Estimation and Inference for Quantile Regression of Longitudinal Data : With Applications in Biostatistics

This thesis consists of four papers dealing with estimation and inference for quantile regression of longitudinal data, with an emphasis on nonlinear models. The first paper extends the idea of quantile regression estimation from the case of cross-sectional data with independent errors to the case of linear or nonlinear longitudinal data with dependent errors, using a weighted estimator. The performance of different weights is evaluated, and a comparison is also made with the corresponding mean regression estimator using the same weights. The second paper examines the use of bootstrapping for bias correction and calculations of confidence intervals for parameters of the quantile regression estimator when longitudinal data are used. Different weights, bootstrap methods, and confidence interval methods are used. The third paper is devoted to evaluating bootstrap methods for constructing hypothesis tests for parameters of the quantile regression estimator using longitudinal data. The focus is on testing the equality between two groups of one or all of the parameters in a regression model for some quantile using single or joint restrictions. The tests are evaluated regarding both their significance level and their power. The fourth paper analyzes seven longitudinal data sets from different parts of the biostatistics area by quantile regression methods in order to demonstrate how new insights can emerge on the properties of longitudinal data from using quantile regression methods. The quantile regression estimates are also compared and contrasted with the least squares mean regression estimates for the same data set. In addition to looking at the estimates, confidence intervals and hypothesis testing procedures are examined