Question

Randomly sample 50% of cases from cohort study C and place them in the cells of Table 4 below. If the sample of cases (or controls) is random it will maintain the same ratio of exposed to unexposed among cases and non-cases that is present in cohort C. Next, determine how many controls will be required in table 4 in order to have 1 control for each case. There are two ways to sample the required number of controls from cohort C. First sample “controls 1” from all persons who entered the cohort (column 2 of Table 3), prior to knowledge of disease status. Then, sample “controls 2” from all persons who did not develop the disease during follow-up (Column 4 of Table 3). Although, it’s not realistic, retain two decimal places in the numbers of controls. As your samples of controls must also be random, they should also maintain the same ratio of exposed to unexposed that is present among potential controls in Cohort C.

Table 3. (4 points) Cohort Study C. Provide an answer for all 9 of the shaded cells. Make the calculation and show an appropriate number of decimal places. For example, 100/500 is not an acceptable answer, calculate the final number. Odds of disease = individuals with disease/individuals without disease.
	Total	Disease	Disease	Risk of	Odds of
		Present	Absent	Disease	Disease
Exposed	1,500	1350	150
Unexposed	28,500	8550	19,950
Total	30,000	9900	20,100
Risk Ratio =			Odds ratio =
Population Attributable Risk (PAR) use formula for cohort =

Table 4. (5 points) Sampling two studies from Cohort C. Provide an answer for all 13 of the shaded cells. Show 2-4 decimal places.
	Cases	Control 1	Control 2
Exposed
Unexposed
Total
CC Study 1: OR 1 (Control 1) =
CC Study 2: OR 2 (Control 2) =
Study 1: Population Attributable Risk (PAR) using ca/co formula =
Study 2: Population Attributable Risk (PAR), Using ca/co formula =

Answer 1

Answer: ‘Odds of Disease’ is defined as the probability that the disease will occur (p) by the probability that the disease will not occur (q).

Table 3

In exposed case

p = 1350/1500 = 0.90

q = 1 – 0.9 = 0.10

Odds of disease = p/q = 9.00

Risk of disease = 1350/1500 = 0.9

In unexposed case

p = 8550/28500 = 0.30

q = 1 – 0.3 = 0.70

Odds of disease = p/q = 0.43

Risk of disease = 8550/28500 = 0.3

In total cases

p = 9900/30000 = 0.33

q = 1 – 0.33 = 0.67

Odds of disease = p/q = 0.49

Risk of disease = 9900/30000 = 0.33

Odds ratio = {(Exposed and disease present)/(Exposed and disease absent)} / {(Unexposed and   
                        disease present)/(Unexposed and disease absent)}

                   = (1350/150)/(8550/19950) = 9/0.43 = 20.93

Risk ratio is the ratio of cumulative incidence of exposed and non-exposed.

Cumulative incidence of exposed = 1350/1500 = 0.9

Cumulative incidence of unexposed = 8550/28500 = 0.3

Risk ratio = 0.9/0.3 = 3

Proportion of all diseased (p1) = 9900/30000 = 0.33

Proportion of disease in unexposed case (p2) = 8550/28500 = 0.30

Population Attributable Risk (PAR) = 0.33 – 0.30 = 0.03