nnt: Calculate the number needed to treat (NNT)

In meta: General Package for Meta-Analysis

Calculate the number needed to treat (NNT)

Description

Calculate the number needed to treat (NNT) from estimated risk difference, risk ratio, odds ratio, or hazard ratio, and a baseline probability, i.e., control group event probability for binary outcomes or survival probability for hazard ratios.

Usage

nnt(x, ...)

## S3 method for class 'meta'
nnt(
  x,
  p.c,
  common = x$common,
  random = x$random,
  small.values = "desirable",
  ...
)

## Default S3 method:
nnt(x, p.c, sm, lower, upper, small.values = "desirable", transf = FALSE, ...)

## S3 method for class 'nnt.meta'
print(
  x,
  common = x$common,
  random = x$random,
  digits = gs("digits"),
  digits.prop = gs("digits.prop"),
  big.mark = gs("big.mark"),
  ...
)

## S3 method for class 'nnt.default'
print(
  x,
  digits = gs("digits"),
  digits.prop = gs("digits.prop"),
  big.mark = gs("big.mark"),
  ...
)

Arguments

x	An object of class meta, or estimated treatment effect(s), i.e., risk difference(s), risk ratio(s), odds ratio(s), or hazard ratio(s).
...	Additional arguments (to catch deprecated arguments).
p.c	Baseline probability, i.e., control group event probability for binary outcomes or survival probability in control group for hazard ratios.
common	A logical indicating whether NNTs should be calculated based on common effect estimate.
random	A logical indicating whether NNTs should be calculated based on random effects estimate.
small.values	A character string specifying whether small treatment effects indicate a beneficial ("desirable") or harmful ("undesirable") effect, can be abbreviated.
sm	Summary measure.
lower	Lower confidence interval limit.
upper	Upper confidence interval limit.
transf	A logical indicating whether treatment estimates and confidence limits are transformed or on the original scale. If transf = TRUE, inputs are expected to be log odds ratios instead of odds ratios for sm = "OR", for example.
digits	Minimal number of significant digits to print NNT and its confidence interval, see print.default.
digits.prop	Minimal number of significant digits for proportions, see print.default.
big.mark	A character used as thousands separator.

Details

The number needed to treat (NNT) is the estimated number of patients who need to be treated with a new treatment instead of a standard for one additional patient to benefit (Laupacis et al., 1988; Cook & Sackett, 1995). This definition of the NNT implies that the new treatment is more beneficial than the standard. If the new treatment is indeed less beneficial than the standard, the NNT gives the number of patients treated with the new treatment to observe an additional harmful event. Accordingly, the abbreviations NNTB and NNTH can be used to distinguish between beneficial and harmful NNTs (Altman, 1998).

NNTs can be easily computed from an estimated risk difference (RD), risk ratio (RR), or odds ratio (OR) and a given baseline probability (Higgins et al., 2023, section 15.4.4). It is also possible to calculate NNTs from hazard ratios (HR) (Altman & Andersen, 1999). Accordingly, NNTs can be calculated for meta-analyses generated with metabin or metagen if argument sm was equal to "RD", "RR", "OR", or "HR". It is also possible to provide only estimated treatment effects and baseline probabilities (see Examples).

The baseline probability can be specified using argument p.c. If this argument is missing, the minimum, mean, and maximum of the control event probabilities in the meta-analysis are used for metabin and control event probabilities of 0.1, 0.2, ..., 0.9 are used for metagen. Note, the survival instead of mortality probability must be provided for hazard ratios.

Argument small.values can be used to specify whether small treatment effects indicate a beneficial ("desirable") or harmful ("undesirable") effect. For small.values = "desirable", odds, risk and hazard ratios below 1 and risk differences below 0 indicate that the new treatment is beneficial. For small.values = "undesirable", odds, risk and hazard ratios above 1 and risk differences above 0 indicate that the new treatment is beneficial.

Interpretation of (positive and negative) NNTs

A positive value for the estimated NNT indicates that the new treatment is beneficial, i.e., the NNT is actually an NNTB. On the other hand, a negative value for the estimated NNT indicates that the new treatment is harmful, i.e., the NNT is actually an NNTH.

The minimal value for the NNTB is 1. In this extreme case the new treatment is 100% effective and the standard treatment is 0% effective, i.e., only one patient has to be treated with the new treatment for one additional patient to benefit. The NNTB increases with decreasing difference between the two risks. If both risks are equal, the NNTB is infinite.

The other extreme is an NNT of -1 if the new treatment is 0% effective and the standard is 100% effective. Here, one additional harmful event is observed for each patient treated with the new treatment. The NNT approaches minus infinity if the difference between the two risks decreases to 0. Finally, an NNT of -1 translates to an NNTH of 1 with possible values from 1 to infinity.

Confidence interval for the NNT

Confidence limits for an NNT are derived from the lower and upper confidence limits of the summary measure using the same formulae as for the NNT (Higgins et al., 2023, section 15.4.4).

A peculiar problem arises if the confidence interval for the summary measure includes the null effect (i.e., RR = 1, OR = 1, HR = 1, or RD = 0). In this case the confidence interval for the NNT contains both NNTB and NNTH values and it seemingly does not include the estimated NNT.

As described above, a positive NNT value corresponds to an NNTB and the absolute value of a negative NNT is equal to an NNTH. Accordingly, a confidence interval for the NNT from 20 to -5 translates to NNTB values between 20 and infinity and NNTH values between 5 and infinity (Altman, 1998).

Author(s)

Guido Schwarzer [e-mail]

References

Altman DG (1998): Confidence intervals for the number needed to treat. British Medical Journal, 317, 1309–12

Altman DG, Andersen PK (1999): Calculating the number needed to treat for trials where the outcome is time to an event. British Medical Journal, 319, 1492–95

Cook RJ, Sackett DL (1995): The number needed to treat: a clinically useful measure of treatment effect. British Medical Journal, 310, 452–54

Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors) (2023): Cochrane Handbook for Systematic Reviews of Interventions Version 6.4 (updated August 2023). Available from https://www.training.cochrane.org/handbook/

Laupacis A, Sackett DL, Roberts RS (1988): An assessment of clinically useful measures of the consequences of treatment. New England Journal of Medicine, 318, 1728–33

See Also

metabin, metagen

Examples

# Calculate NNTs for risk differences of -0.12 and -0.22
# (Cochrane Handbook, version 6.3, subsection 15.4.4.1)
nnt(c(-0.12, -0.22), sm = "RD")

# Calculate NNT for risk ratio of 0.92 and baseline risk of 0.3
# (Cochrane Handbook, version 6.3, subsection 15.4.4.2)
nnt(0.92, p.c = 0.3, sm = "RR")

# Calculate NNT for odds ratio of 0.73 and baseline risk of 0.3
# (Cochrane Handbook, version 6.3, subsection 15.4.4.3)
nnt(0.73, p.c = 0.3, sm = "OR")

# Calculate NNTs for Mantel-Haenszel odds ratio
data(Olkin1995)
m1 <-
  metabin(ev.exp, n.exp, ev.cont, n.cont, data = Olkin1995, random = FALSE)
nnt(m1)

# Calculate NNTs from hazard ratio at two and four years (example from
# Altman & Andersen, 1999). Note, argument 'p.c' must provide survival
# probabilities instead of mortality rates for the control group.
nnt(0.72, lower = 0.55, upper = 0.92, sm = "HR", p.c = 1 - c(0.33, 0.49))

meta documentation built on Oct. 31, 2024, 5:07 p.m.