This function calculates the number needed to treat ($$NTT$$) using event data or effect sizes (such as Cohen's $$d$$ or Hedges' $$g$$).

## Usage

NNT(d, CER, event.e, n.e, event.c, n.c, names, method)

## Arguments

d

A single numeric or concatenated vector of numerics representing the effect size expressed as Cohen's $$d$$ or Hedges' $$g$$. If this is the only parameter specified in the function, the method by Kraemer and Kupfer is used automatically to calculate $$NNT$$s.

CER

The control group event ratio. Furukawa's method (Furukawa & Leucht, 2011) to calculate NNTs from d requires that the assumed response ("event") ratio in the control group ($$\frac{n_{responders}}{N_{total}}$$) is specified. The CER can assume values from 0 to 1. If a value is specified for CER, Furukawa's method is used automatically. Argument method has to be set to "KraemerKupfer" to override this.

event.e

Single number or numeric vector. The number of (favourable) events in the experimental group.

n.e

Single number or numeric vector. The number participants in the experimental group.

event.c

Single number or numeric vector. The number of (favourable) events in the control group.

n.c

Single number or numeric vector. The number of participants in the control group.

names

Optional. Character vector of equal length as the vector supplied to d or event.e containing study/effect size labels.

method

The method to be used to calculate the NNT from d. Either "KraemerKupfer" for the method proposed by Kraemer and Kupfer (2006) or "Furukawa" for the Furukawa method (Furukawa & Leucht, 2011). Please note that the Furukawa's method can only be used when CER is specified.

## Details

This function calculates the number needed to treat ($$NNT$$) from effect sizes (Cohen's $$d$$ and Hedges' $$g$$) or, alternatively, from raw event data.

Two methods to calculate the $$NTT$$ from d are implemented in this function.

• The method by Kraemer and Kupfer (2006), calculates $$NTT$$ from the Area Under the Curve ($$AUC$$) defined as the probability that a patient in the treatment has an outcome preferable to one in the control. This method allows to calculate the NNT directly from d without any extra variables.

• The method by Furukawa calculates the $$NNT$$ from d using a reasonable estimate of $$CER$$, in this context the response rate in the control group.

Furukawa's method has been shown to be superior in predicting the $$NNT$$ compared to the Kraemer & Kupfer method (Furukawa & Leucht, 2011). If reasonable assumptions can be made concerning the $$CER$$, Furukawa's method should therefore be preferred.

When event data is used for the function, the $$CER$$ and $$EER$$ (experimental group event rate) is calculated internally, and the standard definition of the $$NTT$$, $$\frac{1}{EER-CER}$$, is used.

Please note that negative NNT values returned by the function refer to the number needed to harm ($$NNH$$), as the intervention is assumed to be inferior to the control group treatment based on the effect size data supplied to the function.

## References

Harrer, M., Cuijpers, P., Furukawa, T.A, & Ebert, D. D. (2019). Doing Meta-Analysis in R: A Hands-on Guide. DOI: 10.5281/zenodo.2551803. Chapter 9.1.

Furukawa, T. A., & Leucht, S. (2011). How to obtain NNT from Cohen's d: comparison of two methods. PloS one, 6(4), e19070.

Kraemer H.C., Kupfer D.J. (2006) Size of treatment effects and their importance to clinical research and practice. Biol. Psychiatry 59: 990–996.

se.from.p

## Author

Mathias Harrer & David Daniel Ebert

## Examples


# Example 1: Convert Cohen's d using the Kraemer & Kupfer method
d = c(-0.123, 0.234, 0.123, 1.234, 0.12)
NNT(d)
#> Kraemer & Kupfer method used.
#> Negative NNT values refer to the number needed to harm (NNH)
#> [1] -14.428364   7.609168  14.428364   1.620477  14.788175

# Example 2: Convert Cohen's d using the Furukawa method
d = c(-0.123, 0.234, 0.123, 1.234, 0.12)
CER = c(0.42, 0.35, 0.26, 0.21, 0.23)
NNT(d, CER)
#> Furukawa & Leucht method used.
#> Negative NNT values refer to the number needed to harm (NNH)
#> [1] -21.110785  11.128241  24.147924   2.195288  26.309816

# Example 3: Convert event data
NNT(event.e = 10, event.c = 20, n.e = 200, n.c = 200)
#> [1] 20