Logistic quantile regression to model cognitive impairment in Sardinian cancer patients

When analyzing outcome variables that take on values within a finite bounded interval, standard analyses are often inappropriate. The conditional distribution of bounded outcomes given covariates is often asymmetric and bimodal (e.g., J- or U-shaped) and may substantially vary across covariate patterns. Analyzing this type of outcomes calls for specific methods that can constrain inference within the feasible range. The conditional mean is generally not an effective summary measure of a bounded outcome, and conditional quantiles are preferable. In this chapter we present an application of logistic quantile regression to model the relationship between Mini Mental State Examination (MMSE), a cognitive impairment score bounded between 0 and 30, with age and the results of a biochemical analysis (Oil Red O) for the determination of cytoplasmic neutral lipids in peripheral blood mononuclear cells in a sample of 124 cancer patients living in Sardinia, Italy. In addition we discuss an internal cross-validation method to optimally select the boundary correction in the logit transform.