1. Joni’s Section
01/26/10

2. When focusing on causal parameters in an exposed source population (e
When focusing on causal parameters in an exposed source population (e.g., RR1 = R1/R1 = a/a0), there is no confounding if the total proportion of Type 1 and Type 3 individuals is the same in exposed and unexposed groups.
In this situation, the risk of disease in the unexposed group (R0) is equal to what the risk would have been in the exposed group in the absence of exposure (R1).

3. Table 4-1 p 60 ME2 (Rothman and Greenland)
Table 4-1 p 60 ME2 (Rothman and Greenland). An elementary model of causal types and their distribution in two distinct cohorts
1=gets disease, 0=does not get disease
Response under
Cohort 1
Cohort 0
Causal Type
Exposure
Non-exposure
(Exposed)
(Unexposed)
1) Doomed 1 p1 q1
2) Causative p2 q2
3) Preventive p3 q3
4) Immune p4 q4
Causal risk difference: (p1+p2) - (q1+q3)
get disease in cohort 1(=exposed) get disease in cohort 0 (=unexposed)
Causal risk ratio: (p1+p2)
(q1+q3)
Causal odds ratio: (p1+p2) / (p3+p4)
(q1+q3) / (q2+q4)
NOTE: if q1 + q3  p1 + p3 then q1+q3 cannot be exchanged or substituted for p1+p3 the association measure (risk comparisons) are confounded
by the discrepancy between these two quantities
- Now we have and exposed and unexposed cohort

6. Cohort of 2000 men
Genotype the causes headaches at a rate of:
0.2 cases per Person-Yr (PY) in those w/out G
2 cases per PY in those with G
Imagine scenario where entire cohort experiences same chemical exposure that increase rates
0.4 cases per Person-Yr (PY) in those w/out G
4 cases per PY in those with G

7. Why Non-Collapsibility?
Chemical Exposure and Genotype affect both the numerator and denominator of the rates
Chemical Exposure affected how accrued Person Time
Person time is an outcome. When the exposure and covariate (Here Genotype) affect the outcome under study or competing risk, they will alter person-time distribution

8. Key Points Non-collapsibility of rate ratio :
Can happen with or without confounding
Can occur when Outcome is rare
Ex. When competing risks are present
Person time is not affected when everyone remains at risk throughout follow-up