Question

Observational studies have suggested that daily intake of Vitamin E is associated with a lower risk of heart disease. Yet, carefully designed double-blind randomized experiments have shown that vitamin E has no effect in reducing the risk of heart disease.

a) For each study (observational and experiment), what are the response, explanatory variables, and treatments?
b) Outline the design of each study on a diagram
c) For the observational study, identify a lurking variable that may explain the association between Vitamin E intake and risk of heart disease? Explain why your answer satisfies the definition of a lurking variable. (Hint: What can you say about people who regularly take Vitamin E supplements?)

Answer 1

a) For the observational study:

- Response variable: Risk of heart disease.

- Explanatory variable: Daily intake of Vitamin E.

- Treatment: None, as the study is observational and does not involve any intervention.

For the double-blind randomized experiment:

- Response variable: Risk of heart disease.

- Explanatory variable: Assignment to the treatment group (Vitamin E supplementation) or control group (placebo).

- Treatment: Daily intake of Vitamin E (treatment group) or placebo (control group).

b) Design of the observational study:

Vitamin E intake

|

v

Risk of heart disease

b) Design of the double-blind randomized experiment:

Random Assignment

|

v

Treatment Group (Vitamin E) Control Group (Placebo)

| |

v v

Risk of heart disease Risk of heart disease

c) In the observational study, a lurking variable that may explain the association between Vitamin E intake and the risk of heart disease could be the participants' overall health consciousness or lifestyle. People who regularly take Vitamin E supplements may generally exhibit healthier behaviors, such as maintaining a balanced diet, exercising regularly, or following other healthy habits. These lifestyle factors could independently contribute to a lower risk of heart disease, making it appear as if Vitamin E intake is the causal factor, when in fact, it might not be.

This lurking variable satisfies the definition because it confounds the association between Vitamin E intake and the risk of heart disease. It is a variable that is associated with both the explanatory variable (Vitamin E intake) and the response variable (risk of heart disease) but is not accounted for in the analysis. Hence, it creates an alternative explanation for the observed association, potentially leading to an incorrect conclusion about the true effect of Vitamin E on heart disease risk.