Question

Tasmanian researchers conducted a case –control study to investigate the effect of dietary fat intake on skin cancer. They hypothesised that people whose dietary fat intake is low will be more susceptible to skin cancer. The study compared 500 cases of melanoma with 500 controls who were randomly selected from the state’s electoral roll. The researchers categorised the dietary fat intake into three categories High, Moderate and Low. They found that among skin cancer patients 150 were classified at the low and 80 at the high dietary fat intake whereas among control 130 were at the low and 100 were at the high.   

1. Build a table to summarise the data above which will help you estimate the association between dietary fat intake and Skin cancer
2. , pay attention to headings of columns and rows [4 points]

3. Calculate the appropriate measure of relative risk (RR) of having melanoma between those consuming low fat intake versus high fat intake; calculate the appropriated measure of RR of having melanoma between those consuming medium to high fat intake and explain in words the meaning of what you found [4 points].

4. Calculate the percent attributable risk due to exposure to low-dietary fat intake on Melanoma and explain in one or two sentences the meaning of your findings [4 points]

5. Calculated the population attributable risk of low-fat intake on melanoma and explain in words the meaning of such finding [4 points]

e) What do you think about the conclusions of the PAR regarding exposure to low fat diet to reduce melanoma? (no more than 3-4 sentences) [4 points}

Answer 1

Hypothesis - Low fat (exposure) intake leads to skin cancer (outcome).

The date is given can be tabulated as follows

	Case	Control	Total
High	80	100	180
Medium	270	270	540
Low	150	130	280
Total	500	500	1000

Answer a) part 1: The relative risk of developing melanoma in a patient with low fat intake vs high fat can be calculated as follows:

2 x 2 table

	Case (Melanoma)	Control	Total
low ( exposed)	(a)150	(b)130	(a+b)280
High (non-exposed)	(c)80	(d)100	(c +d)180
Total	(a+c) 230	(b+d) 230	(a+b+c+d)460

the formula for relative risk = it is the ratio of the probability of an outcome in the exposed group to the probability of an outcome in the non-exposed group.

therefore relative risk = [a/(a+b)] / [c/(c+d)]

= [150 / ( 150 + 130)] / [ 80 / ( 80 + 100)]

= [ 150 / 280] / [80 / 180 ]

=0.53 / 0.44

=1.2

Interpretation:

• If relative risk = 1 - Exposure doesn't affect the outcome
• If relative risk < 1 - the risk of outcome is decreased by exposure
• If relative risk > 1 - the risk of outcome is increased by exposure

As in this case, the relative risk is > 1

Interpretation: The risk of developing melanoma is increased by exposure to low fat intake.

Answer a) part 2: The relative risk of developing melanoma in a patient with medium fat intake vs high fat intake can be calculated as follows:

2 x 2 table

	Case	Control	Total
Medium (exposed)	(a)270	(b)270	(a+b)540
High(non-exposed)	(c)80	(d)100	(c+d)180
Total	(a+c)350	(b+d)370	(a+b+c+d)

the formula for relative risk = it is the ratio of the probability of an outcome in the exposed group to the probability of an outcome in the non-exposed group.

therefore relative risk = [a/(a+b)] / [c/(c+d)]

= [270 / (270+270)] / [80 / (80 + 100)]

=[270 / 540 ] / [80 / 180]

= 0.5 / 0.4

= 1.2

Interpretation:

• If relative risk = 1 - Exposure doesn't affect the outcome
• If relative risk < 1 - the risk of outcome is decreased by exposure
• If relative risk > 1 - the risk of outcome is increased by exposure

As in this case, the relative risk is > 1

Interpretation: The risk of developing melanoma is increased on exposure to medium fat intake

a) The attributable risk percentage due to exposure to low fat on Melanoma can be calculated as follows

Attributable risk percentage allows determining how much of the outcome in the exposed group is due to the exposure.

2 x 2 table

	Case (Melanoma)	Control	Total
low ( exposed)	(a)150	(b)130	(a+b)280
High (non-exposed)	(c)80	(d)100	(c +d)180
Total	(a+c) 230	(b+d) 230	(a+b+c+d)460

The formula for attributable risk percentage: it is the difference in the disease in the exposed and the non-exposed

attributable risk percentage : Incidence of the outcome in the exposed group - Incidence of the outcome in the non exposed group / Incidence of the outcome in the outcome group

[a/(a+b)] - [c/(c+d)] / [a/(a+b)]

= [150 / (150 + 130)] - [ 80 / (80 + 100)] / [150/ (150 + 30)]

=[150/280] - [80 / 180] / [150/280]

={0.53 - 0.44} */ 0.53

=0.09 / 0.53

= 0.16

attributable risk percentage = 16 %

Interpretation - 16 % of the melanoma in the exposed group is due to the exposure to low dietary fats. By reducing or eliminating low dietary fats from the diet 16% of melanoma can be prevented

Population attributable risk of low fat intake on melanoma can be calculated as follows

2 x 2 table

	Case (Melanoma)	Control	Total
low ( exposed)	(a)150	(b)130	(a+b)280
High (non-exposed)	(c)80	(d)100	(c +d)180
Total	(a+c) 230	(b+d) 230	(a+b+c+d)460

First step - We will need to calculate the odd ratio

The formula for odds ratio is = it is the ratio of odds of exposure in the cases to the odds of exposure in the control

odds ratio = (a/c) / (b/d)

odds ratio = a * d / b *c

= 150 * 100 / 80 *130

= 15000 / 10400

=1.44

Odds ratio (OR) = 1.44

The formula for population attributable risk for case-control study =

= [(b/b+d) * (OR - 1)] / [(b/b+d]) * (OR - 1) + 1] * 100

= [130 / ( 130 + 100) * (1.44 - 1)] / [130 / ( 130 + 100) * (1.44 - 1) + 1] * 100

= [0.56 * 0.44] / [(0.56* 0.44) + 1] * 100

=0.24 / 1.24 * 100

=0.19 * 100

=19 %

• 19 % of the melanoma can be attributed to low dietary fat intake
• 19 % of the melanoma cases could be prevented of low dietary fat intake could be eliminated.