Number needed to treat is intuitive when the outcome is binary. It expresses how many patients must be treated to prevent one additional event. Recurrent outcomes such as exacerbation, relapses, or hospitalizations are different because one patient may experience multiple events. Event-based number needed to treat can represent this repeated-event burden, but the reciprocal transformation used to calculate it creates asymmetric and potentially unstable uncertainty intervals, particularly when the treatment-related rate difference approaches zero.
A simulation analysis compared delta-method and non-parametric bootstrap confidence intervals across 36 recurrent-event scenarios, combining three baseline event rates, four treatment rate ratios, and three time horizons with 500 patients per arm. Event-based number needed to treat was below 1 in 13 of the 36 scenarios, demonstrating that sub-unit values can arise legitimately when more than one event is prevented per treated patient over the stated time horizon. Instability was concentrated in small-effect, low-event-rate, and short-follow-up scenarios. In stable settings, delta-method and bootstrap intervals were similar. As uncertainty increased, bootstrap intervals better reflected the skewness and sign uncertainty introduced by the reciprocal transformation, including the potential for highly asymmetric or unbounded intervals when the underlying rate difference approached or crossed zero.
The methodological value lies in moving beyond the point estimate to define when the metric itself becomes difficult to interpret. The analysis uses sign changes in the underlying rate difference as a practical stability diagnostic and proposes that a high sign-change frequency should trigger caution rather than presentation of a deceptively precise stand-alone number needed to treat. In such settings, greater emphasis should be placed on the confidence interval for the underlying rate difference, with the event-based number needed to treat interpreted as a supplementary measure rather than in isolation. This provides health economic models with a clearer framework for communicating recurrent-event treatment efficiency while explicitly linking the estimate to its time horizon and underlying statistical uncertainty, helping determine when it is sufficiently stable for decision-oriented interpretation.




