Question

A study was conducted to evaluate the relationship between artificial sweeteners and bladder cancer. 3,000 cases and 3,000 controls were enrolled in the study. Among the cases, 1293 had used artificial sweeteners in the past, while 1707 had never used artificial sweeteners. Of the controls, 855 had used sweeteners and 2145 had not.

a.       What is the exposure and what is the disease?

b.       Set up the two by two table for these data with labels for exposures and disease status.

c.       Which measure of association/comparison should we use to assess the strength of the relationship between exposure and disease?

d.       Calculate the correct measure and show your work.

e.       How do we interpret this effect estimate?

Answer 1

a) Exposure: The person's who uses artificial sweeteners
Disease: Bladder cancer.

c) We use $x^{2}$ - test for independence of attribute to measure the relationship between and disease.

d) Expected frequency: $E_{i j}$ $$ \begin{aligned} \therefore E_{11}=& \frac{2147 \times 3000}{6000} \\ =& 1073.5 \end{aligned} $$ Similarly, core compute all expected frequencies $\therefore$ Expected Frequency table:

Hypothesis:

Ho: The attributes disease $\$$ exposure are independent of each other.

H): The given attributes are not independent

Degrees of freedom $=(2-1)(2-1)=1$

Since calculated $x^{2}$ is greater than the critical value, we reject Ho. And conclude that disease depends upon exposure to artificial sweeteners.