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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£ 105 0 "m 0 o 00 0 0 95 30 0 0 00 0 0 0 ~85 en ~75 0 0 0 0 0 0 z 0 w 0 Z 4( 0 :I: 0 U 0 0 10 0 0 65 0 0 ~ en 0 :::l 0 5! 0 ..., 0 0 0 0 0 30 0 w 0 0 0 0 0 0 0 0 m 10 ::::; If 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 o 0 0 0 0 0 ~ ~ U-lO 00 0 0 0 0 0 00 0 0 0 0 co 0 0 0 0 BASELtE DlASTOUC BP 1284 0 000 0 0 0 eO 0 o~o 0 0 0 0 00 0 0 0 0 0°0 0 -20 55 105 o o 4( "s" 0 ~o 0 0 0 0 0 FIGlR: 3 CHANGE tl DlASTOUC lIP ON DRUG VS BASEUE SHOWN3 APPARENT 1£GA11VE llFFERB'ffiAL EFfECT 0 0 0 0 0 0 000 q,0 00 -10 65 75 B5 95 BASELtE DlASTOUC BP iil en 0 0 0 0 0 D~OD o ~2O 0 0 0 0 0 0 0 0 0 Cl 0 00 000 00 0 0 0 0 00 0 00000 00 0 0 0 0 0 0 0 20 0 00 0 0 ~ 0000 0 00 0 0 0 00 0 3 0 0 0 0 0 86 95 BASE1..I£ DlASTOUC BP 65 76 106