Grizzle's Two-Period Changeover Design
/****************************************************************/
/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: CHANGEOV */
/* TITLE: Grizzle's Two-Period Changeover Design */
/* PRODUCT: STAT */
/* SYSTEM: ALL */
/* KEYS: analysis of variance, */
/* PROCS: GLM */
/* DATA: */
/* */
/* SUPPORT: Randy Tobias UPDATE: */
/* REF: Grizzle, James E., "The Two-Period Change-over */
/* Design and its use in Clinical Trials", */
/* Biometrics, June 1965, p467. */
/* Johnson, Dallas E., "Design and Analysis of */
/* Crossover Experiments," notes from course */
/* presented at the Joint Statistical Meetings, */
/* July 2007, Salt Lake City. */
/* */
/* MISC: */
/* */
/****************************************************************/
title1 'Grizzle''s Two-Period Change-over Design';
data Grizzle;
keep Sequence Subject Period Treatment y;
do Sequence = "AB","BA";
do SeqSub = 1 to 8;
do Period = 1 to 2;
input y @@;
Treatment = substr(Sequence,Period,1);
Subject = SeqSub + 8*(Sequence = "BA");
output;
end;
end;
end;
datalines;
0.2 1.0 0.0 -0.7 -0.8 0.2 0.6 1.1
0.3 0.4 1.5 1.2 . . . .
1.3 0.9 -2.3 1.0 0.0 0.6 -0.8 -0.3
-0.4 -1.0 -2.9 1.7 -1.9 -0.3 -2.9 0.9
;
/*
/ GLM can perform an appropriate ANOVA for this data, including
/ estimating and testing differences between treatment and period
/ means. However, a correct analysis assumes a random subject
/ effect, which GLM cannot model correctly. This means that the
/ standard errors and t-tests for individual LS-means from GLM are
/ not appropriate.
/---------------------------------------------------------------------*/
title2 "Fixed effect model analysis with GLM";
title3 "Inappropriate LS-Mean Standard Errors";
proc glm data=Grizzle;
class Subject Treatment Period;
model y = Subject Treatment Period / ss3;
lsmeans Treatment Period / Stderr pdiff;
ods select ModelANOVA LSMeans;
run;
/*
/ MIXED can model the random Subject effect to give correct
/ standard errors and tests for individual LS-means. Note that the
/ tests for Treatment and Period effects, as well as for the
/ differences between LS-means, are the same as with GLM.
/---------------------------------------------------------------------*/
title2 "Mixed effect model analysis with MIXED";
title3 "Appropriate LS-Mean Standard Errors";
proc mixed data=Grizzle;
class Subject Treatment Period;
model y = Treatment Period / ddfm=sat;
lsmeans Treatment Period / pdiff;
random Subject;
ods select Tests3 LSMeans Diffs;
run;
/*
/ TTEST can once again compute the same Treatment and Period tests,
/ and in addition it produces an array of informative graphics to
/ clarify how individual subjects and measurements with subject
/ contribute to this inference.
/---------------------------------------------------------------------*/
title2 "Analysis with TTEST, including graphics";
ods graphics on;
data SideBySide;
merge Grizzle(where=(Period=1) rename=(y=y1))
Grizzle(where=(Period=2) rename=(y=y2));
t1 = substr(Sequence,1,1);
t2 = substr(Sequence,2,1);
keep t1 t2 y1 y2;
proc ttest data=SideBySide plots=all;
var y1 y2 / crossover=(t1 t2);
run;
ods graphics off;