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approach, the odds ratio computation estimates the relative rate (IDR) on the assumption that the
IDR does not change during the follow-up period (assuming matching of controls to cases by time)
(see Greenland and Thomas, 1982 and Rodrigues and Kirkwood, 1990). This study design has been
referred to as a "density case-control study" (Hogue et al., 1983 referred to this design as a "caseexposure
study"; however, Rodrigues and Kirkwood (1990) use that term for the third design
[method (c)]). If a participant selected as a control later develops the disease, then that participant is
also counted as a case; his/her data are used both as a case and as a control (his/her data appear in
both categories).
The third design [method (c)] has been called "case-base" and "case-cohort" (also "case-exposure" –
see Rodrigues and Kirkwood for citations). When such a case-control study is carried out within a
fixed cohort, the odds ratio estimates the risk ratio with no rare disease assumption.
Rodrigues and Kirkwood show that the three ratio measures of association – CIR, IDR, and OR –
can each be expressed so that its numerator is the odds of exposure in cases. Thus, all that differs
are the denominators, and the three different approaches to sampling controls provide estimates for
the respective denominators.
Odds of exposure given disease a / b
a. ORe = Exposure odds ratio = —————————————— = ———
Odds of exposure given non-diseased c / d
(c / d is the odds of exposure in non-cases [never-cases at end of ascertainment period])
ID1 a / py1 a / b
b. IDR = —— = ——— = ————
ID0 b / py0 py1 / py0
(py1 / py0 is ratio of exposed to unexposed person-years, from density sampling)
CI1 a / n1 a / b
c. CIR = —— = ——— = ————
CI0 b / n0 n1 / n0
(n1 / n0 is the odds of exposure in the source population for the cases at the start of the
follow-up)
where "a" = exposed cases, "b" = unexposed cases, and "n" and "py" represent persons and personyears
for exposed (subscript 1) and unexposed (subscript 0).
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www.sph.unc.edu/courses/EPID168, © Victor J. Schoenbach 1999 8. Analytic study designs - 243
rev. 9/6/1999, 10/7/1999, 12/17/1999