# Appendix D: Method for Determining the Confidence Interval Around the Odds Ratio

An approximate 95% confidence interval (*CI*) around the point estimate of the
odds ratio (*OR*) for an unmatched case–control
study can be calculated using the following formula:

where exp is the base of the natural logarithm raised to the
quantity in the brackets, and *A, B, C,* and *D* represent the numerical entries into
the summary format in Table 9–4. This confidence interval
is approximate because it is based on a computational short-cut
to estimating the variance of the natural logarithm of the *OR.* For relatively large sample sizes,
this approximation yields confidence bounds that are quite close
to the exact values, which are much more difficult to calculate.

For the data in Table 9–5 relating l-tryptophan
brand use to eosinophilia-myalgia syndrome in an unmatched case–control
study, the 95% *CI* was calculated
as follows:

Similarly, an approximate 95% *CI* around
the point estimate of an *OR* from a
pair-matched case–control study can be calculated using
the following formula:

where exp is the base of the natural logarithm raised to the
quantity in the brackets, and *X* and *Y* represent the numerical entries in
the summary format in Table 9–6.

For the data in Table 9–7 relating l-tryptophan
use to eosinophilia-myalgia syndrome in a hypothetical pair-matched
case–control study, the 95% *CI* was
calculated as follows:

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