Problems with NNT



I wholeheartedly agree that intervals for p1 - p2 obtained from Wilson intervals for p1 and p2 combined by squaring and adding (now known as MOVER - Method of Variance Estimates Recovery) are greatly preferable to Wald intervals - see Newcombe RG. Interval estimation for the difference between independent proportions: comparison of eleven methods. Statistics in Medicine 1998, 17, 873-890. Nevertheless, that is a quite separate issue. This issue with the NNT happens practically regardless of what method we choose to calculate the interval for p1 - p2. The Wald 95% interval for 47/94 minus 30/75, which is also used in my book, is simply the perfect example to illustrate this point as it happens to give these round figures for p1 - p2 and both lower and upper limits to 4 dp.


The confidence interval anomaly arises because the NNT is a reciprocal of a quantity (the risk difference) whose value can cross zero. A similar thing happens with Fieler’s Theorem. I seem to recall Andy Grieve writing about this many years ago. I see little use for NNTs anyway so I have never got very excited about this.