OR estimating by summary value of case group and true OR
This is an example for investigating the moderate effect of gender on the association between exposure and outcome disease.
The p1 to p7 are the population parameters, and the odds ratios in women (ORw) and in men (ORm) are calculated based on them.
If a researcher want to do a case control study, the expectation of simple combined OR [OR(combined), ORc] is calculated based on Equation 2.1-3, and it is controlled by proportion of males in the case group (k1) and in the control group (k2).
The ORλ is calculated based on the Equation 2.1-5 using k1 to replace m.
Under two our setting assumptions: (1) rare disease, and (2) independent, the log(ORc) and log(ORλ) will be very close.
Introduction of assumptions:
(1) rare disease
p1, p2, p3, p4 are very rare. For example, p1, p2, p3 and p4 are 0.0001, 0.0001, 0.0002 and 0.0006 (Default).
(2) independent
There is no association between the factor of interest and the major independent variable. For example, gender and exposure are independent, and p6 is equal to p7 (Default).