Question 1
A.
Expected OR (multiplicative) = (1.89*3.44) = 6.50
Expected OR (additive) = (1.89+3.44) - 1 = 4.33
B.
There is effect modification on the multiplicative scale, since the observed OR (4.31) is different to the expected OR (6.51). Antagonism, because the observed is less than the expected.
C.
There is no evidence of effect modification on the additive scale, since our observed OR (4.31) is almost exactly the same as the expected OR (4.33).
Question 2
A.
OR = ad/bc = (689*714)/(360*311) = 4.39
Individuals who developed pancreatic cancer had 4.39 times the odds of drinking soda compared to individuals who did not develop pancreatic cancer.
B.
Smokers: Non-smokers:
OR = (660*46)/(264*110) = 1.05 OR = (29*668)/(96*201) = 1.00
Among both smokers and non-smokers, the odds of pancreatic cancer among soda drinkers is at or close to an OR of 1 compared to non-soda drinkers. In other words, we no longer observe an association between soda drinking and pancreatic cancer after stratifying by smoking.
C.
Yes, smoking does confound the effect of soda drinking on pancreatic cancer. We see that the crude estimate (4.39) of the relationship of soda consumption and pancreatic cancer is different from the stratum-specific estimates (1.05 and 1.00) after we adjust for smoking status. We indicate a bidirectional arrow between smoking and soda drinking because it’s not clear whether soda drinkers are more likely to smoke or vice versa. Note, because there is a bidirectional arrow, this is not a DAG.
D.
All participants
| ||
Cancer
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No Cancer
| |
Smokers
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770
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310
|
Nonsmokers
|
230
|
764
|
OR = (770*764)/(310*230) = 8.25
E.
Soda drinkers
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Soda non-drinkers
| |||||
Cancer
|
No Cancer
|
Cancer
|
No Cancer
| |||
Smokers
|
660
|
264
|
Smokers
|
110
|
46
| |
Nonsmokers
|
29
|
96
|
Nonsmokers
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201
|
668
| |
Soda drinkers: Soda non-drinkers:
OR = (660*96)/(264*29) = 8.28 OR = (110*668)/(46*201) = 7.95
No, soda consumption does not confound the association between smoking and pancreatic cancer. After stratifying the data by soda drinking status, we see that the stratified estimates are similar to each other and the crude estimate.
Question 3
A.
Risk = 238/400 = 0.595 x 100 = 59.5%
B.
Risk = 14/415 = 0.034 x 100 = 3.4%
C.
RR = 0.595/0.034 = 17.5
D.
Risk of asthma among youth exposed to high air pollution is 17.5 times the risk of asthma among youth exposed to low air pollution in Los Angeles during this study period.
E.
RR = (174/309) / (11/362) = 18.5 RR = (64/91) / (3/53) = 12.3
F.
Among Los Angeles youth who smoke, the risk of asthma among those who are exposed to high levels of pollution is 18.5 times the risk of developing asthma among youth with low levels of exposure to pollution in this study population.
G.
Among Los Angeles youth who do not smoke, the risk of asthma among those who are exposed to high levels of pollution is 12.3 times the risk of developing asthma among youth with low levels of exposure to pollution in this study population.
H.
The chi-squared test of homogeneity (χ2) assesses whether the differences in the stratum-specific risk ratios are due only to random variation.
I.
The unadjusted RR for asthma among people with high air pollution is high (RR=17.5). After stratifying the data for smoking, we find that air pollution is still strongly associated with the development of asthma. Stratification suggests that the risk of asthma among smokers (RR=18.5) is greater than the risk of asthma among non-smokers (RR=12.3), suggesting that there is effect modification by smoking.
Question 4
a.
Cumulative incidence ratio = (250/500)/(500/1500) = 0.5/0.33 = 1.5
Cumulative incidence difference = (250/500) - (500/1500) = 0.5 – 0.33 = 0.17
b.
Genotype 1:
CIR = (90/280)/(217/700) = 0.321/0.310 = 1.04
CID = (90/280) - (217/700) = 0.321 – 0.310 = 0.011
Genotype 2:
CIR = (170/220)/(300/800) = 0.773/0.375 = 2.06
CID = (170/220) - (300/800) = 0.773 – 0.375 = 0.40
c.
The association is modified by genotype, whether measured via the risk ratio or the risk difference. Among those with Genotype 2, there is a positive association between SSB consumption and obesity (risk ratio = 2.06, risk difference = 0.40). Among those with Genotype 1, there is essentially no evidence of association between SSB consumption and obesity (risk ratio = 1.04, risk difference = 0.011). Therefore, there is evidence of effect modification between SSB and genotype on both the risk difference (additive) and risk ratio (multiplicative) scale.
d.
Genotype | SSB Consumption | Observed cumulative incidence | Expected cumulative incidence(show calculation) |
1 | No | 217/700 = 0.31 | --- |
2 | No | 300/800 = 0.38 | --- |
1 | Yes | 90/280 = 0.32 | --- |
2 | Yes | 170/220 = 0.77 | (0.38 + 0.32) - 0.31 = 0.39 |
e.
The observed cumulative incidence is larger than the expected cumulative incidence. This is evidence of synergy (gene-environment interaction) and supports the estimates above that show effect modification between genotype and SSB consumption on the additive scale.
f.
Stratum-specific associations would be presented, because the effect of SSB consumption on obesity varies across variants of the OBCT gene. This is evidence of effect modification, indicating OBCT genotype modified the association between SSB and obesity. We are interested in the difference between the stratum-specific associations, so we would not mask that by presenting a crude or adjusted association).
Question 5
A.
Age is associated with the exposure (oral contraceptive use is inversely associated with age). Age is associated with the outcome (age is positively associated with stroke).
B.
Crude odds ratio = ad/bc
Crude odds ratio = (258*2877)/(2049*279) = 1.30
C.
Odds ratio (strata) = ad/bc
Odds ratio (age 20-29) = (39*855)/(153*138) = 1.58
Odds ratio (age 30-39) = (93*1389)/(903*90) =1.59
Odds ratio (age 40-49) = (126*633)/(993*51) = 1.57
D.
No, age does not modify the effect of OC use on having a stroke because the stratum-specific odds ratios are almost the same—there is no real difference in effect by age.
E.
Yes. When we stratified by age, we found that the adjusted odds ratios were similar and were appreciably different than the crude odds ratio (~1.58 vs. 1.30).
F.
When the crude and adjusted measures are different, we report the adjusted odds ratio.
Question 6
|
ORcrude
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ORmen
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ORwomen
|
Effect
Modification? (Yes/No)
|
Confounding?
(Yes/No/Maybe)
|
Measure
Reported (unadjusted, adjusted, or stratum specific OR)
|
|
3.0
|
3.0
|
3.0
|
N
|
N
|
Unadjusted
OR
|
|
3.4
|
2.0
|
2.0
|
N
|
Y
|
Adjusted
OR
|
|
1.0
|
4.0
|
1.75
|
Y
|
Y
|
Stratum
Specific OR
|
|
0.7
|
1.2
|
1.1
|
N
|
Y
|
Adjusted
OR
|
|
4.3
|
5.4
|
3.5
|
Y
|
Maybe
|
Stratum
Specific OR
|
Note: Effect modification trumps confounding, so if both are present, do not combine the stratum-specific results.
Question 7
Yes, based on this evidence infant’s HIV status is an effect measure modifier of the relationship between food insecurity and diarrheal illness. If our p-value is lower than the established significance level we have evidence that differences in the stratum-specific estimates of the effect of food insecurity on diarrheal illness are not due to random variation. The relationship between food insecurity and diarrheal illness varies by infant’s HIV status.
Question 8
Additive
Relative
Additive (and also relative)
Relative
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