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Difficulty: MediumMeasures of Association and Impact

A local health department analyzes data from a quality improvement initiative evaluating a novel telehealth monitoring program to prevent 30-day hospital readmissions in patients with decompensated heart failure. A total of 1,000 patients were equally divided between the telehealth intervention and the standard discharge care group. The 30-day readmission outcomes are provided in the table below:

GroupReadmittedNot ReadmittedTotal
Telehealth Program65435500
Standard Care100400500

Based on these findings, how many patients must be managed with the telehealth program rather than standard care to prevent exactly one 30-day hospital readmission?

  1. A
    3
  2. B
    5
  3. C
    7
  4. D
    14
  5. 15Answer

Answer

15
To calculate the Number Needed to Treat (NNT), first determine the Absolute Risk Reduction (ARR). The incidence in the standard care group (IcI_c) is 100/500=0.20100 / 500 = 0.20. The incidence in the telehealth group (IeI_e) is 65/500=0.1365 / 500 = 0.13. The ARR is 0.20−0.13=0.070.20 - 0.13 = 0.07. The NNT is the reciprocal of the ARR: 1/0.07≈14.281 / 0.07 \approx 14.28. In biostatistics, NNT values are always rounded up to the next whole number (ceiling function) because treating a fraction of a patient is impossible, and rounding down would result in less than one full adverse event being prevented. Therefore, 14.2814.28 is correctly rounded up to 15.

Step-by-Step Solution

1
Calculate the incidence of readmission in the standard care group (IcI_c).
Ic=100500=0.20I_c = \frac{100}{500} = 0.20 (or 20%20\%).
Baseline risk in the unexposed/control group is needed to establish the comparative standard.
2
Calculate the incidence of readmission in the telehealth intervention group (IeI_e).
Ie=65500=0.13I_e = \frac{65}{500} = 0.13 (or 13%13\%).
The intervention risk is needed to find how much the risk was reduced by the program.
3
Calculate the Absolute Risk Reduction (ARR).
ARR=Ic−Ie=0.20−0.13=0.07ARR = I_c - I_e = 0.20 - 0.13 = 0.07.
ARR determines the absolute difference in risk between the two groups, which is the denominator for the NNT formula.
4
Calculate the Number Needed to Treat (NNT) and apply the correct rounding rule.
NNT=1ARR=10.07≈14.28NNT = \frac{1}{ARR} = \frac{1}{0.07} \approx 14.28. Rounding up yields 15.
NNT is the inverse of ARR. Because you cannot treat a fraction of a patient, it is standard epidemiological practice to round up to the next whole number to guarantee the prevention of one adverse event.

Key Concept

Number Needed to Treat (NNT) is calculated as the inverse of Absolute Risk Reduction (1/ARR1 / ARR) and must always be rounded up to the next whole integer.
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Topics

Measures of Association and Impact

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