Spontaneous Coronary Artery Dissection: An Updated Comprehensive Review

Spontaneous coronary artery dissection (SCAD) is defined as a non-iatrogenic, non-traumatic separation of the coronary artery wall, which has gained considerable recognition as an important cause of acute coronary syndrome. Despite the emerging evidence, it is still frequently missed and requires a high index of suspicion, as failure to accurately identify SCAD promptly could prove fatal. SCAD is most prevalent among middle-aged women, although it can also be found in men and postmenopausal women. Risk factors of SCAD include exogenous hormone use, physical and emotional stressors, pregnancy, and several inflammatory and connective tissue disorders. COVID-19 also contributes to the prevalence of SCAD. SCAD is classified into four main types based on the angiographic findings - type 1, type 2, type 3, and type 4. The gold standard for diagnosis is coronary angiography; however, intracardiac imaging is useful if diagnostic doubts persist. Despite the increasing recognition of this disease, there is a paucity in the guidelines on the management of SCAD. Management may be conservative, medical, or interventional. Cardiac rehabilitation is also necessary in the management of patients with SCAD. In light of the gaps in evidence, the authors aim to provide a comprehensive review of the existing literature, outlining the pathophysiology, classification, and, most importantly, the evidence and pitfalls circulating diagnosis, acute, and long-term management of SCAD.

Spontaneous Coronary Artery Dissection: A Challenging Diagnosis

Spontaneous coronary artery dissection (SCAD) is a relatively uncommon cause of acute coronary syndrome, which is mainly reported in postpartum patients and patients without typical cardiac risk factors. Our case was a 58-year-old female with a history of diabetes, hypertension, and hyperlipidemia who presented with non-exertional crushing retrosternal chest pain and was found to have ST elevation in inferior leads. Immediate cardiac catheterization was suggestive of spontaneous dissection of the third obtuse marginal artery, which was managed conservatively. Clinical suspicion is crucial for SCAD diagnosis, as it might be difficult to distinguish between coronary artery occlusion and SCAD. Moreover, revascularization in SCAD can be associated with complications. Therefore, SCAD needs to be considered as a differential diagnosis not only in patients without cardiac risk factors but also in patients with known cardiac risk factors like our case.

A Tale of Two Evils: Iatrogenic Propagation of Spontaneous Coronary Artery Dissection

Spontaneous coronary artery dissection (SCAD) is a non-traumatic and non-iatrogenic intimal separation of the coronary arterial wall. While poorly understood, its mechanism confers higher prevalence in younger females, and it is responsible for 25% of acute coronary syndromes (ACS) in women under 50 years of age. SCAD is primarily diagnosed via coronary angiography; however, intraluminal contrast injection and percutaneous coronary interventions (PCI) are associated with an increased risk of propagation and extension of the dissection leading to increased risk of morbidity and mortality. We present the case of a 48-year-old female with multivessel SCAD and subsequent iatrogenic dissection following contrast injection requiring multiple PCI for medical treatment of refractory cardiac angina.

Prevalence of Anxiety, Depression, and Distress in SCAD and Non-SCAD AMI Patients: A Comparative Study

PURPOSE

Spontaneous coronary artery dissection (SCAD) is an increasingly recognized cause of acute myocardial infarction (AMI), particularly in younger women without classic cardiac risk factors. Spontaneous coronary artery dissection is considered to be particularly stressful; however, few studies have quantified SCAD survivor stress levels. This study compared anxiety, depression, and distress levels in SCAD and non-SCAD AMI patients.

METHOD

A sample of 162 AMI (35 [22%] SCAD) patients was recruited from hospitals and via social media, in Australia and the United States. All had had their AMI in the past 6 mo. Participants completed an online questionnaire comprising the Generalized Anxiety Disorder-2 (GAD2), Patient Health Questionnaire-2 (PHQ2), Kessler-6 (K6), and Cardiac Distress Inventory (CDI). T-tests, χ 2 tests, Mann-Whitney tests, and analysis of covariance were used to compare SCAD and non-SCAD samples. Logistic regression was used to identify the unique predictors of anxiety, depression, and distress, controlling for relevant confounders.

RESULTS

Patients with SCAD were more commonly female and significantly younger than non-SCAD patients. Patients with SCAD scored significantly higher on the GAD2, PHQ2, K6, and CDI and a significantly larger proportion was classified as anxious, depressed, or distressed using these instruments. In logistic regression, together with mental health history, having had a SCAD-AMI predicted anxiety, depression, and distress, after controlling for female sex, younger age, and other confounding variables.

CONCLUSION

This study supports the view that anxiety, depression, and distress are more common after SCAD-AMI than after traditional AMI. These findings highlight the psychosocial impacts of SCAD and suggest that psychological support should be an important component of cardiac rehabilitation for these patients.

Spontaneous Coronary Artery Dissection: A Literature Review

Spontaneous coronary artery dissection is a medical condition characterized by the rupture of the coronary artery wall, occurring without any external trauma. This ailment has been linked to various inflammatory, rheumatologic, and connective tissue disorders, as well as pregnancy-related changes. Despite being a less familiar cause of acute coronary syndrome, it has a considerable mortality rate, with incidence rates reaching up to 4%. This review will discuss the occurrence, pathophysiology, categorization, risk factors, diagnostic techniques, and treatment approaches related to spontaneous coronary artery dissection.

Spontaneous Coronary Artery Disease (SCAD) in a Patient With Systemic Lupus Erythematosus (SLE)

Spontaneous coronary artery dissection (SCAD) is a rare phenomenon that emerges as an acute coronary syndrome (ACS) and sudden cardiac death, especially in young women. We report a case of a woman with systemic lupus erythematosus (SLE) who presented with syncope and was found to have SCAD.

The Coronavirus Double Threat: A Rare Presentation of Chest Pain in a Young Female

Severe acute respiratory syndrome coronavirus 2 (SARS-COV 2) led to global coronavirus disease 2019 (COVID-19) pandemic. The virus affects the respiratory system predominantly and has resulted in multiorgan complications. Myocarditis, acute coronary syndrome (ACS), cardiogenic shock, and sudden cardiac death were common cardiac manifestations of COVID-19. Spontaneous coronary artery dissection (SCAD) is a rare form of coronary artery disease that is previously reported in patients with COVID-19. SCAD usually occurs in a middle-aged woman with few or without any cardiovascular risk factors. The gold standard for its diagnosis is coronary angiography. The SCAD treatment recommendations depend on the hemodynamic status: conservative therapy in hemodynamically stable SCAD patients and urgent revascularization in hemodynamically unstable SCAD patients. The exact pathophysiology of COVID-19 associated with SCAD is unknown. It is considered a combination of systemic inflammatory response and localized vascular inflammation. The case reported is of COVID-19-associated SCAD in a patient with no history of cardiovascular disease later complicated by the transient ischemic attack (TIA) and left ventricular (LV) thrombus.

An Overlooked Cause of Myocardial Infarction With Normal Coronaries Presenting as Stress Cardiomyopathy in Females

Spontaneous coronary artery dissection (SCAD) should be considered in the differential diagnosis of patients with provisional Takotsubo cardiomyopathy (TTS). However, because of overlapping clinical features, SCAD with subtle angiographic findings and wall motion abnormality like TTS can be easily missed. Therefore, our case highlights the importance of further investigation for SCAD.

A Case of Peripartum Spontaneous Coronary Artery Dissection in a Woman With a History of Obesity

Spontaneous coronary artery dissection (SCAD) is a rare cause of acute coronary syndrome (ACS) with a high prevalence in young pregnant females. A 38-year-old female with a history of morbid obesity status post-bariatric surgery presented with chest pain. The electrocardiogram (EKG) revealed ST-segment elevation in the inferior leads as well as slightly elevated troponin. Urgent cardiac catheterization showed SCAD, and she was subsequently managed with medical therapy. We hypothesize that the history of obesity leads to a compromise in the coronary vasculature, thereby predisposing the patient to SCAD.

Cardiovascular disease in women: A review of spontaneous coronary artery dissection

Research has demonstrated the disproportionate quality of care for women with cardiovascular disease. These findings have prompted a renewed focus on cardiovascular disease awareness and disease prevention in women. Spontaneous coronary artery dissection (SCAD) is a significant cause of myocardial infarction (MI) and sudden death that primarily affects women. ongoing research has led to improved diagnostic capabilities and changes in approaches to initial and long-term management most importantly this research has provided evidence that SCAD is more common than previously thought and must be evaluated and treated differently from atherosclerotic MI. The difference between SCAD and atherosclerotic MI is highlighted in high rates of recurrent disease, gender distribution, association with exogenous hormones, pregnancy, migraine, physical and emotional stress triggers, concurrent systemic arteriopathies, and connective tissue disease. In this review, we provide updated insights and a summary of the epidemiology, risk factors, clinical presentation, diagnosis, treatment options, prognosis, and recurrence prevention of SCAD. We aim to provide a review of SCAD as a focus on cardiovascular disease awareness and disease prevention in women.

Successful Percutaneous Coronary Intervention in a Patient With aVR ST-Segment Elevation Myocardial Infarction Due to Spontaneous Atherosclerotic Coronary Artery Dissection

Chest pain is a common clinical symptom that leads to a patient's admission to the emergency department, which may be caused by acute coronary syndrome (ACS). Electrocardiography (ECG) is a useful tool for diagnosis, risk stratification, and treatment response monitoring in clinical practice. The coronary angiography should be done in ACS, which may detect spontaneous atherosclerotic coronary artery dissection (SCAD) that should be followed by urgent revascularization. We present a case of a 55-year-old male with the augmented Vector Right (aVR) ST-segment elevation myocardial infarction due to spontaneous atherosclerotic coronary artery dissection. The patient had a good outcome after we performed early coronary angiography, followed by the percutaneous coronary intervention (PCI).

Identification of potential biomarkers and immune cell infiltration in acute myocardial infarction (AMI) using bioinformatics strategy

Acute myocardial infarction (AMI) was considered a fatal disease resulting in high morbidity and mortality; platelet activation or aggregation plays a critical role in participating in the pathogenesis of AMI. The current study aimed to reveal the underlying mechanisms of platelets in the confrontation of AMI and potential biomarkers that separate AMI from other cardiovascular diseases and healthy people with bioinformatic strategies. Immunity analysis revealed that the neutrophil was significantly decreased in patients with SCAD compared with patients with ST-segment elevation myocardial infarction (STEMI) or healthy controls; monocytes and neutrophils showed potential in distinguishing patients with STEMI from patients with SCAD. Six differentially expressed genes (DEGs) showed great performances in differentiating STEMI patients from SCAD patients with AUC greater than 0.9. Correlation analysis showed that these six DEGs were significantly positively correlated with neutrophils; three genes were negatively correlated with monocytes. Weighted gene co-expression network analysis (WGCNA) found that module ‘royalblue’ had the highest correlation with STEMI; genes in STEMI-related module were enriched in cell–cell interactions, blood vessels’ biological processes, and peroxisome proliferator-activated receptor (PPAR) signaling pathway; four genes (FN1, CD34, LPL, and WWTR1) represented the capability of identifying patients with STEMI from healthy controls and patients with SCAD; two genes (ARG1 and NAMPTL) were considered as novel biomarkers for identifying STEMI from SCAD; FN1 represented the potential as a novel biomarker for STEMI. Our findings indicated that the distribution of neutrophils could be considered as a potential molecular trait for separating patients with STEMI from SCAD.

Complicated Spontaneous Coronary Artery Dissection (SCAD) Culminating in Aneurysm Formation: Coronary Artery Bypass Graft Surgery Is Preferable Over Percutaneous Coronary Intervention in Peripartum SCAD

Spontaneous coronary artery dissection (SCAD) is a rare cause of acute coronary syndrome (ACS), most frequently occurring in young females of reproductive age, and has a high mortality rate. Currently, no guidelines are available to direct treatment.

We report a case of a 29-year-old female with complications of SCAD treated with coronary artery bypass graft (CABG), resulting in a better outcome as compared to that of percutaneous coronary intervention (PCI). Our patient presented with class IV angina one-year post-PCI following postpartum SCAD. Left heart catheterization (LHC) reported SCAD involving the ostium of the left circumflex (LCX) and then cutting off the left marginal artery, which was followed by a 2.5 x 28 mm Synergy drug-eluting stent (Boston Scientific, Marlborough, MA) x1 in the lateral branch of the bifurcating marginal system with good coronary stent results. Repeat LHC one-year after the SCAD was significant for a large aneurysm in the distal left main coronary artery (LCA) extending into the LCX with evidence of a residual large false lumen (0.41 sq cm), as compared to the narrow segment of the true lumen (0.15 sq cm). Compared to the distal LCA area (0.49 sq cm), the true lumen of the LCA had severe stenosis. The patient underwent three-vessel CABG (left internal mammary artery (LIMA)-> left anterior descending artery (LAD), right internal mammary artery (RIMA)->first obtuse marginal (OM1), saphenous vein graft (SVG)->second obtuse marginal (OM2)) with sternal plating. The patient was doing well three months post-CABG with complete resolution of the pain, which was unattainable by PCI. Our report suggests that CABG may be preferable over PCI in the peripartum SCAD to avoid complications or sudden cardiac death from the extension of the dissection and aneurysm formation.

Successful Treatment of Spontaneous Coronary Artery Dissection With Cutting Balloon Angioplasty

Spontaneous coronary artery dissection (SCAD) is a rare but serious condition that requires immediate attention. It has a similar presentation to acute coronary syndrome in terms of chest pain, electrocardiogram changes, and an increase in troponins, and is considered to be a significant cause of myocardial infarction. Coronary angiography is needed to confirm the diagnosis, and subsequent repair should be pursued when needed. We describe a case of SCAD in a 72-year-old female treated using the cutting balloon angioplasty technique to create communication between the true and false lumens.

Spontaneous Coronary Artery Dissection: An Unusual Cause of ST-Elevation Myocardial Infarction in Young Males

Spontaneous coronary artery dissection (SCAD) is a non-traumatic, non-iatrogenic, and non-atherosclerotic coronary artery disorder that manifests clinically as an acute coronary syndrome (ACS), arrhythmia, or sudden cardiac death (SCD). It is a rare cause of ACS (1.7-4%) and SCD (0.5%), more commonly in women than men. It is rarely reported in males. We report a case of acute ST-elevation myocardial infarction (STEMI) due to SCAD in a 44-year-old healthy male.

Reidentification of Decapterus macarellus and D. macrosoma (Carangidae) reveals inconsistencies with current morphological taxonomy in China

Decapterusmacarellus and D.macrosoma are economically important pelagic fish species that are widely distributed in tropical and subtropical seas. The two species are often mistakenly identified due to their morphological similarities as described in the Chinese literature on fish identification. In this study, D.macarellus and D.macrosoma samples were collected in the Eastern Indian Ocean and the South China Sea and reidentified using morphological and DNA barcoding techniques. The characteristics that distinguish the two species primarily include the scute coverage of the straight portion of the lateral line (the most indicative characteristic for classification), the shape of the predorsal scaled area and its location relative to the middle axis of the eye, and the shapes of the posterior margin of the maxilla and the posterior margin of the operculum. The results revealed a large number of misidentified sequences among the homologous cytochrome oxidase (COI) sequences of the two species in the NCBI database and that the genus Decapterus may include cryptic species. In terms of genetic structure, the Sundaland has not blocked genetic exchange between D.macarellus populations in the South China Sea and the Eastern Indian Ocean, giving rise to a high level of genetic diversity. In this study, we made corrections to the Chinese classification standards for D.macarellus and D.macrosoma and the erroneous reference sequences in the NCBI database, thereby providing accurate reference points for the future exploration of cryptic species in the genus Decapterus.

Spontaneous Coronary Artery Dissection Associated with Anal Cancer Management with Fluorouracil and Radiotherapy

Spontaneous coronary artery dissection (SCAD) is thought to be a rare condition that is hard to predict due to the lack of easily identifiable warning signs. We report the case of a 49-year-old woman with a locally advanced Stage IIIB anal squamous cell carcinoma who presented with chest pain and a positive stress test, ST elevations in her inferior echocardiogram leads, and induced chest pain with exercise without heart perfusion defects. Coronary catheterization revealed a right coronary artery dissection, which led to the diagnosis of SCAD. Our patient was diagnosed while undergoing a combination treatment of fluorouracil (5-FU), mitomycin, and pelvic radiotherapy. We reviewed the current literature and update the etiologies that have been proposed since the publication of this case report.

Non-Concave Penalized Likelihood with NP-Dimensionality

Penalized likelihood methods are fundamental to ultra-high dimensional variable selection. How high dimensionality such methods can handle remains largely unknown. In this paper, we show that in the context of generalized linear models, such methods possess model selection consistency with oracle properties even for dimensionality of Non-Polynomial (NP) order of sample size, for a class of penalized likelihood approaches using folded-concave penalty functions, which were introduced to ameliorate the bias problems of convex penalty functions. This fills a long-standing gap in the literature where the dimensionality is allowed to grow slowly with the sample size. Our results are also applicable to penalized likelihood with the L(1)-penalty, which is a convex function at the boundary of the class of folded-concave penalty functions under consideration. The coordinate optimization is implemented for finding the solution paths, whose performance is evaluated by a few simulation examples and the real data analysis.

Estimation and Variable Selection for Semiparametric Additive Partial Linear Models (SS-09-140)

Semiparametric additive partial linear models, containing both linear and nonlinear additive components, are more flexible compared to linear models, and they are more efficient compared to general nonparametric regression models because they reduce the problem known as "curse of dimensionality". In this paper, we propose a new estimation approach for these models, in which we use polynomial splines to approximate the additive nonparametric components and we derive the asymptotic normality for the resulting estimators of the parameters. We also develop a variable selection procedure to identify significant linear components using the smoothly clipped absolute deviation penalty (SCAD), and we show that the SCAD-based estimators of non-zero linear components have an oracle property. Simulations are performed to examine the performance of our approach as compared to several other variable selection methods such as the Bayesian Information Criterion and Least Absolute Shrinkage and Selection Operator (LASSO). The proposed approach is also applied to real data from a nutritional epidemiology study, in which we explore the relationship between plasma beta-carotene levels and personal characteristics (e.g., age, gender, body mass index (BMI), etc.) as well as dietary factors (e.g., alcohol consumption, smoking status, intake of cholesterol, etc.).

Penalized Composite Quasi-Likelihood for Ultrahigh-Dimensional Variable Selection

In high-dimensional model selection problems, penalized least-square approaches have been extensively used. This paper addresses the question of both robustness and efficiency of penalized model selection methods, and proposes a data-driven weighted linear combination of convex loss functions, together with weighted L(1)-penalty. It is completely data-adaptive and does not require prior knowledge of the error distribution. The weighted L(1)-penalty is used both to ensure the convexity of the penalty term and to ameliorate the bias caused by the L(1)-penalty. In the setting with dimensionality much larger than the sample size, we establish a strong oracle property of the proposed method that possesses both the model selection consistency and estimation efficiency for the true non-zero coefficients. As specific examples, we introduce a robust method of composite L1-L2, and optimal composite quantile method and evaluate their performance in both simulated and real data examples.

ASYMPTOTIC PROPERTIES OF SUFFICIENT DIMENSION REDUCTION WITH A DIVERGING NUMBER OF PREDICTORS

We investigate asymptotic properties of a family of sufficient dimension reduction estimators when the number of predictors p diverges to infinity with the sample size. We adopt a general formulation of dimension reduction estimation through least squares regression of a set of transformations of the response. This formulation allows us to establish the consistency of reduction projection estimation. We then introduce the SCAD max penalty, along with a difference convex optimization algorithm, to achieve variable selection. We show that the penalized estimator selects all truly relevant predictors and excludes all irrelevant ones with probability approaching one, meanwhile it maintains consistent reduction basis estimation for relevant predictors. Our work differs from most model-based selection methods in that it does not require a traditional model, and it extends existing sufficient dimension reduction and model-free variable selection approaches from the fixed p scenario to a diverging p.

REGULARIZATION FOR COX'S PROPORTIONAL HAZARDS MODEL WITH NP-DIMENSIONALITY

High throughput genetic sequencing arrays with thousands of measurements per sample and a great amount of related censored clinical data have increased demanding need for better measurement specific model selection. In this paper we establish strong oracle properties of non-concave penalized methods for non-polynomial (NP) dimensional data with censoring in the framework of Cox's proportional hazards model. A class of folded-concave penalties are employed and both LASSO and SCAD are discussed specifically. We unveil the question under which dimensionality and correlation restrictions can an oracle estimator be constructed and grasped. It is demonstrated that non-concave penalties lead to significant reduction of the "irrepresentable condition" needed for LASSO model selection consistency. The large deviation result for martingales, bearing interests of its own, is developed for characterizing the strong oracle property. Moreover, the non-concave regularized estimator, is shown to achieve asymptotically the information bound of the oracle estimator. A coordinate-wise algorithm is developed for finding the grid of solution paths for penalized hazard regression problems, and its performance is evaluated on simulated and gene association study examples.

Variable selection in the cox regression model with covariates missing at random

We consider variable selection in the Cox regression model (Cox, 1975, Biometrika 362, 269-276) with covariates missing at random. We investigate the smoothly clipped absolute deviation penalty and adaptive least absolute shrinkage and selection operator (LASSO) penalty, and propose a unified model selection and estimation procedure. A computationally attractive algorithm is developed, which simultaneously optimizes the penalized likelihood function and penalty parameters. We also optimize a model selection criterion, called the IC(Q) statistic (Ibrahim, Zhu, and Tang, 2008, Journal of the American Statistical Association 103, 1648-1658), to estimate the penalty parameters and show that it consistently selects all important covariates. Simulations are performed to evaluate the finite sample performance of the penalty estimates. Also, two lung cancer data sets are analyzed to demonstrate the proposed methodology.

A Selective Overview of Variable Selection in High Dimensional Feature Space

High dimensional statistical problems arise from diverse fields of scientific research and technological development. Variable selection plays a pivotal role in contemporary statistical learning and scientific discoveries. The traditional idea of best subset selection methods, which can be regarded as a specific form of penalized likelihood, is computationally too expensive for many modern statistical applications. Other forms of penalized likelihood methods have been successfully developed over the last decade to cope with high dimensionality. They have been widely applied for simultaneously selecting important variables and estimating their effects in high dimensional statistical inference. In this article, we present a brief account of the recent developments of theory, methods, and implementations for high dimensional variable selection. What limits of the dimensionality such methods can handle, what the role of penalty functions is, and what the statistical properties are rapidly drive the advances of the field. The properties of non-concave penalized likelihood and its roles in high dimensional statistical modeling are emphasized. We also review some recent advances in ultra-high dimensional variable selection, with emphasis on independence screening and two-scale methods.

Variable Selection in Measurement Error Models

Measurement error data or errors-in-variable data are often collected in many studies. Natural criterion functions are often unavailable for general functional measurement error models due to the lack of information on the distribution of the unobservable covariates. Typically, the parameter estimation is via solving estimating equations. In addition, the construction of such estimating equations routinely requires solving integral equations, hence the computation is often much more intensive compared with ordinary regression models. Because of these difficulties, traditional best subset variable selection procedures are not applicable, and in the measurement error model context, variable selection remains an unsolved issue. In this paper, we develop a framework for variable selection in measurement error models via penalized estimating equations. We first propose a class of selection procedures for general parametric measurement error models and for general semiparametric measurement error models, and study the asymptotic properties of the proposed procedures. Then, under certain regularity conditions and with a properly chosen regularization parameter, we demonstrate that the proposed procedure performs as well as an oracle procedure. We assess the finite sample performance via Monte Carlo simulation studies and illustrate the proposed methodology through the empirical analysis of a familiar data set.

Local Linear Regression for Data with AR Errors

In many statistical applications, data are collected over time, and they are likely correlated. In this paper, we investigate how to incorporate the correlation information into the local linear regression. Under the assumption that the error process is an auto-regressive process, a new estimation procedure is proposed for the nonparametric regression by using local linear regression method and the profile least squares techniques. We further propose the SCAD penalized profile least squares method to determine the order of auto-regressive process. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed procedure, and to compare the performance of the proposed procedures with the existing one. From our empirical studies, the newly proposed procedures can dramatically improve the accuracy of naive local linear regression with working-independent error structure. We illustrate the proposed methodology by an analysis of real data set.

Variable Selection for Screening Experiments

The first step in many applications of response surface methodology is typically the screening process. Variable selection plays an important role in screening experiments when a large number of potential factors are introduced in a preliminary study. Traditional approaches, such as the best subset variable selection and stepwise deletion, may not be appropriate in this situation. In this paper we introduce a variable selection procedure via penalized least squares with the SCAD penalty. An algorithm to find the penalized least squares solution is suggested, and a standard error formula for the penalized least squares estimate is derived. With a proper choice of the regularization parameter, it is shown that the resulting estimate is root n consistent and possesses an oracle property; namely, it works as well as if the correct submodel were known. An automatic and data-driven approach was proposed to select the regularization parameter. Examples are used to illustrate the effectiveness of the newly proposed approach. The computer codes (written in MATLAB) to perform all calculation are available through the authors for an automatic data-driven variable selection procedure.

One-step Sparse Estimates in Nonconcave Penalized Likelihood Models

Fan & Li (2001) propose a family of variable selection methods via penalized likelihood using concave penalty functions. The nonconcave penalized likelihood estimators enjoy the oracle properties, but maximizing the penalized likelihood function is computationally challenging, because the objective function is nondifferentiable and nonconcave. In this article we propose a new unified algorithm based on the local linear approximation (LLA) for maximizing the penalized likelihood for a broad class of concave penalty functions. Convergence and other theoretical properties of the LLA algorithm are established. A distinguished feature of the LLA algorithm is that at each LLA step, the LLA estimator can naturally adopt a sparse representation. Thus we suggest using the one-step LLA estimator from the LLA algorithm as the final estimates. Statistically, we show that if the regularization parameter is appropriately chosen, the one-step LLA estimates enjoy the oracle properties with good initial estimators. Computationally, the one-step LLA estimation methods dramatically reduce the computational cost in maximizing the nonconcave penalized likelihood. We conduct some Monte Carlo simulation to assess the finite sample performance of the one-step sparse estimation methods. The results are very encouraging.

Variable Selection in Semiparametric Regression Modeling

In this paper, we are concerned with how to select significant variables in semiparametric modeling. Variable selection for semiparametric regression models consists of two components: model selection for nonparametric components and select significant variables for parametric portion. Thus, it is much more challenging than that for parametric models such as linear models and generalized linear models because traditional variable selection procedures including stepwise regression and the best subset selection require model selection to nonparametric components for each submodel. This leads to very heavy computational burden. In this paper, we propose a class of variable selection procedures for semiparametric regression models using nonconcave penalized likelihood. The newly proposed procedures are distinguished from the traditional ones in that they delete insignificant variables and estimate the coefficients of significant variables simultaneously. This allows us to establish the sampling properties of the resulting estimate. We first establish the rate of convergence of the resulting estimate. With proper choices of penalty functions and regularization parameters, we then establish the asymptotic normality of the resulting estimate, and further demonstrate that the proposed procedures perform as well as an oracle procedure. Semiparametric generalized likelihood ratio test is proposed to select significant variables in the nonparametric component. We investigate the asymptotic behavior of the proposed test and demonstrate its limiting null distribution follows a chi-squared distribution, which is independent of the nuisance parameters. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedures.