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Information-based model selection criteria such as the AIC and BIC employ check loss functions to measure the goodness of fit for quantile regression models. Model selection using a check loss function is robust due to its resistance to outlying observations. In the present study, we suggest modifying the check loss function to achieve a more efficient goodness of fit. Because the cusp of the check loss is quadratically adjusted in the modified version, greater efficiency (or variance reduction) in the model selection is expected. Because we focus on model selection here, we do not modify the model-fitting process. Generalized cross-validation is another common method for choosing smoothing parameters in quantile smoothing splines. We describe how this can be adjusted using the modified check loss to increase efficiency. The proposed generalized cross-validation is designed to reflect the target quantile and sample size. Two real data sets and simulation studies are presented to evaluate its performance using linear and nonlinear quantile regression models.

The check loss function is used to define quantile regression. In cross-validation, it is also employed as a validation function when the true distribution is unknown. However, our empirical study indicates that validation with the check loss often leads to overfitting the data. In this work, we suggest a modified or L2-adjusted check loss which rounds the sharp corner in the middle of check loss. This has the effect of guarding against overfitting to some extent. The adjustment is devised to shrink to zero as sample size grows. Through various simulation settings of linear and nonlinear regressions, the improvement due to modification of the check loss by quadratic adjustment is examined empirically.

Grouping structures in covariates are often ignored in regression models. Recent statistical developments considering grouping structure shows clear advantages; however, reflecting the grouping structure on the quantile regression model has been relatively rare in the literature. Treating the grouping structure is usually conducted by employing a group penalty. In this work, we explore the idea of group penalty to the quantile regression models. The grouping structure is assumed to be known, which is commonly true for some cases. For example, group of dummy variables transformed from one categorical variable can be regarded as one group of covariates. We examine the group quantile regression models via two real data analyses and simulation studies that reveal the beneficial performance of group quantile regression models to the non-group version methods if there exists grouping structures among variables.

A general modeling procedure for analyzing genetic data is reviewed. We review ANOVA type model that can handle both the continuous and discrete genetic variables in one modeling framework. Unlike the regression type models which typically set the phenotype variable as a response, this ANOVA model treats the phenotype variable as an explanatory variable. By reversely treating the phenotype variable, usual high dimensional problem is turned into low dimension. Instead, the ANOVA model always includes interaction term between the genetic locations and phenotype variable to find potential association between them. The interaction term is designed to be low rank with the multiplication of bilinear terms so that the required number of parameters is kept in a manageable degree. We compare the performance of the reviewed ANOVA model to the other popular methods via microarray and SNP data sets.

One benefit of the bias-variance tradeoff is that regression estimators do not have to be strictly unbiased. However, to take full advantage of allowing bias, shrinkage regression estimators requir...

The income or expenditure-related data sets are often nonlinear, heteroscedastic, skewed even after the transformation, and contain numerous outliers. We propose a class of robust nonlinear...

High-dimensional data are often encountered in biomedical, environmental, and other studies. For example, in biomedical studies that involve high-throughput omic data, an important problem is to search for genetic variables that are predictive of a particular phenotype. A conventional solution is to characterize such relationships through regression models in which a phenotype is treated as the response variable and the variables are treated as covariates; this approach becomes particularly challenging when the number of variables exceeds the number of samples. We propose a general framework for expressing the transformed mean of high-dimensional variables in an exponential distribution family via ANOVA models in which a low-rank interaction space captures the association between the phenotype and the variables. This alternative method transforms the variable selection problem into a well-posed problem with the number of observations larger than the number of variables. In addition, we propose a model selection criterion for the new model framework with a diverging number of parameters, and establish the consistency of the selection criterion. We demonstrate the appealing performance of the proposed method in terms of prediction and detection accuracy through simulations and real data analyses.

By releasing the unbiasedness condition, we often obtain more accurate estimators due to the bias–variance trade-off. In this paper, we propose a class of shrinkage proportion estimators which show...

Aim To retrospectively evaluate the potential impact of statin and aspirin use on acute toxicity and pathological complete response (pCR) rate in rectal cancer patients receiving neo-adjuvant long-course radiation therapy (LCRT) with concurrent chemotherapy. Methods A retrospective review was performed of all patients undergoing neo-adjuvant LCRT for rectal adenocarcinoma at the Regional Cancer Treatment Service between 1 September 2007 and 1 June 2011. Data obtained include demographic details; date and radiological TNM stage at diagnosis; medication taken at time of RT; toxicity during LCRT; and surgical histology to determine if a pCR was obtained following LCRT. Results Neo-adjuvant LCRT was administered to 142 patients for rectal cancer during this period; concurrent chemotherapy was omitted in 13 due to significant comorbidities. TNM stage was 2 or 3 radiologically at diagnosis in 127 (89.4%) of patients. At the time of LCRT, 23% were taking a statin and 25% were taking aspirin. Of 135 assessable patients, 34 (13%) achieved a pCR at surgery. On logistic regression, pCR was not significantly associated with the use of chemotherapy, statins, aspirin, other NSAIDs, T-stage or N-stage. There was no significant correlation between statin or aspirin use with bladder or rectal toxicity. Actuarial time to maximum rectal toxicity was not different in statin users or nonusers. Conclusion In contrast to other larger retrospective series, this study did not find improvements in toxicity or pCR rate through statin or aspirin use in rectal cancer patients undergoing LCRT. Their potential benefits in this setting would be best studied prospectively in a large randomized trial.

Outlying observations are often disregarded at the sacrifice of degrees of freedom or downsized via robust loss functions (e.g., Huber's loss) to reduce the undesirable impact on data analysis. In this article, we treat the outlying status of each observation as a parameter and propose a penalization method to automatically adjust the outliers. The proposed method shifts the outliers towards the fitted values, while preserve the non-outlying observations. We also develop a generally applicable algorithm in the iterative fashion to estimate model parameters and demonstrate the connection with the maximum likelihood based estimation procedure in the case of least squares estimation. We establish asymptotic property of the resulting parameter estimators under the condition that the proportion of outliers does not vanish as sample size increases. We apply the proposed outlier adjustment method to ordinary least squares and lasso-type penalization procedure and demonstrate its empirical value via numeric studies. Furthermore, we study applicability of the proposed method to two robust estimators, Huber's robust estimator and Huberized lasso, and demonstrate its noticeable improvement of model fit in the presence of extremely large outliers.

Cross-validation (CV) type of methods have been widely used to facilitate model estimation and variable selection. In this work, we suggest a new K-fold CV procedure to select a candidate ‘optimal’...

Quantile regression (QR) provides estimates of a range of conditional quantiles. This stands in contrast to traditional regression techniques, which focus on a single conditional mean function. Lee et al. [Regularization of case-specific parameters for robustness and efficiency. Statist Sci. 2012;27(3):350–372] proposed efficient QR by rounding the sharp corner of the loss. The main modification generally involves an asymmetric l2 adjustment of the loss function around zero. We extend the idea of l2 adjusted QR to linear heterogeneous models. The l2 adjustment is constructed to diminish as sample size grows. Conditions to retain consistency properties are also provided.

BACKGROUND: The clinical benefit of concomitant atrial fibrillation (AF) ablation at the time of aortic valve replacement (AVR) is uncertain. METHODS AND RESULTS: A total of 124 patients with AF who underwent AVR with (n=50) or without (n=74) a concomitant maze procedure, between 2000 and 2011, were evaluated. There were no significant differences in early postoperative outcomes. During a median clinical follow-up of 18.1 months (interquartile range: 6.9-47.8 months), 19 late deaths (15.3%) and 33 valve-related complications (26.6%) occurred, but the differences between groups were not statistically significant. Major event-free survival at 5 years was 60.9±9.9% vs. 57.0±10.3% (P=0.41). After adjustment, the maze group demonstrated similar risks for major adverse cardiac events (hazard ratio, 1.18; 95% confidence interval, 0.56-2.49; P=0.67). However, the rate of sinus rhythm restoration at 4 years was significantly higher in the maze group (80.6% vs. 3.6%, P

Cross-validation type of methods have been widely used to facilitate model estimation and variable selection. In this work, we suggest a new K-fold cross validation procedure to select a candidate ‘optimal’ model from each hold-out fold and average the K candidate ‘optimal’ models to obtain the ultimate model. Due to the averaging effect, the variance of the proposed estimates can be significantly reduced. This new procedure results in more stable and efficient parameter estimation than the classical K-fold cross validation procedure. In addition, we show the asymptotic equivalence between the proposed and classical cross validation procedures in the linear regression setting. We also demonstrate the broad applicability of the proposed procedure via two examples of parameter sparsity regularization and quantile smoothing splines modeling. We illustrate the promise of the proposed method through simulations and a real data example.

To retrospectively evaluate the potential impact of statin and aspirin use on acute toxicity and pathological complete response (pCR) rate in rectal cancer patients receiving neo-adjuvant long-course radiation therapy (LCRT) with concurrent chemotherapy.A retrospective review was performed of all patients undergoing neo-adjuvant LCRT for rectal adenocarcinoma at the Regional Cancer Treatment Service between 1 September 2007 and 1 June 2011. Data obtained include demographic details; date and radiological TNM stage at diagnosis; medication taken at time of RT; toxicity during LCRT; and surgical histology to determine if a pCR was obtained following LCRT.Neo-adjuvant LCRT was administered to 142 patients for rectal cancer during this period; concurrent chemotherapy was omitted in 13 due to significant comorbidities. TNM stage was 2 or 3 radiologically at diagnosis in 127 (89.4%) of patients. At the time of LCRT, 23% were taking a statin and 25% were taking aspirin. Of 135 assessable patients, 34 (13%) achieved a pCR at surgery. On logistic regression, pCR was not significantly associated with the use of chemotherapy, statins, aspirin, other NSAIDs, T-stage or N-stage. There was no significant correlation between statin or aspirin use with bladder or rectal toxicity. Actuarial time to maximum rectal toxicity was not different in statin users or nonusers.In contrast to other larger retrospective series, this study did not find improvements in toxicity or pCR rate through statin or aspirin use in rectal cancer patients undergoing LCRT. Their potential benefits in this setting would be best studied prospectively in a large randomized trial.

As DNA microarray data contain relatively small sample size compared to the number of genes, high dimensional models are often employed. In high dimensional models, the selection of tuning parameter (or, penalty parameter) is often one of the crucial parts of the modeling. Cross-validation is one of the most common methods for the tuning parameter selection, which selects a parameter value with the smallest cross-validated score. However, selecting a single value as an ‘optimal’ value for the parameter can be very unstable due to the sampling variation since the sample sizes of microarray data are often small. Our approach is to choose multiple candidates of tuning parameter first, then average the candidates with different weights depending on their performance. The additional step of estimating the weights and averaging the candidates rarely increase the computational cost, while it can considerably improve the traditional cross-validation. 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In genome-wide association studies, the primary task is to detect biomarkers in the form of Single Nucleotide Polymorphisms (SNPs) that have nontrivial associations with a disease phenotype and some other important clinical/environmental factors. However, the extremely large number of SNPs comparing to the sample size inhibits application of classical methods such as the multiple logistic regression. Currently the most commonly used approach is still to analyze one SNP at a time. In this paper, we propose to consider the genotypes of the SNPs simultaneously via a logistic analysis of variance (ANOVA) model, which expresses the logit transformed mean of SNP genotypes as the summation of the SNP effects, effects of the disease phenotype and/or other clinical variables, and the interaction effects. We use a reduced-rank representation of the interaction-effect matrix for dimensionality reduction, and employ the L1-penalty in a penalized likelihood framework to filter out the SNPs that have no associations. We develop a Majorization-Minimization algorithm for computational implementation. In addition, we propose a modified BIC criterion to select the penalty parameters and determine the rank number. The proposed method is applied to a Multiple Sclerosis data set and simulated data sets and shows promise in biomarker detection.

Purpose/objectives To survey nurses about their knowledge of cancer survivorship care. Design Descriptive, cross-sectional. Setting Midwestern comprehensive cancer center. Sample 223 registered and advanced practice nurses. Methods Online survey of survivorship knowledge using a 50-item questionnaire derived from the Institute of Medicine report and related publications. Main research variables Concepts of survivorship care and common long-term symptoms. Findings Most nurses reported having knowledge about healthy lifestyle habits; more than 50% of nurses reported having knowledge about chemotherapy, surgery, and radiation therapy, as well as side effects of fatigue, depression, limitations of daily activities, and weight gain; less than 50% of nurses reported having knowledge of impact on family, biologic agents, lymphedema, immunizations or vaccinations, and osteoporosis screening; less than 40% of nurses reported having knowledge about marital and partner relationships, osteoporosis prevention and care, sexuality, side effects of bone marrow transplantation, employment issues, and angiogenesis agents; and less than 25% of nurses reported having knowledge on genetic risks, as well as fertility, financial, and insurance issues. Conclusions Oncology nurses at an academic comprehensive cancer center reported gaps in knowledge consistent with previous studies about knowledge of survivorship care. Implications for nursing The Institute of Medicine has challenged oncology providers to address cancer survivorship care planning. Gaps in cancer survivorship knowledge are evident and will require focused education for this initiative to be successful.

Regularization methods allow one to handle a variety of inferential problems where there are more covariates than cases. This allows one to consider a potentially enormous number of covariates for a problem. We exploit the power of these techniques, supersaturating models by augmenting the "natural" covariates in the problem with an additional indicator for each case in the data set. We attach a penalty term for these case-specific indicators which is designed to produce a desired effect. For regression methods with squared error loss, an $\ell_1$ penalty produces a regression which is robust to outliers and high leverage cases; for quantile regression methods, an $\ell_2$ penalty decreases the variance of the fit enough to overcome an increase in bias. The paradigm thus allows us to robustify procedures which lack robustness and to increase the efficiency of procedures which are robust. We provide a general framework for the inclusion of case-specific parameters in regularization problems, describing the impact on the effective loss for a variety of regression and classification problems. We outline a computational strategy by which existing software can be modified to solve the augmented regularization problem, providing conditions under which such modification will converge to the optimum solution. We illustrate the benefits of including case-specific parameters in the context of mean regression and quantile regression through analysis of NHANES and linguistic data sets., Comment: Published in at http://dx.doi.org/10.1214/11-STS377 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)

The cDNA expression libraries that produce correct proteins are essential in facilitating the identification of protein-protein interactions. The 5'-untranslated regions (UTRs) that are present in the majority of mammalian and non-mammalian genes are predicted to alter the expression of correct proteins from cDNA libraries. We developed a novel cDNA expression library from which 5'-UTRs were removed using a mixture of polymerase chain reaction primers that complement the Kozak sequences we refer to as an "in-frame cDNA library." We used this library with the protein complementation assay to identify two novel binding partners for ras-related ADP-ribosylation factor-like 11 (ARL11), cellular retinoic acid binding protein 2 (CRABP2), and phosphoglycerate mutase 1 (PGAM1). Thus, the in-frame cDNA library without 5'-UTRs we describe here increases the chance of correctly identifying protein interactions and will have wide applications in both mammalian and non-mammalian detection systems.