5. (15 points) In an experiment examining the impact of drug type and dose on ch

Question

5. (15 points) In an experiment examining the impact of drug type and dose on cholesterol levels, 100 subjects were randomly assigned to one of four groups: low-dose Lipitor, high-dose Lipitor, low-dose Zocor, or high-dose Zocor. After three months of treatment cholesterol levels were measured on each subject. The three profile plots in Figure 2 represent possible effects due to dose and drug that the experimenters could see in their experiment. Figure 2: Profile Plots for Problem 4 (a) Which of these plots corresponds to an interaction between dose and drug? (b) Describe the effect displayed in the bottom plot? (c) How would a profile plot look in which there is no drug nor dose effect?

Explanation / Answer

(a)

The plots 1 (top left) and 3 (bottom) are non - intersecting parallel lines.

In plot 1 - The mean cholestrol level is higher for drug Lipitor than the drug Zocor at both the low and high doses and for both the drugs, the mean cholestrol level is lower for high dose than low dose and the difference in the mean cholestrol levels at high and low doses of the two drugs are same. So, there is no intercation effect between dose and drug.

In plot 3 - The cholestrol level is lower for drug Lipitor than the drug Zocor at both the low and high doses and for both the drugs, the cholestrol level is higher for high dose than low dose and the difference in the mean cholestrol levels at high and low doses of the two drugs are same. So, there is no intercation effect between dose and drug.

However in plot 2 (top right),

The cholestrol level is lower for drug Lipitor than the drug Zocor at both the low and high doses and for both the drugs, the cholestrol level is higher for high dose than low dose but the difference in the mean cholestrol levels at high and low doses of the two drugs are not same The difference in the mean cholestrol levels between two drugs is gigher for high dose than at low dose. So, there is an intercation effect between dose and drug.

Thus, profile plot 2 corresponds to an interaction between dose and drug.

(b)

In the bottom plot,

The cholestrol level is lower for drug Lipitor than the drug Zocor at both the low and high doses and the difference in the cholestrol levels between the two drugs at high and low doses are the same.

The cholestrol level is higher for high dose than low dose for both the drugs Lipitor and Zocor and the difference in the cholestrol levels between the two doses for both the drugs are the same.

There is no intercation effect between dose and drug as explained earlier and as the profile plots are non-intersecting parallel lines.

Thus, this effect crresponds to drug effect and dose effect wherein high dose leads to a higher mean cholesterol level than low dose and drug Zocor leads to a higher mean cholesterol level than the drug Lipitor.

(c)

If there is no drug effect nor adose effect,

then the profile plot would be horizontal coinciding lines

for which the mean cholestrol levels at high and low doses of both the drugs would be the same.

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