Patient-reported health-related quality-of-life (HRQoL) measures such as the EuroQol 5 dimension (EQ-5D) index are commonplace when assessing healthcare providers or efficiency of medical techniques. HRQoL measures are generally bounded, and the magnitude of possible improvement depends on the pre-treatment HRQoL value. This paper aimed to assess and illustrated the possibility of modelling the relationship between pre- and post-treatment HRQoL measures with piecewise linear splines.
The method was illustrated using a longitudinal dataset of 36,625 patients with one EQ-5D index before and one a year after total hip arthroplasty. We considered four models: intercept only model, single line regression, and segmented regression with 1 and 2 change points. The post-operative EQ-5D index served as the outcome, while the preoperative EQ-5D index was the predictor.
We found that a two-line regression best described the data with the lines meeting at 0.159 on the preoperative EQ-5D index scale. In the low preoperative group (with an initial preoperative index from -0.594 to 0.159), the predicted post-operative scores ranged from 0.368 to 0.765, with post-operative scores increasing 0.528 points for each unit in the preoperative score. In the high preoperative group (initial range from 0.159 to 1), the predicted post-operative scores ranged from 0.765 to 0.855, increasing 0.106 points for each unit in the preoperative score.
Piecewise linear regression is a straightforward approach to analyse baseline and follow-up HRQoL measures such as the EQ-5D index. It can provide a reasonable approximation of the shape of the underlying relationship where the threshold and slopes prove informative and meaningful.