Estimation Of Regression Parameters Research Articles

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.

Enhanced Model Predictions through Principal Components and Average Least Squares-Centered Penalized Regression

We address the estimation of regression parameters for the ill-conditioned predictive linear model in this study. Traditional least squares methods often encounter challenges in yielding reliable results when there is multicollinearity. Therefore, we employ a better shrinkage method, average least squares-centered penalized regression (ALPR), as it offers a more efficient approach for handling multicollinearity than ridge regression. Additionally, we integrate ALPR with the principal component (PC) dimension reduction method for enhanced performance. We compared the proposed PCALPR estimation technique with existing ones for ill-conditioned problems through comprehensive simulations and real-life data analyses using the mean squared error. This integration results in superior model performance compared to other methods, highlighting the potential of combining dimensionality reduction techniques with penalized regression for enhanced model predictions.

Bayesian relative composite quantile regression approach of ordinal latent regression model with L1/2 regularization

AbstractOrdinal data frequently occur in various fields such as knowledge level assessment, credit rating, clinical disease diagnosis, and psychological evaluation. The classic models including cumulative logistic regression or probit regression are often used to model such ordinal data. But these modeling approaches conditionally depict the mean characteristic of response variable on a cluster of predictive variables, which often results in non‐robust estimation results. As a considerable alternative, composite quantile regression (CQR) approach is usually employed to gain more robust and relatively efficient results. In this paper, we propose a Bayesian CQR modeling approach for ordinal latent regression model. In order to overcome the recognizability problem of the considered model and obtain more robust estimation results, we advocate to using the Bayesian relative CQR approach to estimate regression parameters. Additionally, in regression modeling, it is a highly desirable task to obtain a parsimonious model that retains only important covariates. We incorporate the Bayesian penalty into the ordinal latent CQR regression model to simultaneously conduct parameter estimation and variable selection. Finally, the proposed Bayesian relative CQR approach is illustrated by Monte Carlo simulations and a real data application. Simulation results and real data examples show that the suggested Bayesian relative CQR approach has good performance for the ordinal regression models.

Semiparametric accelerated failure time models under unspecified random effect distributions

Accelerated failure time (AFT) models with random effects, a useful alternative to frailty models, have been widely used for analyzing clustered (or correlated) time-to-event data. In the AFT model, the distribution of the unobserved random effect is conventionally assumed to be parametric, often modeled as a normal distribution. Although it has been known that a misspecfied random-effect distribution has little effect on regression parameter estimates, in some cases, the impact caused by such misspecification is not negligible. Particularly when our focus extends to quantities associated with random effects, the problem could become worse. In this paper, we propose a semi-parametric maximum likelihood approach in which the random-effect distribution under the AFT models is left unspecified. We provide a feasible algorithm to estimate the random-effect distribution as well as model parameters. Through comprehensive simulation studies, our results demonstrate the effectiveness of this proposed method across a range of random-effect distribution types (discrete or continuous) and under conditions of heavy censoring. The efficacy of the approach is further illustrated through simulation studies and real-world data examples.

A new and unified method for regression analysis of interval-censored failure time data under semiparametric transformation models with missing covariates.

This paper discusses regression analysis of interval-censored failure time data arising from semiparametric transformation models in the presence of missing covariates. Although some methods have been developed for the problem, they either apply only to limited situations or may have some computational issues. Corresponding to these, we propose a new and unified two-step inference procedure that can be easily implemented using the existing or standard software. The proposed method makes use of a set of working models to extract partial information from incomplete observations and yields a consistent estimator of regression parameters assuming missing at random. An extensive simulation study is conducted and indicates that it performs well in practical situations. Finally, we apply the proposed approach to an Alzheimer's Disease study that motivated this study.

Joint AFT random-effect modeling approach for clustered competing-risks data

Competing risks data arise when occurrence of an event hinders observation of other types of events, and they are encountered in various research areas including biomedical research. These data have been usually analyzed using the hazard-based models, not survival times themselves. In this paper, we propose a joint accelerated failure time (AFT) modeling approach to model clustered competing risks data. Times to competing events are assumed to be log-linear with normal errors and correlated through a scaled random effect that follows a zero-mean normal distribution. Inference on the model parameters is based on the h-likelihood. Performance of the proposed method is evaluated through extensive simulation studies. The simulation results show that the estimated regression parameters are robust against the violation of the assumed parametric distributions. The proposed method is illustrated with three real competing risks data sets.

Efficient estimation for left-truncated competing risks regression for case-cohort studies.

The case-cohort study design provides a cost-effective study design for a large cohort study with competing risk outcomes. The proportional subdistribution hazards model is widely used to estimate direct covariate effects on the cumulative incidence function for competing risk data. In biomedical studies, left truncation often occurs and brings extra challenges to the analysis. Existing inverse probability weighting methods for case-cohort studies with competing risk data not only have not addressed left truncation, but also are inefficient in regression parameter estimation for fully observed covariates. We propose an augmented inverse probability-weighted estimating equationfor left-truncated competing risk data to address these limitations of the current literature. We further propose a more efficient estimator when extra information from the other causes is available. The proposed estimators are consistent and asymptotically normally distributed. Simulation studies show that the proposed estimator is unbiased and leads to estimation efficiency gain in the regression parameter estimation. We analyze the Atherosclerosis Risk in Communities study data using the proposed methods.

Prediction Penalized Analysis of Stroke Based on New Bayesian Hierarchical Priors Model

The penalized or the regularization methods nowadays are the most statistical popular tools used for model selection and variable selection procedure. The quality of the regression parameter estimates depends on the prediction accuracy of the estimated model and the model interpretability. Penalized operator methods usually produced the most parsimonious model (less number of predictor and more explanation). This paper utilized new scale mixture of Rayleigh mixing with normal density to study the relationship between the stroke size and some predictors. New hierarchical priors model has developed as well new Gibbs sampling algorithm. The results demonstrated that the proposed model is comparable to some exists regularization models.

Empirical likelihood in a partially linear single-index model with censored response data

An empirical likelihood (EL) approach for a partial linear single-index model with censored response data is studied. A bias-corrected EL ratio is proposed, and the asymptotic chi-squared distribution of this ratio is obtained. The result can be directly used to construct the confidence regions of the regression parameters. The estimators of regression parameters and link function are constructed, and their asymptotic distributions are obtained. Also, a confidence band of the link function is constructed. The proposed method has two main features: The first feature is that the EL ratio is calibrated directly from within, instead of multiplying an adjustment factor by an EL ratio, which reflects the nature of EL. The second feature is avoiding undersmoothing of nonparametric functions, thus ensuring that the n-consistency of the parameter estimator. As a byproduct, the EL and estimation of a single-index model with censored response data are studied. The performance of the bias-corrected EL is evaluated by the simulation studies. The proposed method is illustrated with an example of a real data analysis.

Research on the Evaluation and Enhancement Strategies of College Students’ Health Human Capital in “Healthy Hunan” under the Background of Big Data

Abstract This paper precisely explores the structure and characteristics of college students’ healthy human capital and its influencing factors. It aims to enhance students’ positive and healthy mindset and promote optimism in life and learning. A solid analytical framework is constructed by sorting out the ordered multicategorical logistic regression model and parameter estimation methods and the application steps of the propensity score matching model. College students from ten colleges and universities in Hunan Province were selected as research subjects, and a questionnaire was designed to assess their healthy human capital. The specific factors affecting college students’ healthy human capital accumulation were analyzed in depth through the probability density analysis of propensity score matching, standard support hypothesis testing, and the parallel line test and regression results of the ordered multicategorical regression model. The findings show that the curves of the experimental and control groups after propensity score matching almost overlap in the [0.2,0.4] interval, indicating the method’s validity. A more important finding is that the number of college students with poor self-assessed physical health is 8.063 times higher than that of college students with self-assessed mental health as good, which emphasizes the significant impact of mental health on healthy human capital. Therefore, to effectively improve the health human capital of college students, students, families and universities must form a linkage mechanism and work together to cultivate college students’ health awareness.

Biomarker data with measurement error in medical research: A literature review

AbstractA biomarker is a measurable indicator of the severity or presence of a disease or medical condition in biomedical or epidemiological research. Biomarkers may help in early diagnosis and prevention of diseases. Several biomarkers have been identified for many diseases such as carbohydrate antigen 19‐9 for pancreatic cancer. However, biomarkers may be measured with errors due to many reasons such as specimen collection or day‐to‐day within‐subject variability of the biomarker, among others. Measurement error in the biomarker leads to bias in the regression parameter estimation for the association of the biomarker with disease in epidemiological studies. In addition, measurement error in the biomarkers may affect standard diagnostic measures to evaluate the performance of biomarkers such as the receiver operating characteristic (ROC) curve, area under the ROC curve, sensitivity, and specificity. Measurement error may also have an effect on how to combine multiple cancer biomarkers as a composite predictor for disease diagnosis. In follow‐up studies, biomarkers are often collected intermittently at examination times, which may be sparse and typically biomarkers are not observed at the event times. Joint modeling of longitudinal and time‐to‐event data is a valid approach to account for measurement error in the analysis of repeatedly measured biomarkers and time‐to‐event outcomes. In this article, we provide a literature review on existing methods to correct for estimation in regression analysis, diagnostic measures, and joint modeling of longitudinal biomarkers and survival outcomes when the biomarkers are measured with errors.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Robust Methods Statistical and Graphical Methods of Data Analysis > EM Algorithm Statistical Models > Survival Models

REGRESSION ANALYSIS OF ROBUST ESTIMATION-S WITH TUKEY BISQUARE WEIGHTING ON POVERTY LEVEL ON SULAWESI ISLAND

Poverty is a situation where a person experiences difficulty in meeting basic needs. There are several factors that influence poverty, including population, unemployment, gross regional domestic product, human development index, average years of schooling and labor force participation rate. Therefore, it is necessary to carry out regression analysis to determine the relationship between one variable and other variables. One method for estimating regression parameters is the least squares method. Some classic assumptions are not met because there are outlier data. Outliers are data that do not follow the overall distribution pattern, so a method is used that can overcome outliers, namely the S-estimation robust regression method with the Tukey bisquare weighting function. The results of the research show that the best model was obtained from robust S-estimation regression with Tukey bisquare weighting, namely factors that influence the level of poverty on the island of Sulawesi, namely Population Number ), Human Development Index ( ), Average Years of Schooling ( ) and, Force Participation Level. Work .

Subgroup detection based on partially linear additive individualized model with missing data in response

Based on partially linear additive individualized model, a fusion-penalized inverse probability weighted least squares method is proposed to detect the subgroup for missing data in response. Firstly, the B-spline technique is used to approximate the unknown additive individualized functions and then an inverse probability weighted quadratic loss function is established with fusion penalty on the difference of subject-wise B-spline coefficients. Secondly, minimization of such quadratic loss function leads to the estimation of linear regression parameters and individualized B spline coefficients. With a proper tuning parameter, some differences in penalty term are shrunk into zero and thus the corresponding subjects will be clustered into the same subgroup. Thirdly, a clustering method is developed to automatically determine the subgroup membership for the subjects with missing data. Fourthly, large sample properties of resulting estimates are given under some regular conditions. Finally, numerical studies are presented to illustrate the performance of the proposed subgroup detection method.

Robust weighted ridge regression based on S – estimator

Ordinary least squares (OLS) estimator performance is seriously threatened by correlated regressors often called multicollinearity. Multicollinearity is a situation when there is strong relationship between any two exogenous variables. In this case, the ridge estimator offers more reliable estimations when such scenario occurs. Outliers can have significant impact on the estimation of regression parameters leading to biased results. However, both OLS and Ridge estimators are sensitive to outlaying observations (outliers). The outlier – prone dataset in the endogenous variable has been efficiently solved utilizing the Robust M estimator in our recent paper. In recent studies, Robust M estimator has some drawbacks despite its efficient performances with outlier – prone dataset in the dependent (endogenous) variable hence the consideration of the Robust S estimator. The Robust S estimator is less sensitive to outliers in both endogenous and exogenous variables and utilizes standard deviation rather than the median in the case of Robust M estimator to handle outliers in the endogenous variable. The Robust ridge based on the S estimator was well suited to model dataset with multicollinearity and outliers problems in the endogenous variable. Also, it was noted in literature that outliers are one of the causes of heteroscedasticity and non – robust weighted least squares were initially employed to figure out for them. In this study, we introduced proposed Robust S weighted ridge estimator by adding a novel weighting method to address the three problems in a linear regression model. The selected Ridge estimators and Robust S estimator in two weighted versions (True weight (Wo) and suggested new weight (W1)) were combined to respectively develop the Robust S Ridge and Robust S Weighted Ridge estimators. Monte – Carlo simulation experiments were conducted on a linear regression model with three and six exogenous variables exhibiting different degrees of Multicollinearity, with heteroscedasticity structure of powers, size of outlier in endogenous variable and error variances and five levels of sample sizes. The Mean Square Error (MSE) was used as a criterion to evaluate the performances of the new and existing estimators. Simulation findings show categorically that the new approach is preferred over previous approach and hereby recommended.

Inference on regression model with misclassified binary response

Misclassification of binary responses, if ignored, may severely bias the maximum likelihood estimators (MLEs) of regression parameters. For such data, a binary regression model incorporating non-differential classification errors is extensively used by researchers in different application contexts. We strongly caution against indiscriminate use of this model considering the fact that it suffers from a serious estimation problem due to confounding of the unknown misclassification probabilities with the regression parameters, and thus, may lead to a highly biased estimate. To overcome this problem, we propose here the use of an internal validation sample in addition to the main sample. Assuming differential classification errors, we consider MLEs of the regression parameters based on the joint likelihood of the main sample and the internal validation sample. We then develop a rigorous asymptotic theory for the joint MLEs under standard assumptions. To facilitate its easy implementation for inference, we propose a bootstrap approximation to the asymptotic distribution and prove its consistency. The results of the simulation studies suggest that even an extremely small validation sample may lead to a vastly improved inference. Finally, the methodology is illustrated with a real-life survey data.

Robust estimation for function-on-scalar regression models

For the functional linear models in which the dependent variable is functional and the predictors are scalar, robust regularization for simultaneous variable selection and regression parameter estimation is an important yet challenging issue. In this paper, we propose two types of regularized robust estimation methods. The first estimator adopts the ideas of reproducing kernel Hilbert space, least absolute deviation and group Lasso techniques. Based on the first method, the second estimator applies the pre-whitening technique and estimates the error covariance function by using functional principal component analysis. Simulation studies are conducted to examine the performance of the proposed methods in small sample sizes. The method is also applied to the Canadian weather data set, which consists of the daily average temperature and precipitation observed by 35 meteorological stations across Canada from 1960 to 1994. Numerical simulations and real data analysis show a good performance of the proposed robust methods for function-on-scalar models.

Generalized log-logistic proportional hazard model: a non-penalty shrinkage approach

This paper considers the pretest and shrinkage estimation methods for estimating regression parameters of the generalized log-logistic proportional hazard (PH) model. This model is a simple extension of the log-logistic model, which is closed under the PH relationship. The generalized log-logistic PH model also has attributes similar to those of the Weibull model. We consider this model for right-censored data when some parameters shrink to a restricted subspace. This subspace information on the parameters is used to shrink the unrestricted model estimates toward the restricted model estimates. We then optimally combine the unrestricted and restricted estimates in order to define pretest and shrinkage estimators. Although this estimation procedure may increase bias, it also reduces the overall mean squared error. The efficacy of the proposed model and estimation techniques are shown using a simulation study as well as an application to real data. We also compare the performance of generalized log-logistic, Weibull, and Cox PH models for unimodal and increasing hazards. The shrinkage estimator poses less risk than the maximum likelihood estimator when the shrinkage dimension exceeds two; this is shown through simulation and real data applications.

23 The Utility of Global versus Domain-specific Neuropsychological Test Score Dispersion as Markers of Cognitive Decline

Objective:Higher baseline dispersion (intra-individual variability) across neuropsychological test scores at a single time-point has been associated with more rapid cognitive decline, onset of Mild Cognitive Impairment (MCI) and Alzheimer’s disease (AD), faster rates of hippocampal and entorhinal atrophy, and increased AD neuropathology. Comparison between predictions made from test score dispersion within a cognitive domain versus global, cross-domain dispersion is understudied. Global dispersion may be influenced by ability-and test-specific characteristics. This study examined the performance of global versus domain-specific dispersion metrics to identify which is most predictive of cognitive decline over time.Participants and Methods:Data for baseline and five follow-up visits of 308 participants with normal cognition (Mage=73.90, SD=8.12) were selected from the National Alzheimer’s Coordinating Center (NACC) Dataset. Participants were required to have no focal neurological deficits, or history of depression, stroke, or heart attack. Diagnoses and progression to MCI and/or dementia were determined at each visit through consensus conferences. Raw neuropsychological scores were standardized using NACC norms. Global baseline dispersion was defined as the intraindividual standard deviation (ISD) across the 10 scores in the NACC battery. Domain-specific dispersions were calculated by constructing composites and ISD was computed across tests sampling their respective domains (executive functioning/attention/processing speed [EFAS], language, and memory; see Table 1 for details on these tests). Higher values on each of these metrics reflect greater dispersion. Multinomial logistic regression model fit statistics and parameter estimates were compared across four different models (global, EFAS, Language, and Memory dispersion) covarying for age, years of education, sex, race, ethnicity, and ApoE4 status. Models were compared using the Likelihood Ratio Test (LRT) and the Akaike Information Criteria (AIC) of Models statistics.Results:Of the 308 participants, 70 (22.7%) progressed to MCI, and 82 (26.6%) progressed to dementia. Tables 1 and 2 show the results of the logistic regressions for the four models. All models fit the data well, with statistically significant predictions of conversion. Model 1 (global dispersion) showed a better fit than domain-specific models of dispersion per LRT and AIC values. Consistent with the results from mean differences between groups, parameter estimates showed that only global dispersion and EFAS dispersion significantly predicted conversion to dementia (when included with other covariates in models), with higher dispersion reflecting a greater risk of conversion.Conclusions:In this sample, baseline global and EFAS dispersion measures significantly predicted conversion to dementia. Although global dispersion was a stronger predictor of dementia progression, findings suggest that executive functioning performance may be driving this relationship. A single index of global variability, from the calculation of standard deviation across test scores, may be supplementary for clinicians when distinguishing individuals at risk for dementia progression. None of the models were predictive of conversion to MCI. Further research is required to examine cognitive variability differences among patients who progress to MCI and patient-specific factors that may relate to test score dispersion and its utility in predicting the progression of symptoms.

Research on the role of psychological education in college Civic Education under the background of Internet

Abstract Psychological education in colleges and universities can inject new vitality into Civic Education. In this paper, the ridge estimation of regression parameters is based on the linear regression model, the canonical form of ridge regression is constructed, and the selection method of ridge parameters is proposed by combining the ridge trace plot and the Mcdorard-Garaneau method. The prediction accuracy of the ridge regression is optimized by using the idea of partial least squares for the shortcomings of the general ridge regression. After completing the improvement of ridge regression, the quantitative evaluation indexes of psychological education and Civic Education in colleges and universities were established, and the influence of psychological education on Civic Education was studied through regression analysis. The correlation coefficient R of faculty and hardware construction of psychological education on the content richness of Civic Education reached 0.725, and the standardized regression coefficient T of the former was −0.357, while the latter was −4.257, and the former was more significant than the latter. Meanwhile, the regression coefficients of organizational management and institutional setting, faculty construction and work organization and effectiveness on the level of college students’ psychological education were 0.54, 0.26 and 0.24, respectively, with significant joint effects. This study realizes the quantitative analysis of psychological education influencing Civic Education, which helps to promote the integration and development of psychological education and Civic Education.

Imputation methods for the semiparametric transformation models with doubly-truncated and interval-censored data

Interval sampling is often used in epidemiological studies. With interval sampling, data are collected only from individuals who fail within a certain calendar time interval. Such interval sampling induces doubly truncated (DT) data if the calendar time of the failure event can be observed exactly. In practice, the failure time may not be directly observed and it is only recorded within time intervals, leading to doubly truncated and interval censored (DTIC) data. In this article, we analyze DTIC data using a class of semiparametric transformation models. By iterating between an imputation step and an optimization step for DT data, we propose two imputation methods for obtaining parameter estimates for regression parameters and cumulative hazard function of models. Simulation studies indicate that the proposed estimators perform adequately.