The manuscript discusses how to incorporate random effects for quantile regression models for clustered data with focus on settings with many but small clusters. The paper has three contributions: (i) documenting that existing methods may lead to severely biased estimators for fixed effects parameters; (ii) proposing a new two-step estimation methodology where predictions of the random effects are first computed {by a pseudo likelihood approach (the LQMM method)} and then used as offsets in standard quantile regression; (iii) proposing a novel bootstrap sampling procedure in order to reduce bias of the two-step estimator and compute confidence intervals. The proposed estimation and associated inference is assessed numerically through rigorous simulation studies and applied to an AIDS Clinical Trial Group (ACTG) study.
In this work, we propose a zero-adjusted log-symmetric quantile regression model. Initially, we introduce zero-adjusted log-symmetric distributions, which allow for the accommodation of zeros. The estimation of the parameters is approached by the maximum likelihood method and a Monte Carlo simulation is performed to evaluate the estimates. Finally, we illustrate the proposed methodology with the use of a real extramarital affairs data set.
Quantile regression provides a consistent approach to investigating the association between covariates and various aspects of the distribution of the response beyond the mean. When the regression covariates are measured with errors, measurement error (ME) adjustment steps are needed for valid inference. This is true for both scalar and functional covariates. Here, we propose extending the Bayesian measurement error and Bayesian quantile regression literature to allow for available covariates prone to potential complex measurement errors. Our approach uses the Generalized Asymmetric Laplace (GA…
In many industry settings, online controlled experimentation (A/B test) has been broadly adopted as the gold standard to measure product or feature impacts. Most research has primarily focused on user engagement type metrics, specifically measuring treatment effects at mean (average treatment effects, ATE), and only a few have been focusing on performance metrics (e.g. latency), where treatment effects are measured at quantiles. Measuring quantile treatment effects (QTE) is challenging due to the myriad difficulties such as dependency introduced by clustered samples, scalability issues, densit…
Linear mixed-effects models are commonly used to analyze clustered data structures. There are numerous packages to fit these models in R and conduct likelihood-based inference. The implementation of resampling-based procedures for inference are more limited. In this paper, we introduce the lmeresampler package for bootstrapping nested linear mixed-effects models fit via lme4 or nlme. Bootstrap estimation allows for bias correction, adjusted standard errors and confidence intervals for small samples sizes and when distributional assumptions break down. We will also illustrate how bootstrap resa…
In this paper, we study statistical inference in functional quantile regression for scalar response and a functional covariate. Specifically, we consider a functional linear quantile regression model where the effect of the covariate on the quantile of the response is modeled through the inner product between the functional covariate and an unknown smooth regression parameter function that varies with the level of quantile. The objective is to test that the regression parameter is constant across several quantile levels of interest. The parameter function is estimated by combining ideas from f…
The computational prediction algorithm of neural network, or deep learning, has drawn much attention recently in statistics as well as in image recognition and natural language processing. Particularly in statistical application for censored survival data, the loss function used for optimization has been mainly based on the partial likelihood from Cox's model and its variations to utilize existing neural network library such as Keras, which was built upon the open source library of TensorFlow. This paper presents a novel application of the neural network to the quantile regression for survival…
Datasets from field experiments with covariate-adaptive randomizations (CARs) usually contain extra covariates in addition to the strata indicators. We propose to incorporate these additional covariates via auxiliary regressions in the estimation and inference of unconditional quantile treatment effects (QTEs) under CARs. We establish the consistency and limit distribution of the regression-adjusted QTE estimator and prove that the use of multiplier bootstrap inference is non-conservative under CARs. The auxiliary regression may be estimated parametrically, nonparametrically, or via regulariza…
Linear mixed-effects models are widely used in analyzing repeated measures data, including clustered and longitudinal data, where inferences of both fixed effects and variance components are of importance. Unlike the fixed effect inference that has been well studied, inference on the variance components is more challenging due to null value being on the boundary and the nuisance parameters of the fixed effects. Existing methods often require strong distributional assumptions on the random effects and random errors. In this paper, we develop empirical likelihood-based methods for the inference …
In this paper, we present three estimators of the ROC curve when missing observations arise among the biomarkers. Two of the procedures assume that we have covariates that allow to estimate the propensity and the estimators are obtained using an inverse probability weighting method or a smoothed version of it. The other one assumes that the covariates are related to the biomarkers through a regression model which enables us to construct convolution--based estimators of the distribution and quantile functions. Consistency results are obtained under mild conditions. Through a numerical study we …
Continuous response variables often need to be transformed to meet regression modeling assumptions; however, finding the optimal transformation is challenging and results may vary with the choice of transformation. When a continuous response variable is measured repeatedly for a subject or the continuous responses arise from clusters, it is more challenging to model the continuous response data due to correlation within clusters. We extend a widely used ordinal regression model, the cumulative probability model (CPM), to fit clustered continuous response variables based on generalized estimati…
Causal Inference with Multiple Misclassified Exposures: A Control Variate-Adjusted Calibration Weighting Approach
Colorado School of Public Health（科罗拉多公共卫生学院）；Johns Hopkins Bloomberg School of Public Health（约翰斯·霍普金斯大学彭博公共卫生学院）；University of Colorado School of Medicine（科罗拉多大学医学院）；Colorado State University（科罗拉多州立大学）
