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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:

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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.

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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:

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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:

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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.

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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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