Huixia Judy Wang

Quantile regression in partially linear varying coefficient models

Semiparametric models are often considered for analyzing longitudinal data for a good balance between flexibility and parsimony. In this paper, we study a class of marginal partially linear quantile models with possibly varying coefficients. The functional coefficients are estimated by basis function approximations. The estimation procedure is easy to implement, and it requires no specification of the error distributions. The asymptotic properties of the proposed estimators are established for the varying coefficients as well as for the constant coefficients. We develop rank score tests for hypotheses on the coefficients, including the hypotheses on the constancy of a subset of the varying coefficients. Hypothesis testing of this type is theoretically challenging, as the dimensions of the parameter spaces under both the null and the alternative hypotheses are growing with the sample size. We assess the finite sample performance of the proposed method by Monte Carlo simulation studies, and demonstrate its value by the analysis of an AIDS data set, where the modeling of quantiles provides more comprehensive information than the usual least squares approach.

Locally Weighted Censored Quantile Regression

Censored quantile regression offers a valuable supplement to Cox proportional hazards model for survival analysis. Existing work in the literature often requires stringent assumptions, such as unconditional independence of the survival time and the censoring variable or global linearity at all quantile levels. Moreover, some of the work uses recursive algorithms, making it challenging to derive asymptotic normality. To overcome these drawbacks, we propose a new locally weighted censored quantile regression approach that adopts the redistribution-of-mass idea and employs a local reweighting scheme. Its validity only requires conditional independence of the survival time and the censoring variable given the covariates, and linearity at the particular quantile level of interest. Our method leads to a simple algorithm that can be conveniently implemented with R software. Applying recent theory of M-estimation with infinite dimensional parameters, we establish the consistency and asymptotic normality of the proposed estimator. The proposed method is studied via simulations and is illustrated with the analysis of an acute myocardial infarction dataset.

Flexible Bayesian quantile regression for independent and clustered data

Quantile regression has emerged as a useful supplement to ordinary mean regression. Traditional frequentist quantile regression makes very minimal assumptions on the form of the error distribution and thus is able to accommodate nonnormal errors, which are common in many applications. However, inference for these models is challenging, particularly for clustered or censored data. A Bayesian approach enables exact inference and is well suited to incorporate clustered, missing, or censored data. In this paper, we propose a flexible Bayesian quantile regression model. We assume that the error distribution is an infinite mixture of Gaussian densities subject to a stochastic constraint that enables inference on the quantile of interest. This method outperforms the traditional frequentist method under a wide array of simulated data models. We extend the proposed approach to analyze clustered data. Here, we differentiate between and develop conditional and marginal models for clustered data. We apply our methods to analyze a multipatient apnea duration data set.

Influence of genetic background on tumor karyotypes: Evidence for breed-associated cytogenetic aberrations in canine appendicular osteosarcoma

Recurrent chromosomal aberrations in solid tumors can reveal the genetic pathways involved in the evolution of a malignancy and in some cases predict biological behavior. However, the role of individual genetic backgrounds in shaping karyotypes of sporadic tumors is unknown. The genetic structure of purebred dog breeds, coupled with their susceptibility to spontaneous cancers, provides a robust model with which to address this question. We tested the hypothesis that there is an association between breed and the distribution of genomic copy number imbalances in naturally occurring canine tumors through assessment of a cohort of Golden Retrievers and Rottweilers diagnosed with spontaneous appendicular osteosarcoma. Our findings reveal significant correlations between breed and tumor karyotypes that are independent of gender, age at diagnosis, and histological classification. These data indicate for the first time that individual genetic backgrounds, as defined by breed in dogs, influence tumor karyotypes in a cancer with extensive genomic instability.

‘Putting our heads together’: insights into genomic conservation between human and canine intracranial tumors

Numerous attributes render the domestic dog a highly pertinent model for cancer-associated gene discovery. We performed microarray-based comparative genomic hybridization analysis of 60 spontaneous canine intracranial tumors to examine the degree to which dog and human patients exhibit aberrations of ancestrally related chromosome regions, consistent with a shared pathogenesis. Canine gliomas and meningiomas both demonstrated chromosome copy number aberrations (CNAs) that share evolutionarily conserved synteny with those previously reported in their human counterpart. Interestingly, however, genomic imbalances orthologous to some of the hallmark aberrations of human intracranial tumors, including chromosome 22/NF2 deletions in meningiomas and chromosome 1p/19q deletions in oligodendrogliomas, were not major events in the dog. Furthermore, and perhaps most significantly, we identified highly recurrent CNAs in canine intracranial tumors for which the human orthologue has been reported previously at low frequency but which have not, thus far, been associated intimately with the pathogenesis of the tumor. The presence of orthologous CNAs in canine and human intracranial cancers is strongly suggestive of their biological significance in tumor development and/or progression. Moreover, the limited genetic heterogenity within purebred dog populations, coupled with the contrasting organization of the dog and human karyotypes, offers tremendous opportunities for refining evolutionarily conserved regions of tumor-associated genomic imbalance that may harbor novel candidate genes involved in their pathogenesis. A comparative approach to the study of canine and human intracranial tumors may therefore provide new insights into their genetic etiology, towards development of more sophisticated molecular subclassification and tailored therapies in both species.

Inference for censored quantile regression models in longitudinal studies

We develop inference procedures for longitudinal data where some of the measurements are censored by fixed constants. We consider a semi-parametric quantile regression model that makes no distributional assumptions. Our research is motivated by the lack of proper inference procedures for data from biomedical studies where measurements are censored due to a fixed quantification limit. In such studies the focus is often on testing hypotheses about treatment equality. To this end, we propose a rank score test for large sample inference on a subset of the covariates. We demonstrate the importance of accounting for both censoring and intra-subject dependency and evaluate the performance of our proposed methodology in a simulation study. We then apply the proposed inference procedures to data from an AIDS-related clinical trial. We conclude that our framework and proposed methodology is very valuable for differentiating the influences of predictors at different locations in the conditional distribution of a response variable.

Estimation of High Conditional Quantiles for Heavy-Tailed Distributions

Estimation of conditional quantiles at very high or low tails is of interest in numerous applications. Quantile regression provides a convenient and natural way of quantifying the impact of covariates at different quantiles of a response distribution. However, high tails are often associated with data sparsity, so quantile regression estimation can suffer from high variability at tails especially for heavy-tailed distributions. In this article, we develop new estimation methods for high conditional quantiles by first estimating the intermediate conditional quantiles in a conventional quantile regression framework and then extrapolating these estimates to the high tails based on reasonable assumptions on tail behaviors. We establish the asymptotic properties of the proposed estimators and demonstrate through simulation studies that the proposed methods enjoy higher accuracy than the conventional quantile regression estimates. In a real application involving statistical downscaling of daily precipitation in the Chicago area, the proposed methods provide more stable results quantifying the chance of heavy precipitation in the area. Supplementary materials for this article are available online.

Variable selection in quantile varying coefficient models with longitudinal data

In this paper, we develop a new variable selection procedure for quantile varying coefficient models with longitudinal data. The proposed method is based on basis function approximation and a class of group versions of the adaptive LASSO penalty, which penalizes the L γ norm of the within-group coefficients with γ ? 1 . We show that with properly chosen adaptive group weights in the penalization, the resulting penalized estimators are consistent in variable selection, and the estimated functional coefficients retain the optimal convergence rate of nonparametric estimators under the true model. We assess the finite sample performance of the proposed procedure by an extensive simulation study, and the analysis of an AIDS data set and a yeast cell-cycle gene expression data set.

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 Tsiatiss 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.

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.