Re: st: Sample size for a test of equivalence of proportions

[Jeph Herrin <junk@spandrel.net>]

Why not

 sampsi .17 .27, power(.80) onesided

?

This is a one-sided test of two-sample comparison of proportions.

hth,
Jeph




Ángel Rodríguez Laso wrote:
> 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/
*
*   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/