Quantile regression: predicting more than the mean.

Abstract

INTRODUCTION: Interval measurements such as length of hospital stay, depression inventory scores and overall functioning, are typically summarized by the mean with its standard deviation. In instances of asymmetric, highly skewed distributions such as length of hospital stay, the data is often summarized using the 50th percentile (i.e. the median) together with the 25th and 75th percentiles, known as the lower and upper quartiles. The latter are often reported as the "interquartile range" (a measure of the middle 50% of the distribution). However, other percentiles such as the 10th and 90th appear far less frequently. In other words, the top and bottom 25% of data is not captured - reflecting a current research limitation pointed out by Vasista et al (2014). Recent studies have demonstrated the importance of evaluating the upper and lower ends of the distribution together with the median. For example, in a recent study by Westerlund et al (2014), researchers showed that although the overall median body mass index (BMI) was similar between patients with short (<=5hr) and medium length (6-8hr) sleep durations, the 90th percentile of BMI was much higher in the former than in the latter sleep duration. This example illustrates the importance of assessing more than just the median and to consider the whole data distribution. AIMS: To present graphical and statistical methods of examining the higher and lower ends of a given data distribution using quantile regression. METHODOLOGY: Originally formulated in the 18th century by Fr Roger Boscovich SJ, physicist, astronomer and mathematician, but implemented much more recently with the development of fast computers and sophisticated software, quantile regression allows the ready prediction of percentiles such as the 90th, 75th, 25th and 10th as well as the median. Quantile regression is available in standard statistical software packages such as R and Stata. RESULTS: Illustrative published medical data and graphs will be presented in order to demonstrate ways of evaluating the entire distribution of data. [See poster]