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From |
"Philip Ryan" <philip.ryan@adelaide.edu.au> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: Sample size for a test of equivalence of proportions |

Date |
Wed, 26 May 2010 21:59:16 +0930 |

Angel I confess I had quite forgotten I had written -equivsize-. This is not too surprising because it was a quick and dirty response to a question posted on the List and not something destined for the SSC repository. Reading my original email, I see that I wrote: "There are no error traps and no help file but comments embedded in the program tell the story. -equivsize-, in *very* limited testing, appears to give the same answers as the commercial program nQuery Advisor 4 (2000, Statistical Solutions, Cork)." I think all the above disclaimers provide me with sufficient cover for any shortcomings in -equivsize-. But in any case, I see that Philip Jones has recently released his program -ssi- on the SSC and, although I have not used it, it looks to be much more comprehensive than -equivsize-, is very (very) likely to be better tested and should be more useful than -equivsize-. Perhaps you should try -ssi- ? Phil Philip Ryan Professor and Director Data Management & Analysis Centre School of Population Health & Clinical Practice University of Adelaide -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Ángel Rodríguez Laso Sent: Wednesday, 26 May 2010 8:54 PM To: statalist@hsphsun2.harvard.edu Subject: st: Sample size for a test of equivalence of proportions Dear Statalisters, I want to calculate the sample size for an experiment to compare the refusal rate of two strategies to contact participants in a survey. In the usual procedure, I expect a refusal rate of 17%. I would like to detect a 10% increase in refusal with the alternative procedure, with alpha 0.05 (one sided) and power 80%. I consider this a test of equivalence between procedures. After searching Statalist, I?ve come across two possibilities to calculate sample sizes that yield different results: I would appreciate your comments on possible misspecifications when entering values for the programs and the reasons for the differences in the results obtained. 1) The user-written program equivsize by Phil Ryan v0.02 2002-02-06 (http://www.stata.com/statalist/archive/2003-02/msg00204.html) . equivsize .17 .17 .1 .05 .8 n (per group) = 175 2) The user-written artmenu program version 1.0.4 SB/PR 13jan2005: . artbin, pr(.17 .27) ngroups(2) aratios(1 1) distant(0) alpha(0.05) power(0.8) onesided(1) ni(1) ART - ANALYSIS OF RESOURCES FOR TRIALS (version 1.0.0, 3 March 2004) ---------------------------------------------------------------------------- -- A sample size program by Abdel Babiker, Patrick Royston & Friederike Barthel, MRC Clinical Trials Unit, London NW1 2DA, UK. ---------------------------------------------------------------------------- -- Type of trial Noninferiority - binary outcome Statistical test assumed Unconditional comparison of 2 binomial proportions Number of groups 2 Allocation ratio Equal group sizes Anticipated event probabilities 0.170, 0.270 Alpha 0.050 (one-sided) Power (designed) 0.800 Total sample size (calculated) 451 Expected total number of events 100 That is, 225 individuals per group. 3) In addition, in a research methods text book (Argimón, Jiménez. Métodos de investigación clínica y epidemiológica. Elsevier, Madrid, 2004) I?ve found the following formula to calculate sample sizes for equivalence tests (no further reference for the formula is provided, but maybe someone will identify its origin): N(per group)= 2*P*(1-P)*(Zalpha+Zbeta)squared) / (difference of interest)squared Where P would be refusal rate in the usual procedure group (0.17) Zalpha=1.645 (one-sided) Zbeta=0.842 (corresponding to a 0.8 power) Difference of interest=0.1 N(per group)= 2*0.17*0.83*(1.645+0.842)squared / 0.1*0.1 = 175 This matches perfectly the result of 1). Nevertheless, this option does not allow unequal group sizes that could be of interest in this experiment. To complicate things further, the experiment will deal with clustered samples. To correct sample size for clustering, would it be enough to multiply the sample size obtained from these methods by the expected DEFF? Thank you very much for your time and interest. Angel Rodriguez-Laso * * 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/ No virus found in this incoming message. Checked by AVG - www.avg.com Version: 9.0.819 / Virus Database: 271.1.1/2896 - Release Date: 05/26/10 03:56:00 * * 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/

**References**:**st: Sample size for a test of equivalence of proportions***From:*Ángel Rodríguez Laso <angelrlaso@gmail.com>

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