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Re: Distribution of point estimates within confidence intervals

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Wed, 29 Mar 2006 09:57:52 -0700

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 ```>>> Ted Harding <[log in to unmask]> 03/27/06 3:08 AM >>> > Also, does it follow that if a trial is repeated X times, > the observed point estimate for each trial be normally distributed > within the confidence interval of an adequately powered trial? No. First of all, an "adequately powered" trial may be so much adequately powered that the CI for that trial is very short indeed. However, the distribution of the point estimate for a trial differently powered may be scattered ofver a much wider range. Secondly, suppose the point-estimate methodology is unbiased. Now take the CI for the "adequately powered trial". The "midpoint" will be the point estimate from that trial. Even if the methodology is unbiased, that particular value will have an error. So the particular CI you have obtained from that trial will be offset relatively to the true value of the parameter. Hence, when you embark on the X repetitions, you will obtain a series of estimates which, overall, are unbiasedly distributed relative to the true value. Hence their distribution will be offset relative to the CI you obtained from the "adequately powered trial". ........................................... HM : I think this principle is well shown in a graphical representation of the results of simulated trials in this essay : http://jeffmann.net/soapbox/Statistics-smallsampleRCTs.htm Scroll down until you see the graphical representation of the C.I.s of 100 simulated trials (about two-thirds of the way down the page). I'd appreciate any thoughts about the general assertions concerning the problem of low event rates in RCTs, discussed in great detail in the essay. (Disclosure: The author is my brother-physician.) Regards, Howard Mann University of Utah ```