Quantile regression. In statistics, regression is a common method used to obtain a summary of the relationship between a response variable y and a set of covariates x. For instance, a least squares regression captures how the mean of y changes with x of the outcome. Epidemiological research often focuses on inference for high or low values in a population distribution, e.g. high body mass index, low birth weight, high blood pressure. However in some instances, a single mean curve might not be informative enough particularly if the primary interest resides in the tail ends of the distribution. While linear regression speculates the question 'What is the relation between X and Y?' quantile regression extends this to, 'For whom does a relation between X and Y exist' as well as testing for whom a relation is stronger or weaker" (Xxxxxxxx & Xxxxx, 2014). Quantile regression, as introduced by Xxxxxxx and Xxxxxxx (1978), is a method for estimating functional relations between variables for all portions of a probability distribution (Koenker & Xxxxxxx, 1978) . Further, a set of equally spaced quantiles (e.g. every 5% of the population) can define the shape of the distribution in addition to its central location. Thus, conditional quantile functions provide a more complete view. There are various reasons as to why one would choose to perform quantile regression, for example, when the distribution of y might be asymmetric around the mean or heteroscedasticity might exist in the data (Xxxx & Xxxx, 2003; XxXxxxxx, Xxxxxxx, Xxxxxx, Rimm, & Xxxx, 2009). For example, regression models with heterogeneous variances, which are common in epidemiological studies, imply that there is not a single rate of change that describes changes in the probability distributions, therefore, focusing only on changes in the means might underestimate, overestimate, or fail to distinguish real nonzero changes in heterogeneous distributions (Xxxx & Noon, 2003). I used quantiles to describe the distribution of the dependent variables. Quantiles and percentiles are synonymous where, for example, the 0.99 quantile would be the 99th percentile. The best known quantile is the medium that is the 0.50 quantile. One practical consideration is that the distribution of the dependent variable is particularly important and that needs to be continuous with no zeros or too many repeated values. Unlike interpretation of linear regression, the interpretation of the quantile regression results need to specify which quantile of the ...
Quantile regression. To test and estimate the association between different levels of sun-exposure (high and none vs intermediate exposure) and change in the CAPE scale we fitted quantile regression(Xxxx & Noon, 2003).
