I am planning a prospective trial for CE mark of a new cardiovascular device, and wish to use 95% confidence intervals to present, once data are collected, the inferential estimate for the occurrence of the primary endpoint, which is a dichotomous variable (i.e. cardiovascular events at 30 days yes vs no).

The key limitation is the sample size (only 30 patients), and the fact that we expect 3-4 events at most (thus yielding a 10-13% event rate), qualifying the study as a small sample one, at least in the cardiovascular realm.

I am aware of books (e.g. Altman et al) and articles (e.g. Wei and Hutson) on this topic, as well as other CV entries (eg from Jason Todd), and typically know that the most recommended methods are the Wald and the Wilson, even if I would also trust percentile bootstrap.

My question to the CV community is quite simple: which is the most reliable method to compute 95% confidence intervals of proportions for small samples? Is there any parametric approach which tops the others? Is it better to use bootstrap instead?

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    $\begingroup$ Did you try 'exact' intervals like e.g. Clopper-Pearson or Sterne ? $\endgroup$ – user83346 Jul 21 '16 at 10:08
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    $\begingroup$ Presumably you know about Newcombe, R G, 1998, Two-sided confidence intervals for the single proportion comparison of seven methods, Statistics in Medicine, 17, 857--872? $\endgroup$ – mdewey Jul 21 '16 at 12:43
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    $\begingroup$ stats.stackexchange.com/questions/4756/… $\endgroup$ – whuber Jul 21 '16 at 14:07
  • $\begingroup$ @whuber: thanks for pointing out David LeBauer answer. I am not sure however whether it really addresses the issue of small or very small samples... In addition, it does not provide on the potential role for bootstrapping in such setting... $\endgroup$ – Joe_74 Jul 21 '16 at 17:47
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    $\begingroup$ In what sense do you mean "reliable" here? Various of the approaches will do better on different measures in some situations $\endgroup$ – Glen_b Jul 21 '16 at 17:49

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