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 Interpreting results: Attributable risk

## Attributable risk

Here are results from an experimental study:

 Progress No Progress AZT 76 399 Placebo 129 332

In this example, disease progressed in 28% of the placebo-treated patients and in 16% of the AZT-treated subjects.

The difference between proportions (P1-P2), the attributable risk, is 28% - 16% = 12%.

## The Number Needed to Treat (NNT)

The NNT is simply the reciprocal of the difference between the two proportions. In the example above, the difference between the two proportions is 0.12, so the NNT is 1/0.12= 8.3. For every eight people treated with AZT, you'd expect one more to progress than if all were treated with placebo. Especially, when the difference between proportions is a tiny fraction, it can be easier to understand the NNT than the difference between proportions.

In the example above, the drug is used to treat, so the name Number Needed to Treat is apt. In some cases, there is risk or harm, rather than treatment, and the term Number Needed to Harm (NNH) is used. In other nonclinical situations it is not clear which of two outcomes is better, so neither of those phrases really makes sense. Prism always uses the abbreviation NNT, but it is up to you to interpret the value in the context of the study.

## How Prism computes the confidence interval of the attributable risk

On the Options tab of the Contingency table analysis dialog, Prism offers three methods to do the calculation, all explained in Newcombe (1).

Asymptotic with continuity correction. This is the approximate method used by Prism 6 and earlier. We recommend using it only when needed for compatibility.

Newcombe/Wilson score

Newcombe/Wilson score with continuity correction. This is much better than the asymptotic method, so we recommend it. Whether or not you use the continuity correction matters little, but we offer the choice so results will match other programs.

Prism takes the reciprocal of both confidence limits and presents these as the confidence interval of the NNT.

If you choose the asymptotic method  and some of the values are zero, Prism adds 0.5 to all cells before calculating the attributable risk and its confidence interval. Prism shows a floating note on the results page when it does this. In this case, we suggest you switch to the Newcombe/Wilson method.

1. Newcombe, R. G. R. (1998). Interval estimation for the difference between independent proportions: comparison of eleven methods. Statistics in Medicine, 17(8), 873–890.