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j R1\NllOMIZATION SCHEDULES VIA SAS John Steedi', Abbott Labs* The MATRIX procedure also provides a convenient method of computing the number of runs per treatment by block. The two different types of objects for counting the number of runs associated with treatment A, say, are: (I} treatment A and (2) not:. treatment A. Since, within each block, we have R objects of one kind (treatment A) and P-R objects of the other kind (not treatment A) the mean number of runa is In drug research it is often necessary to produce a randomization schedule which a~s1gn8 the treatment each patient is to receive. The purpose af this paper is to demonstrate,·via SAS~ the production of these tables using- Pro~edures PLAN~ PRINIIO and MATRIX, for the Randomized Block Design (balanced). Then, a check for "unusual u rand~izatipn8 is made by computing the. number of runs for each treatment by block. The concepts ~nd methods presentE::d herein can be applied to many statistical designs but OUT discussion and example will trQat only the Randomized Block DesIgn (ba.lanced) with -p.ara.met"ers B, P and T where B ~ number" of Blocks, P number of Patients per Block, T ~ number of Treatments. In OUr'" example which "follows B-3,. P=15 and T=3. Hence, the total number of pat~ents randomized is PROD = B"P ,. 45 and the "number of tTeat~ ment repeats with~n a block 1s R = p/T"= 5. Tha output Qf PROe ~LAN, in this example, is read into a new data set" via:PROC PRINTTO. Then the desired randomization schedule is produced via PROC MATRIX. E(Runs) = 1 + ZR (P-R) P the standard deviation is S.D.~[ZR = (P-R .2R (P-R) - The minimum number of runs is 2 and the maximum is 2R + 1, (when T = 2 the maximum 19 2R). These t~ parameters together with the mean and standard deviation can be used to identify "unusual II raridomizations. Returning to our example, with R=5 and P=15 we "have E (Runs)= 7.67 ana S.D. = 1.64 EXAMPLE (N~te: II EXEC 5AS IlrT2oF~01 ~xpre9Qions that need to be changed fOT. different values of B, P and T a:re preceded by comment statements and underlined). DD URIT=SJSDA,~PAC~:(TR~,{15,5) OPTlOIIS NOD ATE NOllUIlBER) PROC pRINrTO uHn=20 NEW, DATA INlTHL, *PROVIDE .VALUES OF B,P, r.ND T WHERE *S-NUMBER OF B~OCKS * T~NUMaER or TREATMENTS, *P.NUM6ER or PATIENTS P~R BLOCK, *Rep/! MVST Bt AN INT~GERI 8 m3, T-a, P.. t5, ~"PIT ; PI\ODKB"PI DATA I'!.A)l1 PI\OC PLAII I • U TH r CTORS 8"3 p" !'MC P 1111'TO, 5 or BAND 1', NO~RINTI rT~0r11lk111 INPVt~2 BLOCK ~IPUT ~IHrlLt_1 *INPUT T~E VALVE orPAs YPI DATA pTo/FtLE PRINT lNFlLt [jf-BLO¢iC>jjTHf;Nfij pliTY!;Yf51~] IF BLOCF>0 THEN OUTPUt; DROP ijLOCKI DATA DI PROC IlflTI'IIXI FETCH I)lIT O~TA=IUJTIA~1 *Developmental work on this paper was completed prior to ~plQyment at ABBOTT LABS. " p2 (P-l). e"INlT!I'); TIOINlT{t,2)I P=lNll'll,3), R=IlIlT(1,4)1 PIIOD=INITII ,5) I FETtH RANP * ~~TA=PTOI CREAT!: MUIIIC!:!! OF Ij'S ArID 1 's rOR T~1:..J;=RM!Il< (_~R7-+'-!LlLI==;:-:-;==-;-c"---' TIIT.,-=(RA'U.>Il) .. (RAND < 12"R+1lI, TRT.l~RA~D> (2*11) INT liT_I T1I1_2 TR • 1 TilT" TRT_I + (2*TIIT.2) + (3*TRT_Jl; PlltNT TRTI RUHS .. JCII, To! l; E~CH TliT, DO I- I TO U BY I, DO J= 2 TO P BY 1; * CQMPUTE THE NUMbf:R OF RUNS FOR E~H. TREATI4E~'N",T';b;-;'o,....,.......,-;-:----t ·TR'l'.;:rtT~Jl'fE-·T-iit.:;In;J~-ll THEN HUNS! I;i )~RUNSCl, I) +l' ~ I f TFT.HI,J) HE. TRT.2(I,J-ll THEN RUNSCI,2l.RUNS(I,2l+11 IF TRT_3Cl,J) HE TRT_J(I,J-ll THF.N RUNSCI,J).RUNS-n,)HII f,ND, ~NDI OUTPUT RUNS OUT=PUN, TIIT.OUT= JCPIIOD,2.011 DO I-I TO B 6Y I' DO J=1 TO P 51 11 LOC= (V*tI-I» +J I TRT.OUT(LOC,I)=LOCr . TRT.OUTtLOC,2)=TRTIl,J)/ ENDI I!:IID/ OUTPU'!' tRT.OUT OUT=TREAOUT (RENAMt:"(COl;1=PATN"O COL2=TRTl)/ PArA , SET RUN, TITLEI NUMBER OF RUNS lit TREATMENT AND nr,oCK, T1TI;E2 WHERE THE COLUMNS ARE tREATME~TS AND THE ROWS ARE SLaCKS, PRO, PRINTI JO RQ'" DATAl Sl::T l'REAOUTI ,!1~OP ROW, flTt"l RANDQMUATIQN SCHF:DULE / • IIPur TITL~ or STUDY; TITLE2 DIlUG A VS PRUG ~ IN THE TREA1'MEIoIT or KURTOSIS' Tl1')..E3 D,,,", S:rATISTICS; TlTLE4 ~OTOCOL ~01' F 7RT=1 THE'" TRTI1ENT= PLAC!;BO'; IF 'TRl'~2 THEN TRTHE~T='DP\lG.A·1 IF TilT:) TIIEIi T~T~!ENT= 'DRUG_A', pifer-t"RT, PRoe; PRlNTII0 PAT/WI ~HeRE NUMBER Or RUNS II,{ TREATMENT AND I)t.OCK TIfE COI,UHNS ARE: T~EATME:NTS AND TItE ROWS A~E: IIt.OCKS ROW flOW 1 ROW2 R01ll3 CoLI COL2 5 4 8 8 6 11 99 COL3 8 9 8 RANDOMIZATION 5CHEDULE DRUG A va DRUG B IN THE TRE~TMENT or KURTOSIS DR. STATISTICS PROTOCOL 001 PATNO TRTHENT 1 2 1 4 PLACEBO DRUc..B ORUG..A DRUG..B DRUc..A DRUG..A S 6 • • • "0 U 42 43 4r4 45 PLACEBO DRUG..A DRUG..! DRUG~A DRUG.B DRUG_B REFERENCE: Gibbons, J. D., Nonparametric Statistical lnference, McGraw Hill (1971) 100