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372 lines
13 KiB
Plaintext
372 lines
13 KiB
Plaintext
9 months ago
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*! version 3.3 : October 2nd, 2012
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*! Jean-Benoit Hardouin, Myriam Blanchin
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************************************************************************************************************
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* raschpower: Estimation of the power of the Wald test in order to compare the means of the latent trait in two groups of individuals
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*
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* Version 1 : January 25, 2010 (Jean-Benoit Hardouin)
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* Version 1.1 : January 26, 2010 (Jean-Benoit Hardouin)
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* Version 1.2 : November 1st, 2010 (Jean-Benoit Hardouin)
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* version 1.3 : May 2th, 2011 (Jean-Benoit Hardouin)
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* version 1.4 : July 7th, 2011 (Jean-Benoit Hardouin) : minor corrections
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* version 1.5 : July 11th, 2011 (Jean-Benoit Hardouin) : minor corrections
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* version 2 : August 30th, 2011 (Jean-Benoit Hardouin, Myriam Blanchin) : corrections
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* version 3 : October 18th, 2011 (Jean-Benoit Hardouin, Myriam Blanchin) : Extension to the PCM, -method- option, -nbpatterns- options, changes in the presentation of the results
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* version 3.1 : October 25th, 2011 (Jean-Benoit Hardouin, Myriam Blanchin) : POPULATION+GH method
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* version 3.2 : February 6th, 2012 (Jean-Benoit Hardouin, Myriam Blanchin) : minor corrections
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* version 3.3 : October 2nd, 2012 (Jean-Benoit Hardouin, Myriam Blanchin) : minor corrections
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*
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* Jean-benoit Hardouin, jean-benoit.hardouin@univ-nantes.fr
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* Myriam Blanchin, myriam.blanchin@univ-nantes.fr
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* EA 4275 "Biostatistics, Pharmacoepidemiology and Subjectives Measures in Health"
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* Faculty of Pharmaceutical Sciences - University of Nantes - France
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*
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* News about this program : http://www.anaqol.org
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* FreeIRT Project : http://www.freeirt.org
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*
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* Copyright 2010-2012 Jean-Benoit Hardouin, Myriam Blanchin
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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************************************************************************************************************/
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program define raschpower,rclass
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syntax [varlist] [, n0(int 100) n1(int 100) Gamma(real .5) Difficulties(string) Var(real 1) Method(string) NBPatterns(int 2) nodata EXPectedpower(real -1)]
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version 11
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tempfile raschpowerfile
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capture qui save "`raschpowerfile'",replace
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tempname db d
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if "`difficulties'"=="" {
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matrix `d'=[-1.151, -0.987\-0.615, -0.325\-0.184, -0.043\0.246, 0.554\0.782, 1.724]
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}
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else {
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matrix `d'=`difficulties'
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}
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local nbitems=rowsof(`d')
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local nbmodat=colsof(`d')+1
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if "`method'"=="MEAN+GH"&`nbpatterns'*(`n1'+`n0')>=`=`nbmodat'^`nbitems'*2' {
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di in gr "The MEAN+GH will be inefficient compared to GH since the maximal number of pattern's responses"
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di in gr "is lesser than the number of pattern retained by the MEAN+GH method."
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di in gr "The -method- option is replaced by GH."
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local method GH
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}
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else if "`method'"=="" {
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if `nbmodat'^`nbitems'*2<1000 {
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local method GH
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}
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else if `nbmodat'^`nbitems'<10000 {
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local method MEAN+GH
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}
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else if `nbmodat'^`nbitems'<1000000 {
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local method MEAN
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}
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else {
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local method POPULATION+GH
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}
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}
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di in gr "Method: " in ye "`method'"
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di in gr "Number of individuals in the first group: " in ye `n0'
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di in gr "Number of individuals in the second group: " in ye `n1'
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di in green "Group effect: " in ye `gamma'
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di in gr "Variance of the latent trait: " in ye `var'
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di in gr "Number of items: " in ye `nbitems'
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di in green "Difficulties parameters of the items: "
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tempname dd
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matrix `dd'=`d''
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local items
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forvalues i=1/`nbitems' {
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local items "`items' item`i'"
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}
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local modalities
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forvalues i=1/`=`nbmodat'-1' {
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local modalities "`modalities' delta_`i'"
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}
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matrix colnames `dd'=`items'
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matrix rownames `dd'=`modalities'
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matrix list `dd',noblank nohalf noheader
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di in gr "Number of studied response's patterns: " in ye `=`nbmodat'^`nbitems'*2'
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matrix `dd'=`d'
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local gamma=`gamma'
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local tmp=1
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qui matrix `db'=J(`=`nbitems'*(`nbmodat'-1)',1,.)
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forvalues j=1/`nbitems' {
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forvalues m=1/`=`nbmodat'-1' {
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qui matrix `db'[`tmp',1]=`d'[`j',`m']
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local ++tmp
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}
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}
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if "`data'"=="" {
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clear
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if "`method'"!="POPULATION+GH"{
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local temp=`nbmodat'^(`nbitems')
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qui range x 0 `=`temp'-1' `temp'
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qui g t=x
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loc i=`nbitems'
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qui count if t>0
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loc z=r(N)
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qui while `z'>0 {
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qui gen item`=`nbitems'-`i'+1'=floor(t/`nbmodat'^`=`i'-1')
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qui replace t=mod(t,`nbmodat'^`=`i'-1')
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qui count if t>0
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loc z=r(N)
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loc i=`i'-1
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}
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drop t
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qui expand 2
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qui gen group=0 in 1/`temp'
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qui replace group=1 in `=`temp'+1'/`=2*`temp''
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}
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else {
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qui simirt, clear pcm(`difficulties') cov(`var') group(`=`n1'/(`n1'+`n0')') deltagroup(`gamma') nbobs(1000000)
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qui drop lt1
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qui contract item* group, freq(freq)
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qui gen keep=0
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qui gsort +group -freq
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qui replace keep=1 in 1/`=`nbpatterns'*`n0''
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qui gsort -group -freq
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qui replace keep=1 in 1/`=`nbpatterns'*`n1''
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qui keep if keep==1
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qui count
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local tmp=r(N)
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di "Number of kept patterns:`tmp'"
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local method GH
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}
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qui gen mean=-`n1'*`gamma'/(`n0'+`n1') if group==0
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qui replace mean=`n0'*`gamma'/(`n0'+`n1') if group==1
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if "`method'"=="GH" {
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local temp=`nbmodat'^(`nbitems')
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local diff0=0
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qui gen proba=.
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local dixj=10
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qui count
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local tmp=r(N)
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forvalues i=1/`tmp' {
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local dix=floor(`tmp'/10)
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if mod(`i',`dix')==0 {
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if "`dixj'"!="10" {
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di ".." _c
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}
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di "`dixj'%" _c
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local dixj=`dixj'+10
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}
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local int=1
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forvalues j=1/`nbitems' {
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qui su item`j' in `i'
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local rep=r(mean)
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local diff0=0
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local diff1=`d'[`j',1]
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local sum "1+exp(x-`diff1')"
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forvalues m=2/`=`nbmodat'-1' {
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local diff`m'=`diff`=`m'-1''+`d'[`j',`m']
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local sum "`sum'+exp(`m'*x-`diff`m'')"
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}
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local int "(`int'*exp(`rep'*x-`diff`rep''))/(`sum')"
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}
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qui su mean in `i'
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local mean=r(mean)
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qui gausshermite `int',mu(`mean') sigma(`=sqrt(`var')') display
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qui replace proba=r(int) in `i'
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}
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di
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}
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else {
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qui gen proba=1
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forvalues i=1/`nbitems' {
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local diff0=0
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local diff1=`d'[`i',1]
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qui gen eps0=1
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qui gen eps1=exp(mean-`diff1')
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qui gen d=eps0+eps1
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forvalues m=2/`=`nbmodat'-1' {
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local diff`m'=`diff`=`m'-1''+`d'[`i',`m']
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qui gen eps`m'=exp(`m'*mean-`diff`m'')
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qui replace d=d+eps`m'
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}
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local listeps
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forvalues m=0/`=`nbmodat'-1' {
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qui replace proba=proba*eps`m'/d if item`i'==`m'
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local listeps `listeps' eps`m'
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}
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qui drop `listeps' d
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}
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if "`method'"=="MEAN+GH" {
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set tracedepth 1
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qui gen keep=0
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qui gsort -group -proba
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local min=min(`=`nbmodat'^`nbitems'',`=`n1'*`nbpatterns'')
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qui replace keep=1 in 1/`min'
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qui gsort +group -proba
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local min=min(`=`nbmodat'^`nbitems'',`=`n0'*`nbpatterns'')
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qui replace keep=1 in 1/`min'
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qui keep if keep==1
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qui su proba if group==0
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local sumproba0=r(sum)*100
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qui su proba if group==1
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local sumproba1=r(sum)*100
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qui drop keep proba
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local diff0=0
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qui gen proba=.
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qui count
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local nnew=r(N)
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di in gr "Number of studied response's patterns for the GH step: " in ye `nnew'
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di in gr "(" in ye %6.2f `sumproba0' in gr "% of the group 0 and " in ye %6.2f `sumproba1' in gr "% of the group 1)"
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local dixj=10
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forvalues i=1/`nnew' {
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local dix=floor(`nnew'/10)
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if mod(`i',`dix')==0 {
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if "`dixj'"!="10" {
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di ".." _c
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}
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di "`dixj'%" _c
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local dixj=`dixj'+10
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}
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local int=1
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forvalues j=1/`nbitems' {
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qui su item`j' in `i'
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local rep=r(mean)
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local diff0=0
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local diff1=`d'[`j',1]
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local sum "1+exp(x-`diff1')"
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forvalues m=2/`=`nbmodat'-1' {
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local diff`m'=`diff`=`m'-1''+`d'[`j',`m']
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local sum "`sum'+exp(`m'*x-`diff`m'')"
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}
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local int "(`int'*exp(`rep'*x-`diff`rep''))/(`sum')"
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}
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qui su mean in `i'
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local mean=r(mean)
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qui gausshermite `int',mu(`mean') sigma(`=sqrt(`var')') display
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qui replace proba=r(int) in `i'
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}
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}
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}
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qui gen eff=.
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forvalues i=0/1 {
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qui replace eff=proba*`n`i'' if group==`i'
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}
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qui replace eff=proba
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qui keep item* eff group proba
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local p1=1/`n1'
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local p0=1/`n0'
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qui gen eff2=.
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qui replace eff2=floor(eff/`p1') if group==1
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qui replace eff2=floor(eff/`p0') if group==0
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qui replace eff=eff-eff2*(`p1'*group+`p0'*(1-group))
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qui su eff2 if group==1
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local aff1=r(sum)
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qui su eff2 if group==0
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local aff0=r(sum)
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local unaff1=`n1'-`aff1'
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local unaff0=`n0'-`aff0'
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qui gen efftmp=eff2
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qui gsort + group - eff
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qui replace eff2=eff2+1 in 1/`unaff0'
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qui gsort - group - eff
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qui replace eff2=eff2+1 in 1/`unaff1'
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qui drop if eff2==0
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gsort group item*
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qui expand eff2
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qui drop proba eff eff2
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}
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qui alpha item*
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local alpha=r(alpha)
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qui gen groupc=group-.5
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if `nbmodat'==2 {
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qui gen i=_n
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tempname diff
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matrix `diff'=`dd''
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qui reshape long item, i(i)
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qui rename item rep
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qui rename _j item
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qui gen offset=0
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forvalues i=1/`nbitems' {
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qui replace offset=-`diff'[1,`i'] if item==`i'
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}
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constraint 1 _cons=`=ln(`var')'
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qui xtlogit rep groupc ,nocons i(i) offset(offset) constraint(1)
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tempname b V
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}
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else {
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matrix `db'=`db''
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*di "qui pcm item*, fixed(`db') covariates(groupc) fixedmu fixedvar(`var')"
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qui pcm item*, fixed(`db') covariates(groupc) fixedmu fixedvar(`var')
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}
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tempname b V
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matrix `b'=e(b)
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matrix `V'=e(V)
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local gammaest=`b'[1,1]
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local se=`V'[1,1]^.5
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di
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di
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di in gr "{hline 91}"
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di _col(60) "Estimation with the "
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di _col(50) "Cramer-Rao bound" _col(75) "classical formula"
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di in gr "{hline 91}"
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if "`gammafixed'"=="" {
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di in green "Estimated value of the group effect" _col(59) in ye %7.2f `gammaest'
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}
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di in green "Estimation of the s.e. of the group effect" _col(59) in ye %7.2f `se'
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di in green "Estimation of the variance of the group effect" _col(56) in ye %10.4f `=`se'^2'
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local power=1-normal(1.96-`gamma'/`se')+normal(-1.96-`gamma'/`se')
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local poweruni=1-normal(1.96-`gamma'/`se')
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local clpower=normal(sqrt(`n1'*`gamma'^2/((`n1'/`n0'+1)*`var'))-1.96)
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di in green "Estimation of the power" _col(60) in ye %6.4f `poweruni' _col(86) in ye %6.4f `clpower'
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local clnsn=(`n1'/`n0'+1)/((`n1'/`n0')*(`gamma'/sqrt(`var'))^2)*(1.96+invnorm(`poweruni'))^2
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di in green "Number of patients for a power of" %6.2f `=`poweruni'*100' "%" _col(59) in ye `n0' "/" `n1' _col(77) in ye %7.2f `clnsn' "/" %7.2f `=`clnsn'*`n1'/`n0''
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local ratio=(`n0'+`n1')/(`clnsn'*(1+`n1'/`n0'))
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di in green "Ratio of the number of patients" in ye %6.2f _col(68)`ratio'
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if `expectedpower'!=-1 {
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qui sampsi `=-`gamma'/2' `=`gamma'/2', sd1(`=sqrt(`var')') sd2(`=sqrt(`var')') alpha(0.05) power(`expectedpower') ratio(`=`n1'/`n0'')
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local expn_1=r(N_1)
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local expn_2=r(N_2)
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local expn2=`expn_1'*`ratio'
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di in green "Number of patients for a power of" %6.2f `=`expectedpower'*100' "%" _col(51) in ye %7.2f `expn2' "/" %7.2f `=`expn2'*`n1'/`n0'' _col(77) in ye %7.2f `expn_1' "/" %7.2f `expn_2'
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}
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di in gr "{hline 91}"
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return scalar EstGamma=`gammaest'
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return scalar CRbound=`=`se'^2'
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return scalar CRPower=`poweruni'
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return scalar ClPower=`clpower'
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return scalar ClSS=`clnsn'
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return scalar Ratio=`ratio'
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return scalar CronbachAlpha=`alpha'
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capture qui use `raschpowerfile',clear
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end
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