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{* 6february2012}{...}
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help for {hi:raschpower}{right:Jean-Benoit Hardouin, Myriam Blanchin}
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{title:Estimation of the power of the Wald test in order to compare the means of the latent trait in two groups of individuals}

{p 8 14 2}{cmd:raschpower} [{cmd:,} {cmdab:n0}({it:#}) {cmdab:n1}({it:#})
{cmdab:gamma}({it:#}) {cmdab:var}({it:# [#]}) {cmdab:d:ifficulties}({it:matrix}) {cmdab:m:ethod}({it:method}) {cmdab:det:ail} {cmdab:exp:ectedpower}({it:#})]


{title:Description}

{p 4 8 2}{cmd:raschpower} allows estimating the power of the Wald test comparing the means of two groups of patients in the context of the Rasch model or the partial-credit model. The estimation is based
 on the estimation of the variance of the difference of the means based on the Cramer-Rao bound.

{title:Options}

{p 4 8 2}{cmd:n0} and {cmd:n1} indicates the numbers of individuals in the two groups [100 by default].

{p 4 8 2}{cmd:gamma} indicates the group effect (difference between the two means) [0.5 by default].

{p 4 8 2}{cmd:var} is the expected values of the variances of the latent trait (1 by default): if this option contains only one value, variances are considered as equal between the two groups; if this option contains two values, variances are considered as unequal between the two groups.

{p 4 8 2}{cmdab:d:ifficulties} is a matrix containing the item parameters [one row per item, one column per positive modality - (-1.151, -0.987\-0.615, -0.325\-0.184, -0.043\0.246, 0.554\0.782, 1.724) by default].

{p 4 8 2}{cmd:method}({it:method}) indicates the method for constructing data. ({it:method}) may be GH, MEAN, MEAN+GH or POPULATION+GH [default is method(GH) if number of patterns<500, method(MEAN+GH) if 500<=number of patterns<10000, 
method(MEAN) if 10000<=number of patterns<1000000, method(POPULATION+GH) otherwise].

{p 8 14 2} {bf:GH}: The probability of all possible response patterns is estimated by Gauss-Hermite quadratures.

{p 8 14 2} {bf:MEAN}: The mean of the latent trait for each group is used instead of Gauss-Hermite quadratures.

{p 8 14 2} {bf:MEAN+GH}: In a first step, the MEAN method is used to determine the most probable patterns. In a second step, the probability of response patterns is estimated by Gauss-Hermite quadratures on the most probable patterns.

{p 8 14 2} {bf:POPULATION+GH}: The most frequent response patterns are selected from a simulated population of 1,000,000 of individuals. The probability of the selected response patterns is estimated by Gauss-Hermite quadratures.

{p 4 8 2}{cmd:detail} allows a comparison with the classical formula (for manifest variable).

{p 4 8 2}{cmd:expectedpower} allows searching for a sample size in order to reach a fixed level of power (the obtained sample sizes take into account the ratio between $n0$ and $n1$).


{title:Example}

	{p 4 8 2}{cmd:. raschpower}

	{p 4 8 2}{cmd:. raschpower, n0(200) n1(200) gamma(0.4) var(1.3)}

	{p 4 8 2}{cmd:. matrix diff=(-1.47\-0.97\-.23\-0.12\0.02\0.1)}{p_end}
	{p 4 8 2}{cmd:. raschpower, n0(127) n1(134) gamma(0.23) d(diff) var(2.58)}{p_end}
	
	{p 4 8 2}{cmd:. matrix diff=(-0.328,-0.811,0.329\ 0.556,0.818,1.409\ 1.394,1.049,1.288\ 0.560,0.363,0.950)}{p_end}
	{p 4 8 2}{cmd:. raschpower, d(diff) n0(167) n1(205) gamma(0.178) var(0.77) exp(0.8)}{p_end}


{title:References}

	{p 4 8 2}Hardouin J.B., Amri S., Feddag M., S�bille V. (2012) Towards Power And Sample Size Calculations For The Comparison Of Two Groups Of Patients With Item Response Theory Models. Statistics in Medicine, 31(11): 1277-1290.{p_end} 
	{p 4 8 2}Blanchin M., Hardouin J.B., Guillemin F., Falissard B., S�bille V. (2013) Power and sample size determination for the group comparison of patient-reported outcomes with Rasch family models. PLoS ONE, 8(2): e57279.{p_end}
	{p 4 8 2}Feddag M.L., Blanchin M., Hardouin J.B., S�bille V. (2014) Power analysis on the time effect for the longitudinal Rasch model. Journal of Applied Measurement: (under press).{p_end}
	{p 4 8 2}Guilleux A., Blanchin M., Hardouin J.B., S�bille V. (2014) Power and sample size determination in the Rasch model: Evaluation of the robustness of a numerical method to non-normality of the latent trait. Plos One, 9(1): e0083652.{p_end}

	
{title:Author}

{p 4 8 2}Jean-Benoit Hardouin, PhD, assistant professor{p_end}
{p 4 8 2}Myriam Blanchin, PhD, research assistant{p_end}
{p 4 8 2}Bastien Perrot, biostatistician{p_end}
{p 4 8 2}EA4275 "Biostatistics, Pharmacoepidemiology and Subjective Measures in Health Sciences"{p_end}
{p 4 8 2}University of Nantes - Faculty of Pharmaceutical Sciences{p_end}
{p 4 8 2}1, rue Gaston Veil - BP 53508{p_end}
{p 4 8 2}44035 Nantes Cedex 1 - FRANCE{p_end}
{p 4 8 2}Emails:
{browse "mailto:jean-benoit.hardouin@univ-nantes.fr":jean-benoit.hardouin@univ-nantes.fr}{p_end}
{p 13 8 2}{browse "mailto:myriam.blanchin@univ-nantes.fr":myriam.blanchin@univ-nantes.fr}{p_end}
{p 4 8 2}Websites {browse "http://www.anaqol.org":AnaQol}
and {browse "http://www.freeirt.org":FreeIRT}
