Estimation of the maximum flow-mediated brachial artery response using local regression methods

We consider methods for estimating the maximum from a sequence of measurements of flow-mediated diameter of the brachial artery. Flow-mediated vasodilation (FMD) is represented using the maximum change from a baseline diameter measurement after the release of a blood pressure cuff that has been inflated to reduce flow in the brachial artery. The influence of the measurement error on the maximum diameter from raw data can lead to overestimation of the average maximum change from the baseline for a sample of individuals. Nonparametric regression models provide a potential means for dealing with this problem. When using this approach, it is necessary to make a judicious choice of regression methods and smoothing parameters to avoid overestimation or underestimation of FMD. This study presents results from simulation studies using kernel-based local linear regression methods that characterize the relationship between the measurement error, smoothing and bias in estimates of FMD. Comparisons between fixed or constant smoothing and automated smoothing parameter selection using the generalized cross validation (GCV) statistic are made, and it is shown that GCV-optimized smoothing may over-smooth or under-smooth depending on the heart rate, measurement error and measurement frequency. We also present an example using measured data from the Buffalo Cardio-Metabolic Occupational Police Stress (BCOPS) pilot study. In this example, smoothing resulted in lower estimates of FMD and there was no clear evidence of an optimal smoothing level. The choice to use smoothing and the appropriate smoothing level to use may depend on the application.