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Statistical Calculations

Interpreting the Importance and Precision
of Therapeutic Results

Calculators

Centre for Evidence Based Medicine Stats Calculator

Vanderbilt- Power and Sample Size Calculator

Calculations

The magnitude of effect is usually expressed as one of the following, where:

 Yes No Exposed a b Not Exposed c d

Control event rate (CER) = c/c+d

Experimental event rate (EER) = a/a+b

(a) Relative Risk (RR) = EER/CER=(a/a+b)/(c/c+d)

(b) Relative Risk Reduction (RRR) = CER-EER/CER
(commonest reported measure of dichotomous treatment effect)

(c) Absolute Risk Reduction (ARR) = CER-EER

(d) Number Needed to Treat (NNT) = 1/ARR
A certain risk reduction may appear impressive but how many patients would you have to treat before seeing a benefit? This concept is called "number need to treat" and is one of the most intuitive statistics for clinical practice.

For example if:

 Yes No Exposed 8 992 Not Exposed 10 990

The RR = (8/1000) / (10/1000) = 0.8 making the RRR = (1-0.8/1)=0.2 or 20%. Although this sounds impressive, the absolute risk reduction is only 0.01-0.008=.002 or 0.2%. Thus the NNT is 1/0.002=500 patients. It is obvious that on an individual patient basis the pre-intervention risk or probability is a major determinant of the degree of possible post-intervention benefit, yield, or risk reduction.

Confidence Interval

The estimate of where the true value of a result lies is usually expressed in terms of a 95% confidence interval (CI), or confidence limits. These define the range that includes the true relative risk reduction 95% of the time.

If confidence limits are not provided you can calculate them if you have been given standard error of the RRR or relative risk. Just multiply the standard error by 2: the plus and minus values of this are the upper and lower values for the confidence interval.

Alternately the 95% confidence interval for an ARR can be calculated by:

=+/-1.96 ?[CER X (1-CER)/# control patients + EER X (1-EER)/# experimental patients]

The CI for the NNT is just 1/limits of CI for ARR.

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