Shedding new light onto the ceiling and floor? A quantile regression approach to compare EQ-5D and SF-6D responses

An important issue in the measurement of health status concerns the extent to which an instrument displays lack of sensitivity to changes in health status at the extremes of the distribution, known as floor and ceiling effects. Previous studies use relatively simple methods that focus on the mean of the distribution to examine these effects. The aim of this paper is to determine whether quantile regression using longitudinal data improves our understanding of the relationship between quality of life instruments. The study uses EQ-5D and SF-36 (converted to SF-6D values) instruments with both baseline and follow-up data. Relative to ordinary least least-squares (OLS), a first difference model shows much lower association between the measures, suggesting that OLS methods may lead to biased estimates of the association, due to unobservable patient characteristics. The novel finding, revealed by quantile regression, is that the strength of association between the instruments is different across different parts of the health distribution, and is dependent on whether health improves or deteriorates. The results suggest that choosing one instrument at the expense of another is difficult without good prior information surrounding the expected magnitude and direction or health improvement related to a health-care intervention.