Download A SAS Macro for Assessing Differential Drug Effect

A SAS® MACRO FOR ASSESSING DIFFERENTIAL DRUG EFFECT
Terrance L. Fox and Bruce Ekholm, 3M Pharmaceuticals
ABSTRACT
The graphical adjustment is:
Regression to the mean can create an
y
incorrect impression of the
relationship between drug effect and
=
x, - x, +
(1 -
r)
(X, -
X,) •
where r is the Pearson estimate of
the correlation coefficient between XI
baseline measurement. We propose a
SAS® Macro for adjusting for the
regression effect and testing for
differential drug effect. The macro
is applied to blood pressure data.
and ~, and XI is the sample mean.
A
plot of Y VS Xl will properly adjust
for the regression effect, while a
plot of Xl-Xl VS XI could be misleading
(Figure 1).
INTRODUCTION
A nonzero slope for the
plot of Y VS Xl indicates a genuine
differential effect.
A common method for assessing the
effect of a drug or other treatment
on a measurement is to compare
baseline with postdrug, using each
patient or subject as its own
control. If there is an overall
increase between pre- and postdrug,
then the effect may be less important
if the increase is less for patients
with high baselines than for those
with low baselines. The problem is
that an apparent differential effect
may simply reflect a regression to
the mean. Even if there is no drug
effect whatever, patients with high
baselines will tend to have lower
second readings. Similarly,
regression to the mean could mask a
true differential effect.
To test for differential effect, the
statistic
T = j(n - 2)'"
(,L ~)/(1 - r)'"
S2
Sl
has a Student1s t distribution with
n-2 degrees of freedom, where n is
the sample size. This is equivalent
to the Pitman-Morgan test for
equality of correlated variances
(Pitman, 1939; Morgan, 1939).
EXAMPLE
This procedure is illustrated with
diastolic blood pressure data from
141 subjects in a multicenter
clinical trial. The baseline blood
pressure (XI) was recorded after seven
days on placebo, and the on-drug
value (~) was recorded after fourteen
days on drug.
Figure 2 shows the
plot of on-drug vs baseline, and
Figure 3 shows the plot of change
from baseline vs baseline (Xl-XI vs
Xl).
This plot shows an apparen.t
negative differential effect, w1th
large baselines having smaller
changes in blood pressure. Figure 4
shows the plot of adjusted change
from baseline after removing the
regression effect (Y vs XI)' which
demonstrates that there was no
differential effect. The test
statistic was T=O.84, with 139
degrees of freedom, which was not
significant (p=O.4027).
Berry, Eaton, Ekholm, Fox
(Biometrics, 1984), have proposed a
method for adjusting for the
regression effect, and a
corresponding test for differential
drug effect. We propose a SAS macro
which implements this procedure, and
adjusts postdrug differences for the
regression effect. The macro also
provides the Berry, et ale t-test for
differential drug effect, which is
equivalent to the Pitman-Morgan test.
The macro calculations are
illustrated using blood pressure data
from a multicenter clinical trial.
GRAPHICAL ADJUSTMENT AND TEST
STATISTIC
Let XI be the baseline measurement,
and Xl be the on-drug measurement. If
bivariate normality is assumed,
CONCLUSION
Casual analysis of change from
baseline data can be misleading when
trying to assess differential effect.
Proper adjustment for the regression
effect should be done.
(i:) - N{(. ~ <l)' (.:.~, P:t)}
where ~ is the additive effect of the
drug on the measure (note, A could be
zero).
1281
~"'" flND TIlE ctlRRELAlH1N COEFfiCiENT AND SUI"tIARY STAT!STlCS
ACKNOWLEDGMENT
PRoe CORR OUTP-CORROUT
NOP~IHT OA1A~RE;
Uf B~BiB;: UHEH "00;
'lEND;
•
The authors wish to thank 3M
Pharmaceuticals for permission to use
VAil &Xi &X2;
the data displayed in Figures 2-4.
OA1~F tJi~ '~El~~~~Y"~~ARl tBAR2) 10 K£EP-&IIY 10/
so (I:~EP.a.ay SOl S02) CORR (n~p-&BY Rl,S T
COIIIIOI)T;
'lEND;
AUTHOR CONTACT
'IElSE 100·
DATA ~5A~K~~~~~O~B~t~) X~t~~) (~[~~;~~:~~T CORROUT;
'lENO,
For additional information, please
contact
IF xJX:~-.:&~r~AN'xJ~~~
END;
~°i.X2;
IF
TYPE "·10· THEN 00;
ENO~ ~ &Xl;
Terry Fox or Bruce Ekholm
3M Pharmaceuticals, statistical
Data Services
IF
TYPE
•
IF
TYPE •
&Y2.
OUTPUT 10;
'STO· THEN DO·
$02 ~ U2;
ENO~1 .-&XI;
3M Center, Bldg. 270-3A-01
st. paul, MN 55144-1000
(612) 733-4264 or (612) 736-0657.
END~
CORR' AND
OUTPUT rEAN;
NAME
-
OUTPUT SO,
"&Xl" Tl1EN DO,
OiJTPUT CORR;
OATA ",DJ,MERGE MEAN N SO CORR MNOIf;
UF &BY -. UIIEN "00;
IENE; &BY;
REFERENCES
DEN. SCIRTO _ R •• Z)·
S • ASS(SDl I S(2) - lS02 I SOll/,
T_OE - (.5 * SQRl(N - ~l' S) III N;
Rofig~~~(r-7~~pWA t{T_IlE,tt-2)l •. OOOI);
Berry, D.A., Eaton, M.L., Ekholm,
B.P., and Fox, T. L.
(1984).
pJl;
"Assessing Differential Druq Effect .. "
1~ ~=8h\·oggbIT~~~/,,~5IF ~·g~gbil1;
Biometrics 40, 1109-1115.
.,,- PRINT THE TESTS FOR AOOITIVE AND OIFFERHITI",l EFFECTS
Morgan, W.. A.
(1939) .. uA Test for the
PROC PRINT SPLIT··"
Significance of the Difference
Between the Two Variances in a Sample
from a Normal Bivariate Population."
NOOBS;
Ilf B~Bill~~ "THEN '100;
'lEND;
•
V",R 10 XSARl SOl XBAR2 S02 foIN_OIF SO_OIF T_IlIF P_OIF
T_OE P_OE;
Biometrika 31, 13-19.
LABEL 10
XB"RI
,0>
XBAR2
pitman, E.J.G. (1939).
"A Note on
Normal Correlation.'1 Biometrika 31,
9-12.
$02
MM OlF
SO-Olf
T D"IF
P-OIF
~:g~
fORMAT P_DIf P_OE S 4
T elF T_OE 6.2;
IIF &F A_ "THEN IDa;
FORMAT XBARI SOl XBAII2 ::;02 MN "If S:l_OIF B.&f;
l£NO;
-
SAS is a registered trademark of SAS
Institute Inc., Cary, Net USA.
TEtE "T-TESTS FOR Aoonl~E AND DIFFERENTIAL EffECTS';
*""
CALCULATE TilE ADJUSTMENT FOR THE REG.RESSION EFFECT ",NO PLOT
THE RESULTS ",u;
DAlA ADJOIF (OROP=_X _Ill ,MERGE liE AoJ;
"IF &BY -~ nHEN "Oil;
'.I.ENE~ &BY;
-';EL~hl~2'
MACRO LISTING
X _R
IF XBARI ; . THEN 00,
XBARI "_X, R' _R;
ENO;
_x
. . . TillS MACRO ODeS THE ADJUSTI'!G FOR ltiE-REGRESSIOti EFFEel
FOR AMY TWO BEfORE - AFTER ~ARIABLES " ' ;
;<u
'''I,
XBARI;
_R
1
R,
OIF - U2 - &Xl;
ADJOlf ; &X2 _ XB"RI - (R· (UI
~~~I~~~~O (~~~~J~~~ ~~hO~~~~~~L~AM~2 \OA~~~N) 6y!H~A~~lni~E
AMO 11010 MAllY DErIMAlS TO PIIIII-T
DEV "TlONS (F) ,,,...
~
'lENO;
tKf fl£AN ANO STANDARD
XBARll);
PROC PLOT
"IF &BY
nllEN "00;
UNE~ &BY,
A:
'lM"CRO REGEFF(D"TAiN Xl.X2.B~.F);
OPTIONS OClU01£;
nnE (~~lo¥l~lgm~dE;cgl.i.ND ",DJUSTEO DiffERENCES fOil &X2-;
DATA RE;SET &OATAIII-;
--" DElETE RECORDS IOIlI! B"SEL:t!E OR POST IHSSIMG
If &Xl'
(lR &X2"
Olf " &X2 - &.Xl,
lMENO REGEFF;
TkEIO OElETE;
;>R~~f stn ~ATl!~~~B~O~6Y;
'lEND;
""" CALCULATE TilE PAIRED T-TEST
PRDC MEANS ItoPRINI MEAH STO T PRT;
'llf &8Y '= "THEN '100;
BY &BY;
SEND;
~t~p~V ~UT
• MNOIF
MEAN ~ MN_Dlf
SID" SO_OIF
T - T_Otf
PRT" P_OIF,
1282
Figure 1
Bivariate Normal contours Showing Differential
Drug Effect
y
o
No Differential Effect (0',
o
0',)
y
o
Negative Differential Effect (al < a 1 )
o
y
positive Differential Effect (al > all
1283
o
FIGlR: 2
FIGlR: 4
CHANGE tl DIASTOLIC lIP ON DRUG VS BASEUIE
AFTBl AruJSThENT FOR ll£ REGRESSION EFFECT
SHOWtIG NO DFFEREN11AL DRUG EFFECT
DIASTOLIC BLOOD PAESSlIlE ON DRUG VS BASEI..I£
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FIGlR: 3
CHANGE tl DlASTOUC lIP ON DRUG VS BASEUE
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