# Fictional Scenario To Test Your Knowledge of Gene-Environment Interaction: Rheumatoid Arthritis, Herbal Supplements and Fictitious Rheumatoid Arthritis Gene Answers

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#### Question 1

Based on this study, what is the magnitude of the overall association between C677T and rheumatoid arthritis? between ImmuneBlast and rheumatoid arthritis? Show calculations in terms of relative risks and population attributable fractions.

Construct Two by Two tables for genotype and exposure as follows

Genotype Case Control
-
20
60
C707T
80
40

Odds Ratio (OR) = 6 (estimates relative risk)
Population Attributable Fraction = (Miettinen formula)=(Frequency of gene variant among cases) * ([OR-1]/OR)=0.8 * 5/6 = 0.66

Exposure Case Control
No
20
50
Yes
80
50

Odds Ratio= 4
Population Attributable Fraction 0.8 * ¾=0.60

#### Question 2

Is there evidence of gene-environment interaction in this case-control study? Compute the effects of the exposure alone, the genotype alone and the combination. Show calculations in terms of relative risks and population attributable fractions.

Construct a Two by Four table as follows:

Genotype Exposure Case Control OR PAF
- -
10
30
Ref
Ref
- +
10
30
1.0
0
+ -
10
20
1.5
3.3%
+ +
70
20
10.5
63.3%

OR with exposure alone is 1.0, genotype alone is 1.5 and both is 10.5

Based on the above data. It looks like the combined effect of the genotype and exposure is more than multiplicative (10.5 > 1.0 + 1.5 –1), strongly suggesting evidence of gene-environment interaction. Furthermore, it does look like the genotype alone or the exposure alone don't really increase the risk significantly and that most if not all their main effects are due to their interaction (type I interaction). IN fact, it looks like the combination of gene variant and the exposure may account for about 63% cases in this population.

#### Question 3

Discuss the etiologic inference of the authors in terms of causal criteria including comment on study design and analysis.

The following findings enhance biological plausibility for causal association

• Strong relative risks and also high attributable fraction
• Biologic plausibility (yes, strong because of the biology and finding interactions)
• Needs replication in other studies (especially population-based)

Study design: Cases highly selected may not reflect general population of cases and controls may not be comparable to cases (possible selection bias). Because of frequency-matching, we may also need matched analysis (not done here). No adjustment for potential confounding variables (diet, lifestyle, etc.)

#### Question 4

If the authors did not have a control group, what kind of inference on gene-environment interaction could they obtain from a case only analysis? Is this a valid result? Discuss pros and cons of this approach compared to a standard case-control analysis.

Case-only analysis

Genotype + 70 10 10 10
OR case-only is 7
• This is an index of interaction on a multiplicative scale and suggests that the combined effects of exposure and genotype is more than multiplicative.
• This is a valid result only if we assume independence between genotype and exposure in the population. We can test this by repeating same analysis among controls.

Control-only analysis

Genotype + 20 30 20 30

OR case-only is 1

This indicates that there is no association between exposure and genotype in the general population which make results of case-only analysis valid.

Case only analysis:
Pros: quick and efficient, improves statistical power
Cons:
- needs independence assumption and cannot estimate separate effects of exposures and genotype, only the existence of their interaction.
- Also can only test for interaction on a multiplicative scale
- Good screening tool

#### Question 5

Can you comment on the recommendations of the authors to test the general population for the RA gene before taking ImmuneBlast?