Latent group detection in functional partially linear regression models.

In this paper, we propose a functional partially linear regression model with latent group structures to accommodate the heterogeneous relationship between a scalar response and functional covariates. The proposed model is motivated by a salinity tolerance study of barley families, whose main objective is to detect salinity tolerant barley plants. Our model is flexible, allowing for heterogeneous functional coefficients while being efficient by pooling information within a group for estimation. We develop an algorithm in the spirit of the K-means clustering to identify latent groups of the subjects under study. We establish the consistency of the proposed estimator, derive the convergence rate and the asymptotic distribution, and develop inference procedures. We show by simulation studies that the proposed method has higher accuracy for recovering latent groups and for estimating the functional coefficients than existing methods. The analysis of the barley data shows that the proposed method can help identify groups of barley families with different salinity tolerant abilities.

Quantile regression for survival data with covariates subject to detection limits.

With advances in biomedical research, biomarkers are becoming increasingly important prognostic factors for predicting overall survival, while the measurement of biomarkers is often censored due to instruments' lower limits of detection. This leads to two types of censoring: random censoring in overall survival outcomes and fixed censoring in biomarker covariates, posing new challenges in statistical modeling and inference. Existing methods for analyzing such data focus primarily on linear regression ignoring censored responses or semiparametric accelerated failure time models with covariates under detection limits (DL). In this paper, we propose a quantile regression for survival data with covariates subject to DL. Comparing to existing methods, the proposed approach provides a more versatile tool for modeling the distribution of survival outcomes by allowing covariate effects to vary across conditional quantiles of the survival time and requiring no parametric distribution assumptions for outcome data. To estimate the quantile process of regression coefficients, we develop a novel multiple imputation approach based on another quantile regression for covariates under DL, avoiding stringent parametric restrictions on censored covariates as often assumed in the literature. Under regularity conditions, we show that the estimation procedure yields uniformly consistent and asymptotically normal estimators. Simulation results demonstrate the satisfactory finite-sample performance of the method. We also apply our method to the motivating data from a study of genetic and inflammatory markers of Sepsis.

Gastrin Protects Against Myocardial Ischemia/Reperfusion Injury via Activation of RISK (Reperfusion Injury Salvage Kinase) and SAFE (Survivor Activating Factor Enhancement) Pathways.

BACKGROUND: Ischemia/reperfusion injury (IRI) is one of the most predominant complications of ischemic heart disease. Gastrin has emerged as a regulator of cardiovascular function, playing a key protective role in hypoxia. Serum gastrin levels are increased in patients with myocardial infarction, but the pathophysiogical significance of this finding is unknown. The purpose of this study was to determine whether and how gastrin protects cardiac myocytes from IRI. METHODS AND RESULTS: Adult male Sprague-Dawley rats were used in the experiments. The hearts in living rats or isolated Langendorff-perfused rat hearts were subjected to ischemia followed by reperfusion to induce myocardial IRI. Gastrin, alone or with an antagonist, was administered before the induction of myocardial IRI. We found that gastrin improved myocardial function and reduced the expression of myocardial injury markers, infarct size, and cardiomyocyte apoptosis induced by IRI. Gastrin increased the phosphorylation levels of ERK1/2 (extracellular signal-regulated kinase 1/2), AKT (protein kinase B), and STAT3 (signal transducer and activator of transcription 3), indicating its ability to activate the RISK (reperfusion injury salvage kinase) and SAFE (survivor activating factor enhancement) pathways. The presence of inhibitors of ERK1/2, AKT, or STAT3 abrogated the gastrin-mediated protection. The protective effect of gastrin was via CCK2R (cholecystokinin 2 receptor) because the CCK2R blocker CI988 prevented the gastrin-mediated protection of the heart with IRI. Moreover, we found a negative correlation between serum levels of cardiac troponin I and gastrin in patients with unstable angina pectoris undergoing percutaneous coronary intervention, suggesting a protective effect of gastrin in human cardiomyocytes. CONCLUSIONS: These results indicate that gastrin can reduce myocardial IRI by activation of the RISK and SAFE pathways.

Testing for Marginal Linear Effects in Quantile Regression.

This paper develops a new marginal testing procedure to detect the presence of significant predictors associated with the conditional quantiles of a scalar response. The idea is to fit the marginal quantile regression on each predictor one at a time, and then base the test on the t-statistics associated with the most predictive predictors. A resampling method is devised to calibrate this test statistic, which has non-regular limiting behavior due to the selection of the most predictive variables. Asymptotic validity of the procedure is established in a general quantile regression setting in which the marginal quantile regression models can be misspecified. Even though a fixed dimension is assumed to derive the asymptotic results, the proposed test is applicable and computationally feasible for large-dimensional predictors. The method is more flexible than existing marginal screening test methods based on mean regression, and has the added advantage of being robust against outliers in the response. The approach is illustrated using an application to an HIV drug resistance dataset.

Sequential model selection-based segmentation to detect DNA copy number variation.

Array-based CGH experiments are designed to detect genomic aberrations or regions of DNA copy-number variation that are associated with an outcome, typically a state of disease. Most of the existing statistical methods target on detecting DNA copy number variations in a single sample or array. We focus on the detection of group effect variation, through simultaneous study of multiple samples from multiple groups. Rather than using direct segmentation or smoothing techniques, as commonly seen in existing detection methods, we develop a sequential model selection procedure that is guided by a modified Bayesian information criterion. This approach improves detection accuracy by accumulatively utilizing information across contiguous clones, and has computational advantage over the existing popular detection methods. Our empirical investigation suggests that the performance of the proposed method is superior to that of the existing detection methods, in particular, in detecting small segments or separating neighboring segments with differential degrees of copy-number variation.

A Fast EM Algorithm for Fitting Joint Models of a Binary Response and Multiple Longitudinal Covariates Subject to Detection Limits.

Joint modeling techniques have become a popular strategy for studying the association between a response and one or more longitudinal covariates. Motivated by the GenIMS study, where it is of interest to model the event of survival using censored longitudinal biomarkers, a joint model is proposed for describing the relationship between a binary outcome and multiple longitudinal covariates subject to detection limits. A fast, approximate EM algorithm is developed that reduces the dimension of integration in the E-step of the algorithm to one, regardless of the number of random effects in the joint model. Numerical studies demonstrate that the proposed approximate EM algorithm leads to satisfactory parameter and variance estimates in situations with and without censoring on the longitudinal covariates. The approximate EM algorithm is applied to analyze the GenIMS data set.

LOCAL BUCKLEY-JAMES ESTIMATION FOR HETEROSCEDASTIC ACCELERATED FAILURE TIME MODEL.

In survival analysis, the accelerated failure time model is a useful alternative to the popular Cox proportional hazards model due to its easy interpretation. Current estimation methods for the accelerated failure time model mostly assume independent and identically distributed random errors, but in many applications the conditional variance of log survival times depend on covariates exhibiting some form of heteroscedasticity. In this paper, we develop a local Buckley-James estimator for the accelerated failure time model with heteroscedastic errors. We establish the consistency and asymptotic normality of the proposed estimator and propose a resampling approach for inference. Simulations demonstrate that the proposed method is flexible and leads to more efficient estimation when heteroscedasticity is present. The value of the proposed method is further assessed by the analysis of a breast cancer data set.

Interquantile Shrinkage and Variable Selection in Quantile Regression.

Examination of multiple conditional quantile functions provides a comprehensive view of the relationship between the response and covariates. In situations where quantile slope coefficients share some common features, estimation efficiency and model interpretability can be improved by utilizing such commonality across quantiles. Furthermore, elimination of irrelevant predictors will also aid in estimation and interpretation. These motivations lead to the development of two penalization methods, which can identify the interquantile commonality and nonzero quantile coefficients simultaneously. The developed methods are based on a fused penalty that encourages sparsity of both quantile coefficients and interquantile slope differences. The oracle properties of the proposed penalization methods are established. Through numerical investigations, it is demonstrated that the proposed methods lead to simpler model structure and higher estimation efficiency than the traditional quantile regression estimation.

Flexible Modeling of Survival Data with Covariates Subject to Detection Limits via Multiple Imputation.

Models for survival data generally assume that covariates are fully observed. However, in medical studies it is not uncommon for biomarkers to be censored at known detection limits. A computationally-efficient multiple imputation procedure for modeling survival data with covariates subject to detection limits is proposed. This procedure is developed in the context of an accelerated failure time model with a flexible seminonparametric error distribution. The consistency and asymptotic normality of the multiple imputation estimator are established and a consistent variance estimator is provided. An iterative version of the proposed multiple imputation algorithm that approximates the EM algorithm for maximum likelihood is also suggested. Simulation studies demonstrate that the proposed multiple imputation methods work well while alternative methods lead to estimates that are either biased or more variable. The proposed methods are applied to analyze the dataset from a recently-conducted GenIMS study.

Interquantile Shrinkage in Regression Models.

Conventional analysis using quantile regression typically focuses on fitting the regression model at different quantiles separately. However, in situations where the quantile coefficients share some common feature, joint modeling of multiple quantiles to accommodate the commonality often leads to more efficient estimation. One example of common features is that a predictor may have a constant effect over one region of quantile levels but varying effects in other regions. To automatically perform estimation and detection of the interquantile commonality, we develop two penalization methods. When the quantile slope coefficients indeed do not change across quantile levels, the proposed methods will shrink the slopes towards constant and thus improve the estimation efficiency. We establish the oracle properties of the two proposed penalization methods. Through numerical investigations, we demonstrate that the proposed methods lead to estimations with competitive or higher efficiency than the standard quantile regression estimation in finite samples. Supplemental materials for the article are available online.

VARIABLE SELECTION FOR CENSORED QUANTILE REGRESION.

Quantile regression has emerged as a powerful tool in survival analysis as it directly links the quantiles of patients' survival times to their demographic and genomic profiles, facilitating the identification of important prognostic factors. In view of limited work on variable selection in the context, we develop a new adaptive-lasso-based variable selection procedure for quantile regression with censored outcomes. To account for random censoring for data with multivariate covariates, we employ the ideas of redistribution-of-mass and e ective dimension reduction. Asymptotically our procedure enjoys the model selection consistency, that is, identifying the true model with probability tending to one. Moreover, as opposed to the existing methods, our new proposal requires fewer assumptions, leading to more accurate variable selection. The analysis of a real cancer clinical trial demonstrates that our procedure can identify and distinguish important factors associated with patient sub-populations characterized by short or long survivals, which is of particular interest to oncologists.

Variance Estimation in Censored Quantile Regression via Induced Smoothing.

Statistical inference in censored quantile regression is challenging, partly due to the unsmoothness of the quantile score function. A new procedure is developed to estimate the variance of Bang and Tsiatis's inverse-censoring-probability weighted estimator for censored quantile regression by employing the idea of induced smoothing. The proposed variance estimator is shown to be asymptotically consistent. In addition, numerical study suggests that the proposed procedure performs well in finite samples, and it is computationally more efficient than the commonly used bootstrap method.

Corrected-loss estimation for quantile regression with covariate measurement errors.

We study estimation in quantile regression when covariates are measured with errors. Existing methods require stringent assumptions, such as spherically symmetric joint distribution of the regression and measurement error variables, or linearity of all quantile functions, which restrict model flexibility and complicate computation. In this paper, we develop a new estimation approach based on corrected scores to account for a class of covariate measurement errors in quantile regression. The proposed method is simple to implement. Its validity requires only linearity of the particular quantile function of interest, and it requires no parametric assumptions on the regression error distributions. Finite-sample results demonstrate that the proposed estimators are more efficient than the existing methods in various models considered.

Quantile Regression for Competing Risks Data with Missing Cause of Failure.

This paper considers generalized linear quantile regression for competing risks data when the failure type may be missing. Two estimation procedures for the regression co-efficients, including an inverse probability weighted complete-case estimator and an augmented inverse probability weighted estimator, are discussed under the assumption that the failure type is missing at random. The proposed estimation procedures utilize supplemental auxiliary variables for predicting the missing failure type and for informing its distribution. The asymptotic properties of the two estimators are derived and their asymptotic efficiencies are compared. We show that the augmented estimator is more efficient and possesses a double robustness property against misspecification of either the model for missingness or for the failure type. The asymptotic covariances are estimated using the local functional linearity of the estimating functions. The finite sample performance of the proposed estimation procedures are evaluated through a simulation study. The methods are applied to analyze the 'Mashi' trial data for investigating the effect of formula-versus breast-feeding plus extended infant zidovudine prophylaxis on HIV-related death of infants born to HIV-infected mothers in Botswana.

Identification of differential aberrations in multiple-sample array CGH studies.

Most existing methods for identifying aberrant regions with array CGH data are confined to a single target sample. Focusing on the comparison of multiple samples from two different groups, we develop a new penalized regression approach with a fused adaptive lasso penalty to accommodate the spatial dependence of the clones. The nonrandom aberrant genomic segments are determined by assessing the significance of the differences between neighboring clones and neighboring segments. The algorithm proposed in this article is a first attempt to simultaneously detect the common aberrant regions within each group, and the regions where the two groups differ in copy number changes. The simulation study suggests that the proposed procedure outperforms the commonly used single-sample aberration detection methods for segmentation in terms of both false positives and false negatives. To further assess the value of the proposed method, we analyze a data set from a study that identified the aberrant genomic regions associated with grade subgroups of breast cancer tumors.

Efficient Moments-based Permutation Tests.

In this paper, we develop an efficient moments-based permutation test approach to improve the test's computational efficiency by approximating the permutation distribution of the test statistic with Pearson distribution series. This approach involves the calculation of the first four moments of the permutation distribution. We propose a novel recursive method to derive these moments theoretically and analytically without any permutation. Experimental results using different test statistics are demonstrated using simulated data and real data. The proposed strategy takes advantage of nonparametric permutation tests and parametric Pearson distribution approximation to achieve both accuracy and efficiency.