Relative risk

Here are results from an experimental study:

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

The relative risk is 16%/28% = 0.57. A subject treated with AZT has 57% the chance of disease progression as a subject treated with placebo. The word “risk” is not always appropriate. Think of the relative risk as being simply the ratio of proportions.

How Prism computes the confidence interval of the relative risk

Prism computes the confidence interval of the relative risk using either the Method of Katz (reference 1, the only method  used by Prism 6 and earlier) or the Koopman asymptotic score (2), which we recommend because it is more accurate. Choose on the Options tab of the Contingency table dialog. Fagerland (3) reviews the various methods available to compute this confidence interval.

If you choose the method of Katz and some of the values are zero, Prism adds 0.5 to all cells before calculating the relative 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 Koopman method.

The order of the two columns matters, the order of rows not so much

Note that it matters how you enter the data. The relative risk would have been different if you had entered the "progress" data in the example above into the second column and the "no progress" data into the first column. For each row, Prism computes the risk by dividing the value in the first column by the sum of the values in the two columns.

After computing the two risks (see prior paragraph), Prism computes the relative risk by dividing the risk in the second row by the risk in the first. But it also reports the reciprocal of that risk. So it really doesn't matter which order you entered the two rows.

References                                                                                        

1.Katz D, Baptista J, Azen SP and Pike MC. Obtaining confidence intervals for the risk ratio in cohort studies. Biometrics 1978; 34: 469–474.

2.Koopman PAR. Confidence intervals for the ratio of two binomial proportions. Biometrics 1984; 40: 513–517.

3.Fagerland MW, Lydersen S, Laake P. Recommended confidence intervals for two independent binomial proportions. Stat Methods Med Res. SAGE Publications; 2011 Oct 13.