Chapter 7, Problem 59P

Left ventricular mass (LVM) is an important risk factor for subsequent cardiovascular disease. A study is proposed to assess the relationship between childhood blood pressure levels and LVM in children as determined from echocar-diograms. The goal is to stratify children into a normal bp group (< 80th percentile for their age, gender, and height) and an elevated bp group (> 90th percentile for their age, gender, and height) and compare change in LVM between the 2 groups. Before this can be done, one needs to dem-onstrate that LVM actually changes in children over a 4-year period.

To help plan the main study, a pilot study is conducted where echocardiograms are obtained from 10 random children from the Bogalusa Heart Study at baseline and after 4 years of follow-up. The data are given in Table 7.6.

Since this was a pilot study, the main question of interest is how many subjects would be needed to detect an increase of 10 g in mean LVM over 4 years using a two-sided test with $\alpha$ = 0.05 and power = 80%? Hint: Assume that the estimated variance of change in LVM in the pilot study is the true variance of change in LVM.