doi: 10.1161/01.STR.0000021722.37256.74
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(Stroke. 2002;33:1743.)
© 2002 American Heart Association, Inc.
Letters to the Editor |
Timeless
Centre de Recherche, Hôtel-Dieu du Centre Hospitalier de l’Université de Montréal, Montreal, Quebec, Canada
To the Editor:
We were pleased to see that Quilliam et al1 elected to use our number needed to harm (NNTH) in case-control studies2 to express the estimates of bleeding risks they obtained from their case-control study in elderly stroke survivors. However, in reporting their NNTHs, they omitted one crucial element, namely time. This is essential to the interpretation of NNTHs: it makes a vast difference whether the NNTH of 467 reported for serious bleed and aspirin refers to an exposure period of 1, 6, or 12 months—or 12 years.
The authors reported their estimate of the unexposed event rate (UER) as event rates per person-year of follow-up: however, this is not sufficient: an NNHT for case-control studies should always be expressed in terms of the duration of exposure in the case-control study at issue, unless the exposure is a 1-time event with lasting effects, such as in the case of vaccination.
Furthermore, the authors do not specify whether their UER estimate was derived from data applying to a 1-year period or whether it was derived by extrapolation or interpolation from data applying to shorter or longer time periods. This is important because making UER estimates based on interpolations or extrapolations assumes that the risk of events in unexposed persons is constant over the chosen time period. This may not necessarily be the case, and therefore every interpolation and extrapolation used to estimate a UER should be justified based on substantive knowledge.
Finally, there are some calculation errors in the 95% CIs reported by the authors for their NNTHs (page 2301 of their article): 2 of the CIs (those for aspirin and "combination") have infinity as a limit. It is unclear to us how the authors arrived at this result, as this can only occur when the odds ratio (OR) is exactly zero, which was not the case, or when the UER is equal to zero, which was also not the case and is a situation that almost never arises. When calculating CIs for NNTHs, it should be kept in mind that a modified version of the NNTH formula is to be used if the lower limit of the CI for the OR is less than 1.2 We recalculated the NNTHs and their CIs. Correct values are as follows (NNTH given first, CI in parentheses; bold type indicates elements that were erroneous or missing in the Quilliam study report):
NNTH for a any serious bleed, given treatment with: (1) warfarin: 126 (76 to 297) per year; (2) aspirin: 467 (182 to 817) per year; (3) combination: 96 (40-3268) per year.
We hope that other authors will follow suit and use the NNTH for case-control studies. In doing so, however, it is crucial that they pay due attention to congruency between the duration of exposure in the case-control study and the time period over which the incidence was calculated to obtain the UER, lest their results lose their meaning and interpretability.
References
- Quilliam BJ, Lapane KL, Eaton CB, Mor V. Effect of antiplatelet and anticoagulant agents on risk of hospitalization for bleeding among a population of elderly nursing home stroke survivors. Stroke. 2001; 32: 2299–2304.
[Abstract/Free Full Text] - Bjerre LM, LeLorier J. Expressing the magnitude of adverse effects in case-control studies: "the number of patients needed to be treated for one additional patient to be harmed." BMJ. 2000; 320: 503–506.
[Free Full Text]
Response
Center for Gerontology and Healthcare Research, Brown University, Providence, Rhode Island
We thank Bjerre and LeLorier for their helpful letter regarding our presentation of the number needed to treat to harm (NNTH).1 We recognize the apparent controversy in how to estimate the upper boundary of the 95% CI when the interval includes the null value of 1.2,3 As opposed to suggesting the upper bound of the confidence interval is infinity, Bjerre and LeLorier suggest an alternate formula for calculating the upper boundary.2 Yet to our knowledge, this article does not offer either a discussion or a derivation of this formula to allow the reader a better understanding of the utility of this estimating procedure. Despite this, we appreciate the clarification of the proposed methodology and hope that it will initiate further discussion. Nevertheless, we feel the NNTH we estimated for bleeding among aspirin or combination users remains clinically significant whether the upper boundary was reported as infinite (as we did) or as 817 and 3268, respectively, as estimated by Bjerre and LeLorier.2
We also regret omitting the element of time when interpreting the NNTH, although this information could be obtained from both the methodology and discussion sections of the article. We hypothesized that the exposures of interest would occur approximately 6 months prior to hospitalization for a bleeding event.1 We agree with Bjerre and LeLorier that this should be reinforced in the interpretation of the measure. We do, however, believe that the assumption of a relatively constant rate of hospitalization for bleeds used in our estimation of the unexposed event rate (UER) hold up in our data and appear to in previous reports, as well.4
Finally, we support the use of any measures, including the NNTH, that may help physicians and other clinicians make difficult decisions when enumerated by large amounts of technical information. As Bjerre and LeLorier state, the odds ratios derived from case-control studies assessing adverse effects " ... are not intuitively understandable estimates of risk."2 We hope that by our example, others can learn to appreciate both the utilities and the intricacies of this methodology and ultimately advance the dissemination of research results to clinicians and other healthcare professionals.
References
- Quilliam BJ, Lapane KL, Eaton CB, Mor V. Effect of antiplatelet and anticoagulant agents on risk of hospitalization for bleeding among a population of elderly nursing home stroke survivors. Stroke. 2001; 32: 2299–2304.
[Abstract/Free Full Text] - Bjerre LM, LeLorier J. Expressing the magnitude of adverse effects in case-control studies: "the number of patients needed to be treated for one additional patient to be harmed". BMJ. 2000; 320: 506–506.
[Free Full Text] - Altman DG. Confidence intervals for the number needed to treat. BMJ. 1998; 317: 1309–1312.
[Free Full Text] - Garcia Rodriguez LA, Walker AM, Perez Gutthann S. Nonsteroidal antiinflammatory drugs and gastrointestinal hospitalizations in Saskatchewan: a cohort study. Epidemiology. 1992; 3: 337–342.[Medline] [Order article via Infotrieve]
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