The methods of Feinleib, Halperin and Garrison (FHG) [1,4] and maximum likelihood (ML)  were used to analyze the relation between initial value and change over time of serial blood pressure measurements among participants in the Framingham Heart Study . Both methods assume a linear trend in expected blood pressure over time, with variation in intercept and slope over individuals. If individual values of the slope and intercept have a joint normal distribution in the population, the coefficient of regression of slope on initial value over individuals will also be linear. It is shown here that the FHG method tends to underestimate that coefficient of regression. Significantly positive regressions were found under the ML approach while the FHG approach failed to claim significance in most of the age-sex groups analyzed. A direct comparison of the efficacies of the two significance tests shows that the asymptotic relative efficiency (ARE) of the FHG and ML procedures is always less than one indicating that the ML test has larger power, i.e. is more likely to detect an association between change and initial value when one exists. These results establish the ML procedure as the preferred method for this problem. Since significantly positive regressions were found in most age groups for both sexes under the ML approach, we infer that there exists some degree of positive association between blood pressure change and initial value. Although the expected increase in the rate of change of systolic blood pressure (SBP) per mmHg increase in initial value is not very great, a younger woman or a middle-aged man with an SBP initial value 20 mmHg higher than the mean initial level of their age-sex group has an expected rate of increase almost twice the mean rate of increase in their groups.
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