Rank Score Test Research Articles

Quantile regression for partially linear varying coefficient spatial autoregressive models

This article considers the quantile regression approach for partially linear spatial autoregressive models with possibly varying coefficients. B-spline is employed for the approximation of varying coefficients. The instrumental variable quantile regression approach is employed for parameter estimation. The rank score tests are developed for hypotheses on the coefficients, including the hypotheses on the non-varying coefficients and the constancy of the varying coefficients. The asymptotic properties of the proposed estimators and test statistics are both established. Monte Carlo simulations are conducted to study the finite sample performance of the proposed method. Analysis of a real data example is presented for illustration.

Multikink quantile regression for longitudinal data with application to progesterone data analysis.

Motivated by investigating the relationship between progesterone and the days in a menstrual cycle in a longitudinal study, we propose a multikink quantile regression model for longitudinal data analysis. It relaxes the linearity condition and assumes different regression forms in different regions of the domain of the threshold covariate. In this paper, we first propose a multikink quantile regression for longitudinal data. Two estimation procedures are proposed to estimate the regression coefficients and the kink points locations: one is a computationally efficient profile estimator under the working independence framework while the other one considers the within-subject correlations by using the unbiased generalized estimation equationapproach. The selection consistency of the number of kink points and the asymptotic normality of two proposed estimators are established. Second, we construct a rank score test based on partial subgradients for the existence of the kink effect in longitudinal studies. Both the null distribution and the local alternative distribution of the test statistic have been derived. Simulation studies show that the proposed methods have excellent finite sample performance. In the application to the longitudinal progesterone data, we identify two kink points in the progesterone curves over different quantiles and observe that the progesterone level remains stable before the day of ovulation, then increases quickly in 5 to 6 days after ovulation and then changes to stable again or dropsslightly.

A Generalized Quantile Tree Method for Subgroup Identification

One primary goal of subgroup analysis is to identify subgroups of subjects with differential treatment effects. Existing methods have focused on the mean treatment effect and may be ineffective when the two distributions differ in scales or in the upper or lower tails. We develop a new generalized quantile tree method for subgroup identification. The method first uses quantile rank score tests to select split variables and then estimates the split point by minimizing a composite quantile loss. The proposed split rule is free of variable selection bias and robust against outliers and heavy-tailed distributions. In addition, we introduce a generalized quantile treatment effect estimator and a testing method for the selection and confirmation of predictive subgroups. Simulation shows that the proposed method gives more accurate subgroup identification than existing methods for cases with heteroscedastic or heavy-tailed errors. The practical value of the method is demonstrated through the analysis of an AIDS clinical trial data. Supplementary materials for this article are available online.

ZERO-INFLATED QUANTILE RANK-SCORE BASED TEST (ZIQRANK) WITH APPLICATION TO SCRNA-SEQ DIFFERENTIAL GENE EXPRESSION ANALYSIS.

Differential gene expression analysis based on scRNA-seq data is challenging due to two unique characteristics of scRNA-seq data. First, multimodality and other heterogeneity of the gene expression among different cell conditions lead to divergences in the tail events or crossings of the expression distributions. Second, scRNA-seq data generally have a considerable fraction of dropout events, causing zero inflation in the expression. To account for the first characteristic, existing parametric approaches targeting the mean difference in gene expression are limited, while quantile regression that examines various locations in the distribution will improve the power. However, the second characteristic, zero inflation, makes the traditional quantile regression invalid and underpowered. We propose a quantile-based test that handles the two characteristics, multimodality and zero inflation, simultaneously. The proposed quantile rank-score based test for differential distribution detection (ZIQRank) is derived under a two-part quantile regression model for zero-inflated outcomes. It comprises a test in logistic modeling for the zero counts and a collection of rank-score tests adjusting for zero inflation at multiple prespecified quantiles of the positive part. The testing decision is based on an aggregate result by combining the marginal p-values by MinP or Cauchy procedure. The proposed test is asymptotically justified and evaluated with simulation studies. It shows a higher precision-recall AUC in detecting true differentially expressed genes (DEGs) than the existing methods. We apply the ZIQRank test to a TPM scRNA-seq data on human glioblastoma tumors and exclusively identify a group of DEGs between neoplastic and nonneoplastic cells, which are heterogeneous and have been proved to be associated with glioma. Application to a UMI count scRNA-seq data on cells from mouse intestinal organoids further demonstrates the capability of ZIQRank to improve and complement the existing approaches.

Testing linearity in partial functional linear quantile regression model based on regression rank scores

This paper investigates the hypothesis test of the parametric component in partial functional linear quantile regression model in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables. A quantile rank score test based on functional principal component analysis is developed. Under mild conditions, we establish the consistency of the proposed test statistic, and show that the proposed test can detect Pitman local alternatives converging to the null hypothesis at the usual parametric rate. A simulation study shows that the proposed test procedure has good size and power with finite sample sizes. Finally, an illustrative example is given through fitting the Berkeley growth data and testing the effect of gender on the height of kids.

Statistical inference for the functional quadratic quantile regression model

In this paper, we develop statistical inference procedures for functional quadratic quantile regression model in which the response is a scalar and the predictor is a random function defined on a compact set of R. The functional coefficients are estimated by functional principal components. The asymptotic properties of the resulting estimators are established under mild conditions. In order to test the significance of the nonlinear term in the model, we propose a rank score test procedure. The asymptotic properties of the proposed test statistic are established. The proposed method provides a highly efficient and robust alternative to the least squares method, and can be conveniently implemented using existing R software package. Finally, we examine the performance of the proposed method for finite sample sizes by Monte Carlo simulation studies and illustrate it with a real data example.

Estimation and Testing of Varying Coefficients in Quantile Regression

In this article, we establish a novel connection between the null hypothesis H0 on the coefficients and a rank-reducible form of the varying coefficient model in quantile regression. We use B-splines to approximate the varying coefficients in the rank-reducible model, and make use of the fact that the null hypothesis H0 implies a unidimensional structure of a transformed coefficient matrix for the B-spline basis functions. By evaluating the unidimensional structure, we alleviate the difficulty of testing such hypotheses commonly considered in varying coefficient quantile models. We demonstrate through numerical studies that the proposed method can be much more powerful than the rank score test which is widely used in the quantile regression literature. Supplementary materials for this article are available online.

Genomic profiling in locally advanced and inflammatory breast cancer and its link to DCE-MRI and overall survival

Purpose: We have previously reported that dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) perfusion patterns obtained from locally advanced breast cancer (LABC) patients prior to neoadjuvant therapy predicted pathologic clinical response. Genomic analyses were also independently conducted on the same patient population. This retrospective study was performed to test two hypotheses: (1) gene expression profiles are associated with DCE-MRI perfusion patterns, and (2) association between long-term overall survival data and gene expression profiles can lead to the identification of novel predictive biomarkers. Methods: We utilised RNA microarray and DCE-MRI data from 47 LABC patients, including 13 inflammatory breast cancer (IBC) patients. Association between gene expression profile and DCE-MRI perfusion patterns (centrifugal and centripetal) was determined by Wilcoxon rank sum test. Association between gene expression level and survival was assessed using a Cox rank score test. Additional genomic analysis of the IBC subset was conducted, with a period of follow-up of up to 11 years. Associations between gene expression and overall survival were further assessed in The Cancer Genome Atlas Data Portal. Results: Differences in gene expression profiles were seen between centrifugal and centripetal perfusion patterns in the sulphotransferase family, cytosolic, 1 A, phenol-preferring, members 1 and 2 (SULT1A1, SULT1A2), poly (ADP-ribose) polymerase, member 6 (PARP6), and metastasis tumour antigen1 (MTA1). In the IBC subset our analyses demonstrated that differential expression of 45 genes was associated with long-term survival. Conclusions: Here we have demonstrated an association between DCE-MRI perfusion patterns and gene expression profiles. In addition we have reported on candidate prognostic biomarkers in IBC patients, with some of the genes being significantly associated with survival in IBC and LABC.

25-Hydroxyvitamin D levels and survival in advanced pancreatic cancer: findings from CALGB 80303 (Alliance).

Data from animal and cell-line models suggest that vitamin D metabolism plays an important role in pancreatic tumor behavior. Although vitamin D deficiency has been implicated in numerous cancers, the vitamin D status of patients with advanced pancreatic cancer and the effect of baseline vitamin D levels on survival are unknown. Participants in this correlative study (CALGB 151006) were enrolled in CALGB 80303, which was a randomized trial of patients with advanced pancreatic cancer that demonstrated no difference in overall survival (OS) among patients treated with gemcitabine plus placebo vs gemcitabine plus bevacizumab. We measured baseline serum 25-hydroxyvitamin D (25[OH]D) levels and examined associations between baseline 25(OH)D levels and progression-free survival and OS using the Cox rank score test. All statistical tests were two-sided. Of 256 patients with available serum, the median 25(OH)D level was 21.7ng/mL (range 4 to 77). 44.5% of patients were vitamin D deficient (25[OH]D <20ng/mL), and 32.4% were insufficient (25[OH]D ≥20 and <30ng/mL). 25(OH)D levels were lower in black patients compared with white patients, and patients of other/undisclosed race (10.7 vs 22.4 vs 20.9ng/mL, P < .001). Baseline 25(OH)D levels were not associated with PFS (HR = 1.00, 95% CI = 0.99 to 1.01, P = .60) or OS (HR = 1.00, 95% CI = 0.99 to 1.01, P = .95). Vitamin D deficiency was highly prevalent among patients with a new diagnosis of advanced pancreatic cancer. Black patients had statistically significantly lower 25(OH)D levels than white patients. In this cohort of patients with advanced pancreatic cancer receiving gemcitabine-based chemotherapy, baseline 25(OH)D levels were not associated with PFS or OS.

25-hydroxyvitamin D levels and survival in patients with advanced pancreatic cancer (APC): Findings from CALGB 80303.

4022 Background: Data from animal and cell line models suggest that vitamin D metabolism is important in pancreatic tumor maintenance and may contribute to this tumor’s chemoresistance. While vitamin D has been implicated in a variety of cancers, the prevalence of vitamin D deficiency among patients with advanced pancreatic cancer (APC) and the effect of baseline vitamin D levels on survival outcomes are unknown. Methods: CALGB 80303 was a randomized controlled trial of patients with APC which demonstrated no difference in OS among patients treated with gemcitabine (GEM) vs. GEM + bevacizumab. We retrospectively measured baseline serum 25(OH)D levels and examined associations between baseline 25(OH)D levels and selected patient characteristics. Using the Cox rank score test, we examined the association between 25(OH)D level and PFS and OS. The differences in the levels among racial populations were tested using the Kruskal-Wallis test. Results: Of 256 patients with available serum, the median 25(OH)D level was 21.7 (range 4–77). 44.5% of patients were vitamin D deficient (25(OH)D &lt;20), 32.4% were insufficient (25(OH)D ≥20 and &lt;30), and 23% were sufficient (25(OH)D≥30). Serum 25(OH)D levels were lower in patients self-reported as black compared to white patients and patients of other/undisclosed race (median 10.7 [4.0–36.3] vs. 22.4 [4.0–77.0] vs. 20.9 [12.6 – 31.8], respectively; p&lt;0.00001). Adjusting for race, baseline 25(OH)D levels were not associated with PFS (HR 1.00, 95% CI 0.98–1.01) or OS (HR 1.00, 95% CI 0.99-1.01). Conclusions: Vitamin D deficiency was highly prevalent among patients with a new diagnosis of APC. Black patients had significantly lower 25(OH)D levels than white patients. In this cohort of patients with APC receiving GEM-based chemotherapy, baseline 25(OH)D levels were not associated with PFS or OS.

A robust test for non-nested hypotheses

This paper uses a modified rank score test for non-nested linear regression models. The modified rank score test is robust with respect to models with non-normal distributions and can be viewed as a robust version of the J test of Davidson and MacKinnon (Econometrica 49:781–793, 1981). Therefore, this test does not require a specification of error density function and is easy to implement. Also, a modified rank score test for multiple non-nested models is provided. Monte Carlo simulation results show that the test has good finite sample performances. Financial applications for two competing theories, the capital asset pricing model and the arbitrage pricing theory, are considered herein. Empirical evidence from the modified rank score test shows that the former is a better model for asset pricing.

An encompassing test for non-nested quantile regression models

We propose an encompassing test for non-nested linear quantile regression models and show that it has an asymptotic χ 2 distribution. It is also shown that the proposed test is a regression rank score test in a comprehensive model under conditional homogeneity. Our simulation results indicate that the proposed test performs very well in finite samples.

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.

Rank tests and regression rank score tests in measurement error models

The rank and regression rank score tests of linear hypothesis in the linear regression model are modified for measurement error models. The modified tests are still distribution free. Some tests of linear subhypotheses are invariant to the nuisance parameter, others are based on the aligned ranks using the R -estimators. The asymptotic relative efficiencies of tests with respect to tests in models without measurement errors are evaluated. The simulation study illustrates the powers of the tests.

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.

An Enhanced Quantile Approach for Assessing Differential Gene Expressions

Due to the small number of replicates in typical gene microarray experiments, the performance of statistical inference is often unsatisfactory without some form of information-sharing across genes. In this article, we propose an enhanced quantile rank score test (EQRS) for detecting differential expression in GeneChip studies by analyzing the quantiles of gene intensity distributions through probe-level measurements. A measure of sign correlation, delta, plays an important role in the rank score tests. By sharing information across genes, we develop a calibrated estimate of delta, which reduces the variability at small sample sizes. We compare the EQRS test with four other approaches for determining differential expression: the gene-specific quantile rank score test, the quantile rank score test assuming a common delta, a modified t-test using summarized probe-set-level intensities, and the Mack-Skillings rank test on probe-level data. The proposed EQRS is shown to be favorable for preserving false discovery rates and for being robust against outlying arrays. In addition, we demonstrate the merits of the proposed approach using a GeneChip study comparing gene expression in the livers of mice exposed to chronic intermittent hypoxia and of those exposed to intermittent room air.

A note on self-weighted quantile estimation for infinite variance quantile autoregression models

This article focuses attention on quantile autoregressive (QAR) models in which the autoregressive coefficients can be dependent on the quantile function. We use the self-weighted quantile regressive estimation for infinite variance QAR models. The asymptotic normality of the estimated parameters are established conditionally on lagged values of the response. In addition, the Wald test statistics are developed for the linear restriction on the parameters. Finally, we discuss the regression rank score test and empirical likelihood method as alternative inference approaches, which do not require the estimations of nuisance parameters.

Detecting Differential Expressions in GeneChip Microarray Studies

In this article we consider testing for differentially expressed genes in GeneChip studies by modeling and analyzing the quantiles of gene expression through probe level measurements. By developing a robust rank score test for linear quantile models with a random effect, we propose a reliable test for detecting differences in certain quantiles of the intensity distributions. By using a genomewide adjustment to the test statistic to account for within-array correlation, we demonstrate that the proposed rank score test is highly effective even when the number of arrays is small. Our empirical studies with real experimental data show that detecting differences in the quartiles for the probe level data is a valuable complement to the usual mixed model analysis based on Gaussian likelihood. The methodology proposed in this article is a first attempt to develop inferential tools for quantile regression in mixed models.

Rank Score Tests

Nonparametric statistical methods are useful tools for data analysis when there is reason to believe that the outcome variables of interest may fail certain distributional assumptions required for parametric methods. Variables may be ordered categories in nature and thereby not suitable for analysis methods that assume normally distributed variables, such as t tests or analyses of variance and covariance. Variables may also be metric or continuous but subject to excessive variability or the presence of outliers. When the research hypothesis involves comparing a sample of subjects under 2 conditions or at 2 time points or comparing 2 samples of subjects with respect to an outcome variable of interest, then univariate nonparametric methods based on rank score tests can be invoked. A study design feature such as random assignment of conditions or treatments is typically all that is required for these methods to be valid. Furthermore, the methods can be quite powerful under a number of alternatives, particularly those involving shifts in the median. The Wilcoxon signed rank test, the Spearman rank correlation coefficient, and the Wilcoxon rank sum test are among the most commonly used nonparametric tests and cover a variety of research questions. These tests are described here. Although the focus is on hypothesis testing, related methods for estimation of confidence intervals are also presented. Extensions of nonparametric methods to handle stratification and covariate adjustment are also described. Scenarios in which nonparametric methods may be most useful and the power they can be expected to yield are discussed. The methods are illustrated with data from a clinical trial assessing the impact of exposure to low levels of carbon monoxide on exercise capacity in patients with ischemic heart disease. When the response variable of interest is a metric measurement that follows a symmetrical distribution with substantial variability or outliers, then …

Conditional growth charts

Growth charts are often more informative when they are customized per subject, taking into account prior measurements and possibly other covariates of the subject. We study a global semiparametric quantile regression model that has the ability to estimate conditional quantiles without the usual distributional assumptions. The model can be estimated from longitudinal reference data with irregular measurement times and with some level of robustness against outliers, and it is also flexible for including covariate information. We propose a rank score test for large sample inference on covariates, and develop a new model assessment tool for longitudinal growth data. Our research indicates that the global model has the potential to be a very useful tool in conditional growth chart analysis.