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Bias of estimates of the number needed to treat
Author(s) -
Duncan Bradford W.,
Olkin Ingram
Publication year - 2005
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.2076
Subject(s) - statistics , estimator , mathematics , confidence interval , number needed to treat , population , bias of an estimator , econometrics , relative risk , medicine , minimum variance unbiased estimator , environmental health
There are several commonly used measures of association between treatment and control event rates in the population (π T and π C , respectively). One such measure, the number needed to treat (NNT) indicates the number of patients, on average, who must be treated in order to prevent one additional adverse event, and is equal to 1/(π C ‐π T ). Because the population values π C and π T are unknown, the sample proportions (rates) p C and p T are used as estimates. The precision of a sample‐based estimator is usually exhibited in terms of confidence intervals. However, the accuracy of the estimator (i.e., its bias) is often ignored. The purpose of the present study is to examine the degree of bias. Using exact calculations based on the binomial theorem, we determined the bias of an estimate of NNT conditional on p C ≠ p T , and the bias of an adjusted estimator of the NNT for various sample sizes ( n = 10, 20, 30, 40, 50, 100) and population parameters (0.01⩽π C ⩽0.9; 0.01⩽π C −π T ⩽0.8). The magnitude and non‐monotonic nature of the bias are due to the NNT scale. The bias of the adjusted estimator can be approximated for some studies using the tabular results in this analysis. Copyright © 2005 John Wiley & Sons, Ltd.