Question

1) A group of researchers would like to study the effect of electronic cigarettes (e-cigarettes) use on getting lung cancer. 500 subjects were randomly sampled from e-cigarettes users and 500 subjects were randomly sampled from non-users for monitoring. The incidence of lung cancer for the two groups are reported in the following contingency table.

	Lung Cancer	No Lung Cancer
e-cigarette Users	120	380
Non e-cigarette Users	50	450

Based on this sample, what is an estimated population risk ratio of getting lung cancer between e-cigarette users and non-users (correct to 2 decimal places)?

A) 2.84

B) 0.35

C) Cannot be determined.

D) 2.40

2) A basket consists of 3 red balls and 2 white balls which are identical in all other respects. 3 balls are chosen at random with replacement. Let A be the event of obtaining at least 1 white ball. Let W represent the number of white balls obtained. For example, P(W=1) is the chance of obtaining exactly one white ball. Which of the following is equal to P(A)?
(I)   P(W=1) x P(W=2) x P(W=3)
(II)   1 – P(W=0)

A) Neither (I) nor (II).

B) Only (II).

C) Both (I) and (II).

D) Only (I).

3) A researcher wants to investigate if excessive gaming in adolescents increases the risk of a child having Attention-Deficit/Hyperactivity Disorder (ADHD). A person who spends at least 6 hours on gaming per week is classified as a gamer; otherwise a non-gamer. For simplicity, assume that ADHD can be diagnosed quite accurately. If the researcher wants to do a cohort study, which of the following statements indicate how he should carry out his study?

A) He should randomly sample from “Gamer” and “Non-gamer” populations and compare r(ADHD | Gamer) with r(ADHD | Non-gamer)

B) He should randomly sample from “ADHD” and “no ADHD” populations and compare r(Gamer | ADHD) and r(Gamer | no ADHD).

C) He should randomly sample from “Gamer” and “Non-gamer” populations and compare r(Gamer | ADHD) with r(Non-gamer | ADHD).

D) He should randomly sample from “ADHD” and “no ADHD” populations and compare r(ADHD | Gamer) and r(no ADHD | Gamer).

4) Let E and F be two events in a sample space. Which of the following statements is/are definitely true?   
I) If P(E) + P(F) > 1 then E and F are not mutually exclusive.
II) If E and F are mutually exclusive, then P(E) = P(F) = 0.5

A) Only (II).

B) Neither (I) nor (II).

C) Both (I) and (II).

D) Only (I).

5) Which of the following statements is/are true?
I) Cohort studies have no control group whereas case control studies do.
II) Case control studies are better than cohort studies for rare events/diseases.
A) Only I is true

B) Only II is true.

C) Both I and II are true

D) Neither I nor II are true.

*PLEASE TYPE YOUR ANSWER (NO SCREENSHOTS OR IMAGES). THANK YOU IN ADVANCE

Answer 1

Solution:

Risk ratio is given as as follows:

Where, CI_{​​​​​e} is cumulative incidence in exposed group and CI_{​​​​​u} is cumulative incidence in unexposed grouped.

In our question exposed group is e-cigarette users and unexposed group is non e-cigarette group.

CI_{​​​​​e} = Number of subjects who have the disease in exposed group/total number of subjects in exposed group

Number of subjects who have the disease in exposed group = 120

Total number of subjects in exposed group = 120 + 380 = 500

Hence, CI_{​​​​​e} = 120/500 = 0.24

CI_​​​u = Number of subjects who have the disease in unexposed group/total number of subjects in unexposed group

Number of subjects who have the disease in unexposed group = 50

Total number of subjects in unexposed group = 50+450 = 500

Hence, CI_​​​u = 50/500 = 0.10

Hence, Risk ratio = 0.24/0.10 = 2.40

The estimated value of population risk ratio is 2.40.