Hello Tomasz,

(Edited to fix error in scenario A)

There's nothing to prevent you from computing NNT (number needed to treat) for a given data set. Including a confidence interval estimate for NNT is probably a good idea in general, as the values could be volatile with small sample sizes.

A non-significant RR (risk ratio) simply means that you can't dependably differentiate risk (of the targeted outcome) as different from equality (e.g., a 1:1 ratio) between the two conditions being compared. This, too, can be sensitive to sample size; all other things equal, it's easier to show significant risk differences with large N studies than small N studies. With large N, a non-significant risk ratio would generally imply a very large estimated value for NNT.

The more "puzzling" outcome is that of a non-significant RR but a significant RD (risk reduction, or absolute risk reduction: ARR). This can occur when risk levels become high. For example:

Scenario A:

Treatment A: Risk = 6/100 = .06

Treatment B: Risk = 3/100 = .03

AD or ARR = .06 - .03 = .03

RR = .06 / .03 = 2.00

Scenario B:

Treatment A: Risk = 96/100 = .96

Treatment B: Risk = 93/100 = .93

AD or ARR = .96 - .93 = .03 (just as in scenario A)

RR = .96 / .93 = 1.03 (far lower than in scenario A)

Note that NNT = 33.3 for both examples, as it tracks AD/ARR, not RR.

Good luck with your work.

David Morse, nice example, but I think you meant Treatment B: Risk = 3/100 = .03 in your Scenario A. ;-)

Interestingly, the CIs for the risk difference do change a bit between your two scenarios. The user-written -rdci- command for Stata generates 4 different confidence intervals for the risk difference. Here are my two commands:

rdcii 6 3 94 97 // Scenario A

rdcii 96 93 4 7 // Scenario B

And here are the results. Copy and paste into an editor that allows you to use a fixed font to make things align.

Scenario A

Confidence intervals for risk difference

Risk for unexposed (p0): 0.030

Risk for exposed (p1): 0.060

Risk difference (p1 - p0): 0.030

-----------------------------------------

Method [95% Conf. Interval]

-----------------------------------------

Agresti-Caffo -0.032 0.091

Newcombe Method 10 -0.033 0.098

Wallenstein -0.027 0.086

Miettinen-Nurminen -0.033 0.099

Scenario B

Confidence intervals for risk difference

Risk for unexposed (p0): 0.930

Risk for exposed (p1): 0.960

Risk difference (p1 - p0): 0.030

-----------------------------------------

Method [95% Conf. Interval]

-----------------------------------------

Agresti-Caffo -0.038 0.096

Newcombe Method 10 -0.038 0.102

Wallenstein -0.033 0.092

Miettinen-Nurminen -0.038 0.103

HTH.