SCAD-penalized regression in high-dimensional partially linear models

We consider the problem of simultaneous variable selection and estimation in partially linear models with a divergent number of covariates in the linear part, under the assumption that the vector of regression coefficients is sparse. We apply the SCAD penalty to achieve sparsity in the linear part and use polynomial splines to estimate the nonparametric component. Under reasonable conditions, it is shown that consistency in terms of variable selection and estimation can be achieved simultaneously for the linear and nonparametric components. Furthermore, the SCAD-penalized estimators of the nonzero coefficients are shown to have the asymptotic oracle property, in the sense that it is asymptotically normal with the same means and covariances that they would have if the zero coefficients were known in advance. The finite sample behavior of the SCAD-penalized estimators is evaluated with simulation and illustrated with a data set.Comment: Published in at http://dx.doi.org/10.1214/07-AOS580 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Asymptotic oracle properties of SCAD-penalized least squares estimators

We study the asymptotic properties of the SCAD-penalized least squares estimator in sparse, high-dimensional, linear regression models when the number of covariates may increase with the sample size. We are particularly interested in the use of this estimator for simultaneous variable selection and estimation. We show that under appropriate conditions, the SCAD-penalized least squares estimator is consistent for variable selection and that the estimators of nonzero coefficients have the same asymptotic distribution as they would have if the zero coefficients were known in advance. Simulation studies indicate that this estimator performs well in terms of variable selection and estimation.Comment: Published at http://dx.doi.org/10.1214/074921707000000337 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

The effects of cardiac structure, valvular regurgitation, and left ventricular diastolic dysfunction on the diagnostic accuracy of Murray law–based quantitative flow ratio

ObjectiveThe study aimed to investigate the diagnostic accuracy of Murray law–based quantitative flow ratio (μQFR) from a single angiographic view in patients with abnormal cardiac structure, left ventricular diastolic dysfunction, and valvular regurgitation.BackgroundμQFR is a novel fluid dynamics method for deriving fractional flow reserve (FFR). In addition, current studies of μQFR mainly analyzed patients with normal cardiac structure and function. The accuracy of μQFR when patients had abnormal cardiac structure, left ventricular diastolic dysfunction, and valvular regurgitation has not been clear.MethodsThis study retrospectively analyzed 261 patients with 286 vessels that underwent both FFR and μQFR prior to intervention. The cardiac structure and function were measured using echocardiography. Pressure wire–derived FFR ≤0.80 was defined as hemodynamically significant coronary stenosis.ResultsμQFR had a moderate correlation with FFR (r = 0.73, p < 0.001), and the Bland–Altman plot presented no difference between the μQFR and FFR (0.006 ± 0.075, p = 0.192). With FFR as the standard, the diagnostic accuracy, sensitivity, specificity, positive predictive value, and negative predictive value of μQFR were 94.06% (90.65–96.50), 82.56% (72.87–89.90), 99.00% (96.44–99.88), 97.26 (89.91–99.30), and 92.96% (89.29–95.44), respectively. The concordance of μQFR/FFR was not associated with abnormal cardiac structure, valvular regurgitation (aortic valve, mitral valve, and tricuspid valve), and left ventricular diastolic function. Coronary hemodynamics showed no difference between normality and abnormality of cardiac structure and left ventricular diastolic function. Coronary hemodynamics demonstrated no difference among valvular regurgitation (none, mild, moderate, or severe).ConclusionμQFR showed an excellent agreement with FFR. The effect of abnormal cardiac structure, valvular regurgitation, and left ventricular diastolic function did not correlate with the diagnostic accuracy of μQFR. Coronary hemodynamics showed no difference in patients with abnormal cardiac structure, valvular regurgitation, and left ventricular diastolic function

SCAD-Penalized Regression in High-Dimensional Partially Linear Models

Summary. We consider the problem of simultaneous variable selection and estimation in partially linear models with a divergent number of covariates in the linear part, under the assumption that the vector of regression coefficients is sparse. We apply the SCAD penalty to achieve sparsity in the linear part and use polynomial splines to estimate the nonparametric component. Under reasonable conditions it is shown that consistency in terms of variable selection and estimation can be achieved simultaneously for the linear and nonparametric components. Furthermore, the SCAD-penalized estimators of the nonzero coefficients are shown to be asymptotically normal with the same means and covariances that they would have if the zero coefficients were known in advance. Simulation studies are conducted to evaluate the finite sample behavior of the SCAD-penalized estimators. Key Words and phrases. Asymptotic normality, high-dimensional data, oracle property, penalized estimation, semiparametric models, variable selection,. Short title. High-dimensional PLM AMS 2000 subject classification. Primary 62J05, 62G08; secondary 62E2

Regularized estimation in the accelerated failure time model with high dimensional covariates. Biometrics

Summary The need for analyzing failure time data with high-dimensional covariates arises in investigating the relationship between a censored survival outcome and microarray gene expression profiles. We consider two regularization approaches, the LASSO and the threshold gradient directed regularization, for variable selection and estimation in the accelerated failure time model with high-dimensional covariates based on Stute’s weighted least squares method. The Stute estimator uses the Kaplan-Meier weights to account for censoring in the least squares criterion. The weighted least squares objective function makes the adaption of this approach to high dimensional covariate settings computationally feasible. We use the V-fold cross validation and a modified Akaike’s Information Criterion for tuning parameter selection, and a bootstrap approach for variance estimation. The proposed method is evaluated using simulations and demonstrated with a real data example

Least Absolute Deviations Estimation for the Accelerated Failure Time Model

Summary The accelerated failure time (AFT) model assumes a linear relationship between the event time and the covariates. We propose a robust weighted least-absolute-deviations (LAD) method for estimation in the AFT model with right-censored data. This method uses the Kaplan-Meier weights in the LAD objective function to account for censoring. We show that the proposed estimator is root-n consistent and asymptotically normal under mild assumptions. The proposed estimator can be easily computed using existing software, which makes it especially useful for data with medium to high dimensional covariates. The proposed method is evaluated using simulations and demonstrated with two clinical data sets