Quantile Linear Modeling: A Primer for the Working Statistician (Part 2)

• Activity Number: 402
• Type: Invited
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Consulting
• Author(s): Ralph G. O'Brien*+
• Companies: Case Western Reserve University
• Keywords: quantile regression ; statistical modeling ; L1 regression ; survival analysis

Abstract

In ordinary linear modeling, we assess how a set of predictors {X} relates to the mean of Y, E[Y] ~ f{X}. Yet, other aspects of Y may be more relevant. The median (or 0.50 quantile, or 50th percentile) may better depict Y's central tendency. Other quantiles (e.g., 0.10 or 0.90) may better capture the heart of the Y ~ f{X} relationship. Quantile linear modeling (QLM) gives us such a tool. For example, a study might compare two surgical techniques (X=0 vs. X=1) with respect to time under general anesthesia (Y), adjusting for patients' pre-surgery characteristics. Rather than using ANCOVA to compare adjusted means for Y, QLM lets us compare the two techniques at, say, the 0.90 quantile for Y. To depict the entire Y ~ f{X} relationship, QLMs can be fit, graphed, and tested over a range of quantiles. This example-driven tutorial begins with the basic two-group comparison, considers complex designs (several Xs), and ends with a time-to-event analysis that avoids the proportional hazards assumption. All examples are handled using R with all slides and code downloadable (epbiwww.case.edu/qlmstats). We seek to motivate and enable working statisticians to add QLM to their everyday toolbox.