| With medical devices to measure subclinical disease, there is often a baseline measurement, then a perturbation (such as occluding blood flow), followed by a dense series of measurements taken over a period of time (e.g. for S minutes). In this dissertation, I explore statistical issues in modeling this type of data. Features of the response time-course are identified and statistical methods are described to estimate values of those features for individuals. The maximum value and time to maximum are estimated using two methods: binning and a locally weighted regression method (Loess). Based on six representative response curves, simulations are performed in which the residual error structure is altered. I compare performance of binning and Loess estimates of the maximum and time to maximum.;Of interest are the change and percent change from baseline when pre- and postmeasurements are made. Researchers commonly use OLS regression (OLS) on percent change variables versus baseline; sometimes this violates the assumption of homoscedasticity. Simulations are performed to compare several regression methods to OLS, including WLS regression, as well as unweighted and weighted non-linear regression. If the pre- and post-measurements are highly correlated or linearly related, percent change will be a function of pre-measurement values.;Data collected from brachial reactivity studies at the Framingham Heart Study is used as an example throughout this dissertation. Flow-mediated dilation (FMD%), a percent change variable, represents the relative dilation of the brachial artery from baseline and is the primary outcome. Modeling FMD% with OLS violates the assumption of homoscedasticity and there is a curvilinear relationship between FMD% and baseline. This warrants the use of more advanced statistical methods such as weighted regression or non-linear models. Baseline and maximum value are extremely highly correlated (r > 0.983) across subsets such as men/women, smokers/non-smokers, and obese/non-obese. A non-linear relationship is produced solely due to the computation of percent change and this causes the correlation of percent change with baseline to be dramatically lower and negative (r = -0.314). I explore this circumstance in other datasets and discuss the implications of calculating percent change. |
