Fractional polynomial and restricted cubic spline models as alternatives to categorising continuous data: applications in medicine

Continuous predictor variables are often categorised when reporting their influence on the outcome of interest. This does not make use of within category information. Alternative methods of handling continuous predictor variables such as fractional polynomials (FPs) and restricted cubic splines (RCS) exist. This thesis first investigates the current extent of categorisation in comparison to these alternative methods. The performances of categorisation, linearisation, FPs and RCS approaches are then investigated using novel simulations, assuming a range of plausible scenarios including tick-shaped associations. The simulation starts with continuous outcomes, and then move onto predictive models where the outcome itself is dichotomised into a binary outcome. Finally, a novel application of the four methods is performed using the UK Biobank data – incorporating additional issues of confounding and interaction. This thesis shows that the practice of categorisation is still widely used in epidemiology, whilst alternative methods such as FPs and RCS are not. In addition, this research shows that categorising continuous variable into few categories produce functions with large RMSEs, obscure true relations and have less predictive ability than the linear, FP and RCS models. Finally, this thesis shows that nonlinearity and interaction terms are more easily detected when applying FPs and RCS methods. The thesis concludes by encouraging medical researchers to consider the application of FPs and RCS models in their studies