<?xml version="1.0" encoding="utf-8"?><!DOCTYPE article  PUBLIC '-//OASIS//DTD DocBook XML V4.4//EN'  'http://www.docbook.org/xml/4.4/docbookx.dtd'><article><articleinfo><title>FAQ/power/llogPow</title><revhistory><revision><revnumber>22</revnumber><date>2017-05-09 08:50:19</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>21</revnumber><date>2017-05-09 08:43:53</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>20</revnumber><date>2017-05-03 10:59:40</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>19</revnumber><date>2013-03-08 10:17:28</date><authorinitials>localhost</authorinitials><revremark>converted to 1.6 markup</revremark></revision><revision><revnumber>18</revnumber><date>2012-12-05 15:49:06</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>17</revnumber><date>2012-02-06 10:41:49</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>16</revnumber><date>2012-02-06 10:35:59</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>15</revnumber><date>2011-07-04 11:19:34</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>14</revnumber><date>2011-07-04 11:09:45</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>13</revnumber><date>2009-07-30 12:00:08</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>12</revnumber><date>2009-07-30 11:19:32</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>11</revnumber><date>2009-07-30 10:52:45</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>10</revnumber><date>2009-07-30 10:49:10</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>9</revnumber><date>2009-07-30 10:48:41</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>8</revnumber><date>2009-07-30 10:31:20</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>7</revnumber><date>2009-07-30 10:30:11</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>6</revnumber><date>2009-07-30 10:25:50</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>5</revnumber><date>2009-07-30 10:25:39</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>4</revnumber><date>2009-07-30 10:25:17</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>3</revnumber><date>2009-07-30 10:23:56</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>2</revnumber><date>2009-02-18 15:10:17</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>1</revnumber><date>2007-08-29 16:18:24</date><authorinitials>PeterWatson</authorinitials></revision></revhistory></articleinfo><section><title>A single predictor in a multiple binary logistic regression</title><para>A power calculator is given <ulink url="http://www.dartmouth.edu/~eugened/power-samplesize.php">here</ulink> for upto two binary covariates using Demidenko (2007, 2008) and were <ulink url="http://biostat.hitchcock.org/MeasurementError/Analytics/SampleSizeCalculationsforLogisticRegression.asp">here</ulink> although it is anticipated this page could reappear pending a redesign of the <ulink url="http://biostat.hitchcock.org/"/> website (April 2017). An example of using Demidenko's programme is <ulink url="https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/power/llogPow/statswiki/FAQ/demidenko#">here.</ulink> </para><para>Hsieh FY (1989) gives formulae and tables for odds ratios between 0.6 and 3.0 and ONE-tailed type I error to compute power for given total sample size in a multiple binary logistic regression for continuous covariates associated with a change of 1 sd in the value of the covariate. These calculations can be done using a <ulink url="https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/power/llogPow/statswiki/FAQ/power/llogPow?action=AttachFile&amp;do=get&amp;target=llogpow1.xls">spreadsheet.</ulink> </para><para>Hsieh, Bloch and Larsen (1998) showed that sample size for multiple logistic regression predictors could be approximated using t-tests for a single predictor. A spreadsheet to compute power using their approach for a binary covariate is given <ulink url="https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/power/llogPow/statswiki/FAQ/power/llogPow?action=AttachFile&amp;do=get&amp;target=hblbin_pow.xls">here</ulink> and using a continuous covariate <ulink url="https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/power/llogPow/statswiki/FAQ/power/llogPow?action=AttachFile&amp;do=get&amp;target=hblcont_pow.xls">here.</ulink> The odds ratio in the latter represents an increase of one standard deviation in the covariate.  </para><para><ulink url="http://www.medcalc.org/manual/logistic_regression.php">(The following is reproduced from this website).</ulink> A less complex approach is based upon the work of Peduzzi et al. (1996) who offer the following guideline for a minimum number of cases to include in your study. </para><para><ulink url="https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/power/llogPow/statswiki/FAQ/power/llogPow?action=AttachFile&amp;do=get&amp;target=powrisk.pdf">Whitaker HJ, Farrington, CP, Spiessens B and Musonda P (2005)</ulink> give simple sample size formulae for an odds which takes the length of the risk period into account e.g. what fraction of the observation period you are exposed to an adverse event (see also <ulink url="https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/power/llogPow/statswiki/FAQ/power/llogPow?action=AttachFile&amp;do=get&amp;target=resrep.pdf">Musonda et al here.</ulink>)  </para><para><emphasis role="underline">References</emphasis> </para><para>Demidenko E (2007) Sample size determination for logistic regression revisited. <emphasis>Statistics in Medicine</emphasis> <emphasis role="strong">26</emphasis> 3385-3397.  </para><para>Demidenko E (2008) Sample size and optimal design for logistic regression with binary interaction. <emphasis>Statistics in Medicine</emphasis>, <emphasis role="strong">27</emphasis> 36-46. </para><para>Hsieh FY (1989) Sample size tables for logistic regression. <emphasis>Statistics in Medicine</emphasis> <emphasis role="strong">8</emphasis> 795-802. </para><para>Hsieh, FY, Block, DA, and Larsen, MD (1998). A Simple Method of Sample Size Calculation for Linear and Logistic Regression. Statistics in Medicine, Volume 17, pages 1623-1634. </para><para>Musonda P, Farrington CP and Whitaker HJ. (2005) Sample sizes for self-controlled case series studies. Research report:The Open University. </para><para>Whitaker HJ, Farrington, CP, Spiessens B and Musonda P (2005). Tutorial in biostatistics: the self-controlled case series method. <emphasis>Statistics in Medicine</emphasis> <emphasis role="strong">24</emphasis> 4035-4044. </para></section></article>