Efficient translational rehabilitation randomised controlled trial designs using disease progress modelling and trial simulation

Abstract

Given the challenges inherent in randomised trials of rehabilitation interventions, methods are required to increase trial efficiency and information yield. This paper discusses, in a non-technical manner, a class of statistical models that is particularly suited to the task of detecting potential treatment effects against a background of spontaneous change.

Keywords:

• Disease progress modelling
• Non-linear mixed effects modelling
• Trial simulation
• Trial design

I am very grateful to Nick Holford and Thuy Vu of the University of Auckland for their support in introducing me to these techniques. The dataset used for illustrative purposes was obtained by Cynthia Salorio and Jim Christensen at the Kennedy Krieger Institute, Johns Hopkins School of Medicine, Baltimore MA, USA and is reported more fully in a companion paper (Forsyth, Vu, Solorio, Christensen, & Holford, 2009).

Notes

¹Although I am using language implying pharmacological interventions, the analogy extends to non-pharmacological rehabilitation interventions, where the need to identify “active ingredients” and to quantify “dose” are important issues in their own right.

²Although mixed effect models are well suited to modelling change over time they are not limited to this. For example, the application of these techniques in the pharmacology sector relates to the modelling of pharmacokinetics and pharmacodynamics: drug effects are modelled as a mixed-effect function of administered dose, where the fixed effects might include body weight, renal function and other factors that influence circulating drug levels.

³“Linear” has a specific mathematical meaning here of a function the form y = a₀ + a₁x + a₂x² + … + a_nxⁿ. Linear functions thus include the straight-line function y = a₀ + a₁x as well as quadratic and other polynomial functions. It is typically possible to approximate a non-linear function with a linear polynomial function to an arbitrary degree of accuracy over a defined range, but the approximation will usually break down badly outside that range.

⁴An alternative means of generating pseudoreplicate datasets in this situation is to use an advanced empirical sampling technique known as Markov Chain Monte Carlo (MCMC) sampling which is available in R.