

The purpose is to study the relationship between health investment and economic growth in China. The research design involves empirical research using semi parametric regression models and instrumental variable methods. The results indicate that on the one hand, Chinese health investment can promote economic growth, and its promoting effect on economic growth is non-linear; On the other hand, healthcare investment in the form of human capital is more conducive to promoting regional economic growth than healthcare investment in the form of material capital. The conclusion is that it is necessary to increase health investment in the form of human capital such as the number of health personnel in the eastern region, as well as in the form of material capital such as the number of beds in the central and western regions, in order to better promote regional economic growth.

Tail risk forecasting with semiparametric regression models by incorporating overnight information

AbstractThis research incorporates realized volatility and overnight information into risk models, wherein the overnight return often contributes significantly to the total return volatility. Extending a semiparametric regression model based on asymmetric Laplace distribution, we propose a family of RES‐CAViaR‐oc models by adding overnight return and realized measures as a nowcasting technique for simultaneously forecasting Value‐at‐Risk (VaR) and expected shortfall (ES). We utilize Bayesian methods to estimate unknown parameters and forecast VaR and ES jointly for the proposed model family. We also conduct extensive backtests based on joint elicitability of the pair of VaR and ES during the out‐of‐sample period. Our empirical study on four international stock indices confirms that overnight return and realized volatility are vital in tail risk forecasting.

Smoothed quantile residual life regression analysis with application to the Korea HIV/AIDS cohort study

BackgroundThe residual life of a patient with human immunodeficiency virus (HIV) is of major interest to patients and their physicians. While existing analyses of HIV patient survival focus mostly on data collected at baseline, residual life analysis allows for dynamic analysis based on additional data collected over a period of time. As survival times typically exhibit a right-skewed distribution, the median provides a more useful summary of the underlying distribution than the mean. In this paper, we propose an efficient inference procedure that fits a semiparametric quantile regression model assessing the effect of longitudinal biomarkers on the residual life of HIV patients until the development of dyslipidemia, a disease becoming more prevalent among those with HIV.MethodsFor estimation of model parameters, we propose an induced smoothing method that smooths nonsmooth estimating functions based on check functions. For variance estimation, we propose an efficient resampling-based estimator. The proposed estimators are theoretically justified. Simulation studies are used to evaluate their finite sample performances, including their prediction accuracy. We analyze the Korea HIV/AIDS cohort study data to examine the effects of CD4 (cluster of differentiation 4) cell count on the residual life of HIV patients to the onset of dyslipidemia.ResultsThe proposed estimator is shown to be consistent and normally distributed asymptotically. Under various simulation settings, our estimates are approximately unbiased. Their variances estimates are close to the empirical variances and their computational efficiency is superior to that of the nonsmooth counterparts. Two measures of prediction performance indicate that our method adequately reflects the dynamic character of longitudinal biomarkers and residual life. The analysis of the Korea HIV/AIDS cohort study data shows that CD4 cell count is positively associated with residual life to the onset of dyslipidemia but the effect is not statistically significant.ConclusionsOur method enables direct prediction of residual lifetimes with a dynamic feature that accommodates data accumulated at different times. Our estimator significantly improves computational efficiency in variance estimation compared to the existing nonsmooth estimator. Analysis of the HIV/AIDS cohort study data reveals dynamic effects of CD4 cell count on the residual life to the onset of dyslipidemia.

Semiparametric regression modelling of current status competing risks data: a Bayesian approach

Semiparametric regression modelling of current status competing risks data: a Bayesian approach

Centralization of Pancreaticoduodenectomy: A Systematic Review and Spline Regression Analysis to Recommend Minimum Volume for a Specialist Pancreas Service.

Through a systematic review and spline curve analysis, to better define the minimum volume threshold for hospitals to perform (pancreaticoduodenectomy) and the high-volume center. The pancreaticoduodenectomy (PD) is a resource-intensive procedure, with high morbidity and long hospital stays resulting in centralization towards high-volume hospitals; the published definition of high volume remains variable. Following a systematic review of studies comparing PD outcomes across volume groups, semiparametric regression modeling of morbidity (%), mortality (%), length of stay (days), lymph node harvest (number of nodes), and cost ($USD) as continuous variables were performed and fitted as a smoothed function of splines. If this showed a nonlinear association, then a "zero-crossing" technique was used, which produced "first and second derivatives" to identify volume thresholds. Our analysis of 33 cohort studies (198,377 patients) showed 55 PDs/year and 43 PDs/year were the threshold value required to achieve the lowest morbidity and highest lymph node harvest, with model estimated df 5.154 ( P <0.001) and 8.254 ( P <0.001), respectively. The threshold value for mortality was ~45 PDs/year (model 9.219 ( P <0.001)), with the lowest mortality value (the optimum value) at ~70 PDs/year (ie, a high-volume center). No significant association was observed for cost ( edf =2, P =0.989) and length of stay ( edf =2.04, P =0.099). There is a significant benefit from the centralization of PD, with 55 PDs/year and 43 PDs/year as the threshold value required to achieve the lowest morbidity and highest lymph node harvest, respectively. To achieve mortality benefit, the minimum procedure threshold is 45 PDs/year, with the lowest and optimum mortality value (ie, a high-volume center) at approximately 70 PDs/year.

Platelet Modeling in DHF Patients Using Local Polynomial Semiparametric Regression on Longitudinal Data

Regression analysis is one of the statistical methods used to model the relationship between response variables and predictor variables. Semiparametric regression is a combination of parametric and nonparametric regression. The estimator used in estimating the semiparametric regression model in this research is the Local Polynomial. Longitudinal data can be found in the health sector, including dengue hemorrhagic fever (DHF) data. The laboratory criteria for indication of DHF is thrombocytopenia. This research aims to obtain platelets model for DHF patients that can be used for forecasting so that it is hoped that it can provide information to the medical team in treating DHF patients. The estimated model used is Local Polynomial semiparametric regression on longitudinal data. The response variables in this research were platelets of DHF patients, which were influenced by hemoglobin as parametric predictor variable and examination time while hospitalized as nonparametric predictor variable. In the local polynomial regression model, it is necessary to select the optimal bandwidth and polynomial order method, GCV. The optimum bandwidth selection based on the GCV method obtained is 1.5 and polynomial order of 2, then applied to DHF patient platelet data, producing an estimated local polynomial semiparametric regression model that follows the actual data pattern. Modeling the platelets of DHF patients obtained using a local polynomial estimator resulted in an R2 value of 84.25% and MAPE of 4.5%, indicating highly accurate forecasting, so it can be concluded that the resulting model is better at predicting.

Separation of the Linear and Nonlinear Covariates in the Sparse Semi-Parametric Regression Model in the Presence of Outliers

Determining the predictor variables that have a non-linear effect as well as those that have a linear effect on the response variable is crucial in additive semi-parametric models. This issue has been extensively investigated by many researchers in the area of semi-parametric linear additive models, and various separation methods are proposed by the authors. A popular issue that might affect both estimation and separation results is the existence of outliers among the observations. In order to address this lack of sensitivity towards extreme observations, robust estimating approaches are frequently applied. We propose a robust method for simultaneously identifying the linear and nonlinear components of a semi-parametric linear additive model, even in the presence of outliers in the observations. Additionally, this model is sparse in that it may be used to determine which explanatory variables are ineffective by giving accurate zero estimates for their coefficients. To assess the effectiveness of the proposed method, a comprehensive Monte Carlo simulation study is conducted along with an application to investigate the dataset, which includes Boston property prices dataset.

Semiparametric modeling for the cardiometabolic risk index and individual risk factors in the older adult population: A novel proposal.

Multivariate semiparametric regression models were used to study the association between the CMRI with the individual risk factors, which was achieved using secondary analysis the data from the SABE study (Survey on Health, Well-Being, and Aging in Colombia, 2015). The risk factors were selected through a stepwise procedure. The covariates included showed evidence of non-linear relationships with the CMRI, revealing non-linear interactions between: BMI and age (p< 0.00); arm and calf circumferences (p<0.00); age and females (p<0.00); walking speed and joint pain (p<0.02); and arm circumference and joint pain (p<0.00). Semiparametric modeling explained 24.5% of the observed deviance, which was higher than the 18.2% explained by the linear model.

Excess Mortality Risk Due to Heat Stress in Different Climatic Zones of India.

India is at a high risk of heat stress-induced health impacts and economic losses owing to its tropical climate, high population density, and inadequate adaptive planning. The health impacts of heat stress across climate zones in India have not been adequately explored. Here, we examine and report the vulnerability to heat stress in India using 42 years (1979-2020) of meteorological data from ERA-5 and developed climate-zone-specific percentile-based human comfort class thresholds. We found that the heat stress is usually 1-4 °C higher on heatwave (HW) days than on nonheatwave (NHW) days. However, the stress on NHW days remains considerable and cannot be neglected. We then showed the association of a newly formulated India heat index (IHI) with daily all-cause mortality in three cities - Delhi (semiarid), Varanasi (humid subtropical), and Chennai (tropical wet and dry), using a semiparametric quasi-Poisson regression model, adjusted for nonlinear confounding effects of time and PM2.5. The all-cause mortality risk was enhanced by 8.1% (95% confidence interval, CI: 6.0-10.3), 5.9% (4.6-7.2), and 8.0% (1.7-14.2) during "sweltering" days in Varanasi, Delhi, and Chennai, respectively, relative to "comfortable" days. Across four age groups, the impact was more severe in Varanasi (ranging from a 3.2 to 7.5% increase in mortality risk for a unit rise in IHI) than in Delhi (2.6-4.2% higher risk) and Chennai (0.9-5.7% higher risk). We observed a 3-6 days lag effect of heat stress on mortality in these cities. Our results reveal heterogeneity in heat stress impact across diverse climate zones in India and call for developing an early warning system keeping in mind these regional variations.

Pemodelan Kadar Hemoglobin pada Pasien Demam Berdarah di Kota Samarinda Menggunakan Regresi Semiparametrik Spline Truncated

This article discusses the innovation of statistical modeling in regression analysis with a semiparametric approach applied to health data. Regression analysis is a method in statistics that takes a lot of roles in statistical modeling. Regression analysis is used to model the relationship between the independent variable (x) and the dependent variable (y). There are three approaches to regression analysis, namely parametric, nonparametric, and a combination of the two, namely semiparametric. Semiparametric regression is used when the dependent variable has a known relationship with some of the independent variables and has an unknown pattern of a relationship with some of the other independent variables. The purpose of this study was to model hemoglobin levels in dengue fever patients, with the independent variables used being the number of hematocrits (x1) and the number of leukocytes (x2). The method used is spline truncated semiparametric regression. The truncated spline estimator was chosen for the nonparametric component because it has many advantages in modeling, one of which is being able to model patterns where the form of the relationship is unknown. The parameter estimation used is the maximum estimation. Selection of the optimal knot point using Generalized Cross-Validation (GCV). Based on the results of the analysis, the truncated spline semiparametric regression model was obtained which was applied to the hemoglobin level data in a model with three knots which have a coefficient of determination of 89.074%. Based on the results of testing the hypothesis simultaneously, it can be concluded that simultaneously the independent variable has a significant effect on the dependent variable. In the partial test, it is concluded that the variables x1 and x2 have a significant influence on the dependent variable y .

Complete f-moment convergence for m-asymptotic negatively associated random variables and related statistical applications

In this article, the complete f-moment convergence for m-asymptotic negatively associated random variables is investigated. As applications, we establish the strong consistency of the least square estimator in the simple linear errors-in-variables models and the complete consistency for estimator in the semiparametric regression model based on m-asymptotic negatively associated errors. We also give some simulations to assess the finite sample performance of the theoretical results.

Semi-parametric single-index predictive regression models with cointegrated regressors

This paper considers the estimation of a semi-parametric single-index regression model that allows for nonlinear predictive relationships. This model is useful for predicting financial asset returns, whose observed behaviour resembles a stationary process, if the multiple nonstationary predictors are cointegrated. The presence of cointegrated regressors imposes a single-index structure in the model, and this structure not only balances the nonstationarity properties of the multiple predictors with the stationarity properties of asset returns but also avoids the curse of dimensionality associated with nonparametric regression function estimation. An orthogonal series expansion is used to approximate the unknown link function for the single-index component. We consider the constrained nonlinear least squares estimator of the single-index (or the cointegrating) parameters and the plug-in estimator of the link function, and derive their asymptotic properties. In an empirical application, we find some evidence of in-sample nonlinear predictability of U.S. stock returns using cointegrated predictors. We also find that the single-index model in general produces better out-of-sample forecasts than both the historical average benchmark and the linear predictive regression model.

Complications and associated risk factors after surgical management of proximal femoral fractures.

This work aimed at answering the following research questions: 1) What is the rate of mechanical complications, nonunion and infection for head/neck femoral fractures, intertrochanteric fractures, and subtrochanteric fractures in the elderly USA population? and 2) Which factors influence adverse outcomes? Proximal femoral fractures occurred between 1 January 2009 and 31 December 2019 were identified from the Medicare Physician Service Records Data Base. The Kaplan-Meier method with Fine and Gray sub-distribution adaptation was used to determine rates for nonunion, infection, and mechanical complications. Semiparametric Cox regression model was applied incorporating 23 measures as covariates to identify risk factors. Union failure occured in 0.89% (95% confidence interval (CI) 0.83 to 0.95) after head/neck fracturs, in 0.92% (95% CI 0.84 to 1.01) after intertrochanteric fracture and in 1.99% (95% CI 1.69 to 2.33) after subtrochanteric fractures within 24 months. A fracture-related infection was more likely to occur after subtrochanteric fractures than after head/neck fractures (1.64% vs 1.59%, hazard ratio (HR) 1.01 (95% CI 0.87 to 1.17); p < 0.001) as well as after intertrochanteric fractures (1.64% vs 1.13%, HR 1.31 (95% CI 1.12 to 1.52); p < 0.001). Anticoagulant use, cerebrovascular disease, a concomitant fracture, diabetes mellitus, hypertension, obesity, open fracture, and rheumatoid disease was identified as risk factors. Mechanical complications after 24 months were most common after head/neck fractures with 3.52% (95% CI 3.41 to 3.64; currently at risk: 48,282). The determination of complication rates for each fracture type can be useful for informed patient-clinician communication. Risk factors for complications could be identified for distinct proximal femur fractures in elderly patients, which are accessible for therapeutical treatment in the management.