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From |
Ángel Rodríguez Laso <angelrlaso@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Wed, 26 May 2010 13:24:11 +0200 |

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/

**Follow-Ups**:**Re: st: Sample size for a test of equivalence of proportions***From:*Jeph Herrin <junk@spandrel.net>

**st: RE: Sample size for a test of equivalence of proportions***From:*"Philip Ryan" <philip.ryan@adelaide.edu.au>

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