Modeling a cross-sectional response variable with longitudinal predictors: an example of pulse pressure and pulse wave velocity

We wish to model pulse wave velocity (PWV) as a function of longitudinal measurements of pulse pressure (PP) at the same and prior visits at which the PWV is measured. A number of approaches are compared. First, we use the PP at the same visit as the PWV in a linear regression model. In addition, we use the average of all available PPs as the explanatory variable in a linear regression model. Next, a two-stage process is applied. The longitudinal PP is modeled using a linear mixed-effects model. This modeled PP is used in the regression model to describe PWV. An approach for using the longitudinal PP data is to obtain a measure of the cumulative burden, the area under the PP curve. This area under the curve is used as an explanatory variable to model PWV. Finally, a joint Bayesian model is constructed similar to the two-stage model.