Question

Table 3:

	Total	Disease	Disease	Risk of	Odds of
		Present	Absent	Disease	Disease
Exposed	1,500	1350	150	0.9000	9.0000
Unexposed	28,500	8550	19,950	0.3000	0.4286
Total	30,000	9900	20,100	0.3300	0.4925
Risk Ratio =3.00			Odds ratio =21.00
Population Attributable Risk (PAR) use formula for cohort =3%

Provide an answer for all of the shaded cells. 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. (Hint: When you are selecting your controls, the key wording in the question is "if the sample of cases (or controls) is random it will maintain the same ratio of exposed to unexposed among the cases and non-cases that is present in cohort C". This gives you the information to create the ratios required to sample your controls for both "Control 1" and "Control 2". When you are sampling those groups, make sure you maintain the same ratio of exposed and unexposed in your final Table 4 as what you observe in Table 3 for the column you are sampling from. )

Table 4:

	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 exposed 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 case:

• 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

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