A 65-year-old woman with low bone density in 2002 was treated with alendronate t

Question

A 65-year-old woman with low bone density in 2002 was

treated with alendronate through the year 2009. Bone density

was measured irregularly over this period. The results

for change in bone density of the lumbar spine are shown

in Table 11.24.

11.79 What is the estimated rate of increase in bone density

of the lumbar spine per year? What is the standard error

of the estimated rate of increase per year?

11.80 Provide a significance test to assess whether the

mean bone density has changed significantly over time.

Provide a two-tailed p-value.

11.81 The normal change in bone density over time from

age 40 to age 80 is a decrease of 0.15 g/cm2. Does the

rate of change in this woman differ significantly from the

expected age-related change?

Table 11.24 Change in bone density, lumbar

spine, over time

Time from baseline Bone density,

Visit (i), (months) (ti), lumbar spine (g/cm2) (xi)

1, 0, 0.797

2, 8, 0.806

3, 18, 0.817

4, 48, 0.825

5, 64, 0.837

6, 66, 0.841

7, 79, 0.886

8, 92, 0.881

Explanation / Answer

11.79

First we convert the data in years and then perform the regression test.

The regression ouput is as follows,

Thus the estimated rate of increase in bone denisty of the lumbar spine per year is 0.011

The standard error of the estimated rate of increase per year will be 0.002

11.80

The P-value as can be seen from the previous regression output is 0.001

11.81

The change in bone density over 40 years according to the regression model will be 0.011*40 = 0.44 which is significantly different from 0.15 as suggested here.

Visit Months Lumbar Spine Years 1 0 0.797 0.00 2 8 0.806 0.67 3 18 0.817 1.50 4 48 0.825 4.00 5 64 0.837 5.33 6 66 0.841 5.50 7 79 0.886 6.58 8 92 0.881 7.67

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