Left ventricular mass (LVM) is an important risk factor for subsequent cardiovascular disease. A study is proposed to assess the relationship be- tween childhood blood pressure levels and LVM in children as determined from echocardiograms. The goal is to stratify children into a normal bp group (< 80th percentile for their age, gender, and height) and an ele- vated 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 demonstrate 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 1 ID Baseline LVM (g) 1 139 2 134 3 86 4-year LVM (g) 163 126 142 Change (g) 24 -8 56 4 98 96 -2 5 78 6 90 7 102 8 73 82 9 9 93 77 -16 10 162 Mean 105.5 172 10 124.4 18.9 35.2 26.4 sd 29.4 Table 1: Pilot data on left ventricular mass (a)  What test can be used to assess if there is a change in mean LVM over 4 years? (b)  Implement the test in (a) and provide a two-tailed p-value. (c)  Provide a 95% CI for the change in LVM over 4 years. (d)  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 twosided test with α = 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.

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Left ventricular mass (LVM) is an important risk factor for subsequent cardiovascular disease. A study is proposed to assess the relationship be- tween childhood blood pressure levels and LVM in children as determined from echocardiograms. The goal is to stratify children into a normal bp group (< 80th percentile for their age, gender, and height) and an ele- vated 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 demonstrate 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 1

ID Baseline LVM (g) 1 139
2 134
3 86

4-year LVM (g) 163
126
142

Change (g) 24
-8
56

4 98 96 -2

5 78
6 90
7 102
8 73 82 9 9 93 77 -16

10 162 Mean 105.5

172 10 124.4 18.9 35.2 26.4

sd 29.4
Table 1: Pilot data on left ventricular mass

  1. (a)  What test can be used to assess if there is a change in mean LVM over 4 years?

  2. (b)  Implement the test in (a) and provide a two-tailed p-value.

  3. (c)  Provide a 95% CI for the change in LVM over 4 years.

  4. (d)  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 twosided test with α = 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.

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