American Journal of Epidemiology Advance Access originally published online on June 22, 2005
American Journal of Epidemiology 2005 162(2):196; doi:10.1093/aje/kwi177
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LETTERS TO THE EDITOR |
THE AUTHORS REPLY
1 Division of Biostatistics, Department of Epidemiology and Biostatistics, School of Medicine, University of California, San Francisco, CA 94143-0560
2 Program in Medical Ethics, Department of Medicine, School of Medicine, University of California, San Francisco, CA 94143-0560
We thank Halpern et al. (1
) for responding to our paper in the Journal (2). We appreciate this opportunity to emphasize key points concerning the per-participant formulation, altruistic satisfaction, and the scope of our paper.
Halpern et al. in fact reassert the very premises we used to show that the argument for condemning low-power studies fails on its own terms. They propose that the study value is "the product of the value of the new treatment per patient [call this V] and the number of those afflicted [call this N]" (1, p. 195). The expected study value is then "the product of the net social benefit and the probability that it is obtained" (1, p. 195), which we can write as NV x Pn, where Pn is the power attained with sample size n. We proposed that, to be ethical, this projected value should exceed the projected total burden on participants, which is nB when the average net burden per participant is B. The ethical requirement related to sample size is then
 | (1) |
) and our response (3) to the commentary by Prentice (4), this is equivalent to
 | (2) |
Consider a specific case. Suppose that n = 20 (10 per arm) produces only 15 percent power, which occurs for a standardized effect size of about 0.43. To attain 80 percent power, we need n = 172. If n = 172 is ethically acceptable, then, according to inequality 1, we have 0.8NV > 172B or NV > 215B, which implies that 0.15NV > (0.15)215B = 32.25B > 20B. So, inequality 1 must also be met for the study in which n = 20.
We do not believe that participants' altruistic satisfaction is relevant for assessing sample size at the planning and approval stages. If a study fails on a criterion such as inequality 1, no amount of participant satisfaction can make it acceptable; there is no real net benefit, and any satisfaction would be created under false pretenses. In addition, there is no reason for research ethics committees to preempt participants' own decisions about what gives them satisfaction. Our analysis shows that it is not irrational for participants to derive satisfaction from contributing to a small study, because their personal contribution to the value produced will on average be more than if they had constituted a smaller fraction of the total sample size in a comparable larger study. Disapproving a study because a committee thinks it is too small to reward participants' altruistic motives would therefore fail to show proper respect for participant autonomy.
Our paper (2) addressed only the influence of sample size on ethical acceptability with all other aspects of the study acceptable and remaining fixed. We should have emphasized this more clearly in the introduction and did not intend to misrepresent prior work. We did explicitly write in the Discussion section of our paper, "We do not address ... selection of the study population" (2, p. 108) and so clearly did not address the trade-offs between homogeneity and generalizability.
We hope this response fully clarifies the issues raised by Halpern et al. (1). While larger studies produce more value, they also burden more participants, which cannot be ignored when assessing ethical acceptability.
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ACKNOWLEDGMENTS |
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Conflict of interest: none declared.
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References |
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 TOP References |
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- Halpern SD, Karlawish JHT, Berlin JA. Re: "Ethics and sample size." (Letter). Am J Epidemiol 2005;162:195–6.
[Free Full Text] - Bacchetti P, Wolf LE, Segal MR, et al. Ethics and sample size. Am J Epidemiol 2005;161:105–10.
[Abstract/Free Full Text] - Bacchetti P, Wolf LE, Segal MR, et al. Bacchetti et al. respond to "ethics and sample size—another view." (Letter). Am J Epidemiol 2005;161:113.
[Free Full Text] - Prentice R. Invited commentary: ethics and sample size—another view. Am J Epidemiol 2005;161:111–12.
[Free Full Text]
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