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st: power simulation in longitudinal trial


From   Munyaradzi Dimairo <mdimairo@gmail.com>
To   Statalist <statalist@hsphsun2.harvard.edu>
Subject   st: power simulation in longitudinal trial
Date   Wed, 8 Dec 2010 10:44:14 +0000

Hi folks

Can anyone help me on this;

I am running a power simulation for a longitudinal clinical trials and
i have a problem simulating longitudinal data which will preserve the
observed correlation between follow-up measurements and also
covariance structure of the random intercept and coefficient. here is
my basic model;

Y[ijk] is a continous outcome for ith participant and time j [0,1,2]
and treatment k[0,1]

Y[ijk]= b0[j] + b1[j]*time[ij] +b2*treat[k] + e[ijk]

where b0[j] and b1[j] are subject specific intercept and slope
respectively which jointly follows a bivariate normal distribution
with mean[M]= (b0 \ b1) and
covariance structure[COV]= (sig2[u0], sig[01] \ sig[01],sig2[u1]). The
expected mean and covariance structure estimates came from a pilot
study.

i generated b0[j] and b1[j] jointly using ;

drawnorm b0[j] b1[j], means(M) cov(COV)

b2 is the treatment effect (effect size of 2.5 point mean difference).
study power will be the proportion of significant results from the
model below using the simulated data set

xtmixed yijk] baseline time i1.treat||id:time, reml cov(unstr)
/*baseline adjusted*/


my main problem is on how to impose the observed correlation structure
on the outcome through the error terms (e[ijk]). That is, the
correlation between follow-up measurements, in this case a 3 by 3
matrix since we have 3 time points (in rows: 1,a,b / a,1,c / b,c,1);
basically 3 parameters (3*(3-1)/2).

can anyone please help me on how to do this!! by the way, am using STATA
11.1


with many thanks

Munya

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