Source: Statist. Sci. Volume 12, Number 3
(1997), 185-194.
Some analyses of longitudinal blood pressure data have focused on
the question of whether a current value of blood pressure is predictive of
subsequent rate of change. A positive correlation between blood pressure values
at the beginning of a longitudinal study and rate of change over the course of
the study has been found in studies of adults. Negative correlation, however,
has been found in a study of children. These studies, either implicitly or
explicitly, rely on linear growth curve models in which subjects' blood
pressure observations are assumed to follow simple linear regression models
with slopes and intercepts varying among subjects, but with the slopes constant
over time.
Our analysis of a longitudinal data set of 2,203 measurements of
systolic blood pressure from 216 children also provided a negative estimate of
the correlation. However, smoothed plots of cross products of residuals
suggested that an alternative random effects model, in which rate of change of
systolic blood pressure is not treated as constant over time, might better fit
the data. It is possible that the negative estimates of the correlation found
in children's blood pressure data are an artifact of assuming a constant rate
of change when the data actually follow the alternative model. It is shown that
the expected result of fitting the linear growth curve model to data that
follow the alternative model is an apparent negative correlation between slope
and intercept. In the data, the observed estimates of the parameters of the
linear growth curve model are consistent with the observed estimates of the
parameters of the alternative model.
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