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From |
stephen.kay@adelphigroup.com |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: Sample Size Calcs, Multiple testing and CI's |

Date |
Wed, 25 Feb 2009 10:18:43 -0000 |

I'm trying to come up with a sample size calculation for a proposed patient study which has fourteen equally important endpoints - different quality of life measures (assume all continuous). All endpoints involve the same patients being statistically compared against published norm values (t tests). Each of these norm values themselves have come from a different study (14 in all - one for each providing norm mean, SD and Nnorm). Once the study is finished I'll be asked to provide 95% CI's for mean differences against norms for each of the fourteen endpoints. I can't find any references that cover my problems: Problem 1: If I adopt a family wise error rate approach, FWER, am I right in thinking that my sample size calculation should focus on an "ANOVA like" test statistic that tests Ho: All mean differences are zero? If yes, how do I form such a statistic? If no, can I compute a corrected individual P value for each of the 14 tests using a recognised correction method (e.g. Sidak or Holm) and base the sample size on the largest sample generated across the fourteen that achieves 80% power for alpha = corrected P value? Problem 2 (follows on from a "no" response in problem 1): On reading about corrected P value threshold methods, one way of classifying them is by step type (one-step e.g. Bonferroni, step up - e.g. Hochberg and step up e.g. Holm). I appreciate that Bonferroni is the most conservative and the other methods are better to apply once the data is in. However the most stringent P value generated by the step up and step down methods is often almost identical to the one P value generated by Bonferroni and surely it is the most stringent P value I am forced to use in the sample size calculations? If this is so then I'm no better off using these methods than Bonferroni in terms of study planning. Is this correct? I don't think I'm justified in taking the average corrected P value across the steps in an up or down procedure? Problem 3: I'm at a bit of a loss concerning generating 95% CI's for individual mean differences once the data is back in. Obviously it has to correspond to the methods proposed in the sample size calculations. I'm perplexed as to how I would calculate these for a step up or down P correction method? I assume for a one step method such as Bonferroni, I'd just apply standard formula to the adjusted critical P value (e.g. 0.05/14 for Bonferroni) to generate 95% CI's for the individual mean differences? I realise I have not mentioned FDR methods - which I may well be forced to adopt given the number of comparisons I'm forced to make. I don't think there's any point in performing an "ANOVA type" test if you are controlling the FDR? Although every other difficulty mentioned above still applies? In particular I'm really uncertain how to generate individual confidence intervals for the mean differences under this approach? Any help or relevant references that could solve my problems would be most appreciated. Stephen Kay DISCLAIMER: The information in this message is confidential and may be legally privileged. It is intended solely for the addressee. Access to this message by anyone else is unauthorised. If you are not the intended recipient, any disclosure, copying, or distribution of the message, or any action or omission taken by you in reliance on it, is prohibited and may be unlawful. Please immediately contact the sender if you have received this message in error. Thank you. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Sample Size Calcs, Multiple testing and CI's***From:*Ronan Conroy <rconroy@rcsi.ie>

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