Evaluation of a flexible piecewise linear mixed‐effects model in the analysis of randomized cross‐over trials

Abstract

Cross‐over designs are commonly used in randomized clinical trials to estimate efficacy of a new treatment. They have received a lot of attention, particularly in connection with regulatory requirements for new drugs. The main advantage of using cross‐over designs over conventional parallel designs is increased precision, thanks to within‐subject comparisons. In the statistical literature, more recent developments are discussed in the analysis of cross‐over trials, in particular regarding repeated measures. A piecewise linear model within the framework of mixed effects has been proposed in the analysis of cross‐over trials. In this article, we report on a simulation study comparing performance of a piecewise linear mixed‐effects (PLME) model against two commonly cited models—Grizzle's mixed‐effects (GME) and Jones & Kenward's mixed‐effects (JKME) models—used in the analysis of cross‐over trials. Our simulation study tried to mirror real‐life situation by deriving true underlying parameters from empirical data. The findings from real‐life data confirmed the original hypothesis that high‐dose iodine salt have significantly lowering effect on diastolic blood pressure (DBP). We further sought to evaluate the performance of PLME model against GME and JKME models, within univariate modeling framework through a simulation study mimicking a 2 × 2 cross‐over design. The fixed‐effects, random‐effects and residual error parameters used in the simulation process were estimated from DBP data, using a PLME model. The initial results with full specification of random intercept and slope(s), showed that the univariate PLME model performed better than the GME and JKME models in estimation of variance–covariance matrix (G) governing the random effects, allowing satisfactory model convergence during estimation. When a hierarchical view‐point is adopted, in the sense that outcomes are specified conditionally upon random effects, the variance–covariance matrix of the random effects must be positive‐definite. The PLME model is preferred especially in modeling an increased number of random effects, compared to the GME and JKME models that work equally well with random intercepts only. In some cases, additional random effects could explain much variability in the data, thus improving precision in estimation of the estimands (effect size) parameters.