Statistical Inference in Quantile Regression Models

The main purpose of this dissertation is to collect different innovative statistical methods in quantile regression. The contributions can be summarized as follows: -- A new method to construct prediction intervals involving median regression and bootstrapping the prediction error is proposed. -- A plug-in bandwidth selector for nonparametric quantile regression has been proposed, that is based on nonparametric estimations of the curvature of the quantile regression function and the integrated sparsity. -- Two lack-of-fit tests for quantile regression models have been presented. The first test is based on the cumulative sum of residuals with respect to unidimensional linear projections of the covariates in order to deal with high-dimensional covariates. The second test is based on interpreting the residuals from the quantile model fit as response values of a logistic regression. Then a likelihood ratio test in the logistic regression is used to check the quantile model

A plug-in bandwidth selector for nonparametric quantile regression

This is a post-peer-review, pre-copyedit version of an article published in TEST. The final authenticated version is available online at: https://doi.org/10.1007/s11749-018-0582-6In the framework of quantile regression, local linear smoothing techniques have been studied by several authors, particularly by Yu and Jones (J Am Stat Assoc 93:228–237, 1998). The problem of bandwidth selection was addressed in the literature by the usual approaches, such as cross-validation or plug-in methods. Most of the plug-in methods rely on restrictive assumptions on the quantile regression model in relation to the mean regression, or on parametric assumptions. Here we present a plug-in bandwidth selector for nonparametric quantile regression that is defined from a completely nonparametric approach. To this end, the curvature of the quantile regression function and the integrated squared sparsity (inverse of the conditional density) are both nonparametrically estimated. The new bandwidth selector is shown to work well in different simulated scenarios, particularly when the conditions commonly assumed in the literature are not satisfied. A real data application is also givenThe authors gratefully acknowledge the support of Projects MTM2013–41383–P (Spanish Ministry of Economy, Industry and Competitiveness) and MTM2016–76969–P (Spanish State Research Agency, AEI), both co-funded by the European Regional Development Fund (ERDF). Support from the IAP network StUDyS, from Belgian Science Policy, is also acknowledged. Work of M. Conde-Amboage has been supported by FPU grant AP2012-5047 from the Spanish Ministry of EducationS

Quantile regression: estimation and lack-of-fit tests

Although mean regression achieved its greatest diffusion in the twentieth century, it is very surprising to observe that the ideas of quantile regression appeared earlier. While the beginning of the least-squares regression can be dated in the year 1805 by the work of Legendre, in the mid-eighteenth century Boscovich already adjusted data on the ellipticity of the Earth using concepts of quantile regression. Quantile regression is employed when the aim of the study is centred on the estimation of the different positions (quantiles). This kind of regression allows a more detailed description of the behaviour of the response variable, adapts to situations under more general conditions of the error distribution and enjoys robustness properties. For all that, quantile regression is a very useful statistical technology for a large diversity of disciplines. In this paper a review on quantile regression methods will be presentedS

Predicting trace gas concentrations using quantile regression models

This is a post-peer-review, pre-copyedit version of an article published in Stoch Environ Res Risk Assess. The final authenticated version is available online at: https://doi.org/10.1007/s00477-016-1252-4Quantile regression methods are evaluated for computing predictions and prediction intervals of NOx concentrations measured in the vicinity of the power plant in As Pontes (Spain). For these data, smaller prediction errors were obtained using methods based on median regression compared with mean regression. A new method to construct prediction intervals involving median regression and bootstrapping the prediction error is proposed. This new method provides better coverage for NOx data compared with classical and bootstrap prediction intervals based on mean regression, as well as simpler prediction intervals based on quantile regression. A simulation study illustrates the features of this proposed method that lead to a better performance for obtaining prediction intervals for these particular NOx concentration data, as well as for any other environmental dataset that do not meet assumptions of homoscedasticity and normality of the error distributionThis study was supported by Project MTM2013-41383P from the Spanish Ministry of Economy and Competitiveness, as well as the European Regional Development Fund (ERDF). Support from the IAP network StUDyS from the Belgian Science Policy is also acknowledged. M. Conde-Amboage was supported by FPU grant AP2012-5047 from the Spanish Ministry of EducationS

Impact of abutment geometry on early implant marginal bone loss. A double-blind, randomized, 6-month clinical trial

Objectives The objective of this study was to analyze the impact of the abutment width on early marginal bone loss (MBL). Material and Methods A balanced, randomized, double-blind clinical trial with two parallel experimental arms was conducted without a control group. The arms were “cylindrical” abutment and “concave” abutment. Eighty hexagonal internal connection implants, each with a diameter of 4 × 10 mm, were placed in healed mature bone. The main variable was the peri-implant tissue stability, which was measured as MBL at 8 weeks and 6 months. Results The final sample consisted of 77 implants that were placed in 25 patients. 38 (49.4%) were placed using the cylindrical abutment, and the other 39 (50.6%) were placed using the concave abutment. The early global MBL of −0.6 ± 0.7 mm in the cylindrical abutment group was significantly higher than it was in the concave abutment group, in which the early global MBL was −0.4 ± 0.6 mm (p = .030). The estimated effect size (ES) was negative for the cylindrical abutment (ES = −1.3730, CI −2.5919 to −0.1327; t-value = −2.4893; p = .0139), therefore implying a loss of mean bone level, and it was positive for the concave abutment (ES = 2.8231; CI: 1.4379 to 4.2083; t-value = 4.0957; p = .0002), therefore implying an increase in the average bone level. Conclusions The concave abutments presented significantly less early MBL at 6 months post-loading than classical cylindrical abutments did

Quantitative proteomics in medication-related osteonecrosis of the jaw: a proof-of-concept study

Objective: Medication-related osteonecrosis of the jaw (MRONJ) is a paradoxical effect associated with bone-modifying agents (BMAs) and other drugs. Currently, no valuable diagnostic or prognosis biomarkers exist. The goal of this research was to study MRONJ-related salivary proteome. Materials and Methods: This case–control aimed to study salivary proteome in MRONJ versus control groups (i) formed from BMAs consumers and (ii) healthy individuals to unravel biomarkers. Thirty-eight samples of unstimulated whole saliva (18 MRONJ patients, 10 BMA consumers, and 10 healthy controls) were collected. Proteomic analysis by SWATH-MS coupled with bioinformatics analysis was executed. Results A total of 586 proteins were identified, 175 proteins showed significant differences among MRONJ versus controls. SWATH-MS revealed differentially expressed proteins among three groups, which have never been isolated. These proteins had distinct roles including cell envelope organization, positive regulation of vesicle fusion, positive regulation of receptor binding, or regulation of low-density lipoprotein particle clearance. Integrative analysis prioritized 3 proteins (MMP9, AACT, and HBD). Under receiver-operating characteristic analysis, this panel discriminated MRONJ with a sensitivity of 90% and a specificity of 78.9%. Conclusion: These findings may inform a novel biomarker panel for MRONJ prediction or diagnosis. Nonetheless, further research is needed to validate this panelS

Circulating Proteins Associated with Response and Resistance to Neoadjuvant Chemotherapy in HER2-Positive Breast Cancer

Despite the increasing use of neoadjuvant chemotherapy (NAC) in HER2-positive breast cancer (BC) patients, the clinical problem of predicting individual treatment response remains unanswered. Furthermore, the use of ineffective chemotherapeutic regimens should be avoided. Serum biomarker levels are being studied more and more for their ability to predict therapy response and aid in the development of personalized treatment regimens. This study aims to identify effective protein networks and biomarkers to predict response to NAC in HER2-positive BC patients through an exhaustive large-scale LC-MS/MS-based qualitative and quantitative proteomic profiling of serum samples from responders and non-responders. Serum samples from HER2-positive BC patients were collected before NAC and were processed by three methods (with and without nanoparticles). The qualitative analysis revealed differences in the proteomic profiles between responders and non-responders, mainly in proteins implicated in the complement and coagulation cascades and apolipoproteins. Qualitative analysis confirmed that three proteins (AFM, SERPINA1, APOD) were correlated with NAC resistance. In this study, we show that serum biomarker profiles can predict treatment response and outcome in the neoadjuvant setting. If these findings are further developed, they will be of significant clinical utility in the design of treatment regimens for individual BC patients