Download Generating Statistical Tables Meeting NDA Guidelines the Lazy Way

GENERATING STATISTICAL
TABLES MEETING NDA GUIDELINES
THE LAZY WAY
JohnC. Lue
Allergan, Inc.
4. Generate tables using PROCTABULATE and have an
administraive person type the p-values and perform other
cosmetic work to this electronic table.
Introduction
Generating statistical tables that will satisfy Food and Drug
Administration (FDA) guidelines for a New Drug Application
(NOA) can be an onerous, time consuming task. According to
the guidelines (FDA), the statistical tables summarizing the
following analyses of the main efficacy variable(s) are required:
The disadvantage of #-3 is that when a new version of $ASl'M
comes out. the program may need to be rewritten to
accommodate the possible shift in columns on the printout. The
disadvantage of #-4 is that it is very time consuming and
potentially disastrous if errors in the data set warrant reanalysis.
1. A n overall analysis including p-values for the drug and
drug-by-investigator interaction effect.
2. 95% confidence intervals
3. power calculations
4.5 tatistical analysis variable broken down by investigators.
5. A nalysis of variance tables
Generating Tables In Version 5 vs. 6
In version 5 of SAS, the process of generating statistical tables
might involve the use OfpROC TABULATE. Tables are transferred
electronically -to a word processor Q.e. WOR£YM, WORD
PERFEClTM, etc.), p-values produced byGLM ARE transcribed to
the table by a secretary (very time consuming)10 produce a final
product.
6.1 ntent-to-treat analysis
This is only a portion of the NDA application and does not
include the safety section.
In using version 6, the process of generating tables might look
like the following:
The purpose of this paper is to present a way of generating
statistical tables quickly eliminating much of the drudgery by
utilizing SAS"" and SASjSTATI'M This paper discusses:
1. Descriptive statistics are produced by PROC MEANS
2,p·values are produced bYGLM and merged to a table
1. Past and present procedures in generating
produced byPROC MEANS. The result?
statistical tables.
2. Producing a table which includes p-values for
the drug and drug-by-investigator effects for a twoarm parallel trial
3. Producing a table for a two-arm parallel trial
table with statistics broken down by investigator.
4. What you can do with an output of least squares
means.
5. Producing tables for a combination drug trial
6. Creating analysis of variance tables
7. Generating tables with least squares means, confidence
intervals, and power calculations
8. Comment on preferred and Intent-to-treat
no transcription
minimal use of administrative support
Example #1 :Two Arm Parallel Trial
A typical pivotal study for a NDA will usually have multiple
investigators, two treatment groups (drug and placebo), subjects
randomized to one of the treatment groups, baseline period, and
follow-up visits. One wants to produce a statistical table in the
format as shown in Table 1. To do this, the following is
suggested:
analysis
data step
(select protocol specific data -preferred an
This paper is restricted to the case where the main efficacy
variable is continuous, normaJlydistributed, and analysis of
variance is the statistical method of choice.
'lysis)
create data set with baseline data (dsnBL)
create data set with changes from baseline (dsn:CHNG)
append data setsBL andCHNG
compute descriptive statistics (dsnDATA1)
compute p-vaJues viaGLM (dsnPVAwE)
Statistical Tables. Past and Present
In the past and possibly the present, statistical tables were
produced by the following procedures:
PROC GlM OUTSTAT=PVALUE NOPRINT;
1. produce tables by Writing own procedure in FORTRAN, BASIC.
DRUG INVlD~Y WEEK;
MODEL DIFF =DRUG lNVlD DRUG'llfNVIDjss3;
CLASS
PL1,etc.
2. Produce printouts utilizingSAS'nII. BMDp'l"M, SPSSTH, etc. and
(OIFF is the dependent variable, invid is the investigator
then photocopy the printouts.
3. Use SAS's PROCPRlNTTO in which one transfers certain
statistics from an electronic printout to a SASTM data set, and
effect,)
mergeDATA1 andpvALUE data sets
output a hard copy in the format you want.
1185
to create, a table is shown in Appendix 4. For power calculations
one can use the following algorithm (or an equivalent) to
compute the power of the test (Dixon and Massey):
output table (procPRINT,PUT, etc.)
Appendix 1 presents a suggested SAS code for this example.
Example #2: By Investigator Analysis
where d = tJ. /standard error
tJ. = clinical difference
df = degrees of freedom
(The normal approximation can be replaced by the tdistribution for small sample sizes.)
In breaking down the analysis by investigator the following
strategy was carried out:
.• compute descriptive statistics by investigator, drug,
time
The power is based on the probability associated with Z1{j'
• compute Levene's test (see Appendix 3 for the SAS
code) for the test of homogeneity of variances (Milliken
and Johnson)
A source code is presented in Appendix 4.
Example #4: Three Treatment Groups or More
• use PROC GlM with the ~ option to compute the
p-values, degrees of freedom and other statistics
There are times when there are three treatment groups involved
in a pivotal study, For instance, in an adjuvant drug trial, the
sponsoring company must show that the combination drug must
be significantly better than the individual components, To
generate a statistical table summarizing this type of trial, the
following strategy is suggested:
i.e. (SAS CODE)
PROC GlM OUTSTAT =STAT2NOPRINTj:LASS DRUG;
BY INVID WEEK; MODEL DIFF =DRUGjss3;
compute descriptive statistics rROC MEANS)
from data setsTA12, compute t-statistic
• utilize GLM and output p-values and least squares mean
estimates as discussed before
I=sqr\(f)
Table 2 presents the desired statistical table summarizing the
analysis broken down by investigator. Appendix 3 presents the
source code to produce the table.
• perform data steps to get data in usable format (I,e.
PROC TRANSPOSE)
• compute t·statistics from output of lSM 's using the
strategy suggested in Example #3.
Example #" 3: lSM's, Confidence Intervals. Power
Calculations:
• merge data sets
Since most clinical trials are unbalanced because of missing
data, drop-outs, disqualifications, etc. , a table of least squares
means (LSM) is necessary (see Milliken and Johnson) ..
• output
Table 4 presents a statistical table where the degrees of freedom
from the ANOVA, t-statistic of the pair-wise comparisons along
with the p-values and other statistics. Appendix 5 presents the
source code.
In creating a table of LSM's, the following source code was used
in which a sas data set of LSM's PUT=SUGIA.LSM) is created,
PROC GlM OUTSTAT =PVAlUE NOPRINT;
CLASS DRUG INVID~Y WEEK;
MODEL DIFF =DRUG lNVlD DRUG "INVID jss 3;
lSMEANS DRUGtPD1FF STOERR OUT=SUG1A,lSM;
Example #5: ANOVA Tables
lastly, if ANOVA is performed, anANQVA table should also be
presented. In creating analysis of variance tables, one should
use output from ~ = option in GLM. The data set created
by~ contains statistics shown in Appendix 6. With this
data set, one can manipulate the numbers to produce tables
shown in Tables 5 and 6 which describes ANOVAat each visit for
a two-way analysis of variance and a table for repeated
measures ANOVA, respectively.
The following statistics is contained in a least squares means
data set:
OBS YEEK _NAME_ DRUG LSMEAN STDERR
3
6
7
o
1
4
DIFF
DIFF
DIFF
1
2
1
190.952 0.20708
-21.9480.45822
-22.665 0.29601
lotent-To-Treat Analysis
From the above, one can create a table as shown in Table 3.
Two types of analyses are most likely presented in an NOA:
preferred analysis and an intent-to-treat analysis (ITI), A
preferred analysis focuses on data that is protocol-specific. M
intent-to-treat analysis may include all data or may data specific
Tables summarizing confidence interval and power calculations
can also be created from the statistics contained in a least
squares means data set output. A source code describing how
1186
to definitions described by Gillings and Koch.
The result is minimal use of adminitrative support, cuts down the
amount of time in generating tables of analyses of patient
subsets, and saves time.
Using the strategies already discussed, one can produce tables
quickly for both types of analyses by utilizing one of the
following strategies:
REFERENCES
1. Create a SAS program that hard codes data that is to be
1. Dixon W. and Massey F. Introduction to Statistical Analysis.
excluded due to protocol violations and use a %INCLUDE in the
main body of a program described above. For instance:
MC9raw Hill, 1969: pgs. 270-272
2 Gillings O. and Koch G. The Application of the Principle of
Intention·To-Treat to the Analysis of Clinical Trails. Drug
information Journal, Vol. 25, pp. 411-424, 1991
/* subjects deleting from the statistical analysis */
1* exclude INVEST #
1
•/
if invid::: 1438 then delete;
1* disqualified
*/
if patid:::. 404 then delete;
1* never received drug
*/
if patid =200 then delete;
1* changed mind (e participation */
if patid=512 then delete;
/* change of bp medication
*/
if (patid =202 and visit> = 4) then delete;
/* multiple visits within a study period */
if (patid=409 and visit=6) then delete;
3. Food and Drug Administration. Guideline for the Format
and Content of the Clinical and Statistical Sections of an
Application. July, 1988
4. Milliken G. and Johnson D. Analysis of Messy Data,
Vol. I: DeSigned Experiments. Lifetime Learning
Publications, 1984.
Author Contact:
John C. Lue, M.S.
OR
Allergan, Inc.
2525 Dupont Dr.
Irvine, Ca. 92715
Create a code for each protocol violation in a SAS data set.
(714) 752-4737
I.E.
value code
0= 'Data Analyzed';
1 ='BPS < 140/90 mm Hg'
2",,'Short Washout'
3='PM Exam'
4 = 'AM Drops'
5 = 'Multiple Visit'
6='Change Meds'
7 = 'Interim Visit'
8='PM BL Exam'
9 = 'Improper Entry'
10='Not Enter Study'
11 = 'Disqualified'
=
Insert IF CODE 0; for the preferred analysis in the program.
For the ITT analysis, if the codes 8 and 9 do not meet the
definition of an ITT, just insert If (code=8 or code=9) then
de1ete in the programs. Tables should be quickly generated.
SJMMARY
UTILIZINGPROCS MEANS ANDGLM WITH THEOUTSTAT
ANDOUT=LSM OPTIONS, TABLES CAN BE EASILY
GENERATED TO MEET NDA GUIDELINES REQUIRING TABLES
WITH:
A. DESCRIPTIVE STATISTICS WITH P-VALUES
B. ANALYSIS BY INVESTIGATORS
C. CONFIDENCE INTERVALS
D. POWER CALCULATIONS
E.ANALYS!S OF VAR!ANCETABLES
1187
1* STATS
SAS, SASjBASE and SASjSTAT are registered trademarks of
SAS Institute, Inc.
1* 10P2 IS
IS THE DATA SET FOR THE GROUP MEANS
/* REF: MIWKEN AND JOHNSON
1*
ANALYSIS OF MESSY DATA, 1984 PG. 19
APPENDICES
*'
THE DATA SET FOR THE RAW DATA
"
APPENDIX 1: Two-ARM PARALLEL TRIAL
PROC SORT DATA =STATS1=\Y INVlD DRUG WEEK;
DATAALL;SETSUGI.lOP2;
DATA BASE;SET ALL; IF WEEK=O; j*MERGE BASEUNE WITH
DATA LEVENE;r..1ERGE IOP2 STATS1=\Y INVID DRUG WEEK;
"
"
PROC SORT DATA =IOP213Y INVlD DRUG WEEK;
CHANGE FROM
Z =ABS PIFF -MEAN);
1<1
PAOC SORTt\Y INVID WEEK;
*j
DROP DIFF;
j*BASEUNE
DATA BASE;SET BASE;
PROC GLM NOPRINT OUTSTAT =LEV':::LASSES DRUG 1=\Y INVID WEEK;
MODEL Z = DRUG foS
3;
DIFF =lOP;
DATA lEV2;SET LEV;
DATASET;SET ALL;
IF WEEK = 0 THEN DELETE;
IF _SOURCE _ ='ORUG';
PROC APPEND BASE =SET DATA = BASE; /*APPEND BASEUNE WITH
KEEP INVID WEEK LEVENEP;
LEVENEP :PROB;
wI
CHANGES
/* LEVENE TEST
l*cAlCULATE DESCRIPTIVE STATISTICS
*j
END
1</
Appendix 3: Analysis By Investigator
PROC SORT DATA =ALL3~Y DRUG WEEK;
PAOC MEANS N MEAN 8TO NOPRINT DATA =AlL3;SY DRUG WEEK;VAR
DIFF;
/*GENERATE P.lJAlUES FOR EACH INVESTIGAlUR
OUTPUT OUT =STATS N =N MEAN =MEAN STD =SlD;
PROC GLM OUTSTAT=STAT2NOPRINT;CtASS ORUGt\Y INVID WEEK;
DATA DRG1;SET STATS;
IF DRUG = 1;
j*OATA STEP
wI
/*CAN MODIFY TO SUIT FORMAT Of TABLE
MODEL DIFF =ORUG/3S3;
*1
DATA OF;SET STAT2;
N 1 =N;
IF _SOURCE _ ='ERROR';
MEAN 1 =MEAN ;
KEEP INVID WEEK OF;
SID 1 =SID;
DATA PVAL;SET STAT2;
= 'SS3';
KEEP WEEK N 1 MEAN 1 SID 1;
IF JYPE _
DATA DRG 2;SET STATS;
/*CALCULATE THE T .:fSTATlSTIC
IF DRUG =2;
N2""N;
IF _TYPE_ ='SS3'THEN T=SQRTf):
*/
PVALUE =PROB;
MEAN 2 ""MEAN;
KEEP INVID WEEK T PVALUE;
5T02=5TO;
KEEP weEK N2MEAN2STD2;
DATA ALL;fv1ERGE OF PVAL13Y INVID WEEK;
PROC SORT DATA =LEV2;BY INVID WEEK;
DATA ALLST;fv1ERGE DRG 1 DRG2;SV WEEK;
DATA ALLST;MERGE ALLST ALL LEv2t\y INVID WEEK;
PROC SORTt\Y INVID;
j*GENERATE PoVALUES,LEAST SQUARES MEANS AND STANDARD
ERRORS
*/
*1
PAOC PRINT SPUT ='*'OATA =ALLST;
PROC SORT DATA =ALL3;SY WEEK;
tABEllNVID = 't-lVESTIGATOR 'OF = 'D:GREES OF *FREEDOM'
PROC GLM OUTSTAT=SUGIA.STAT2 NOPR!NT;t::tASS DRUG !NVID,:3Y
PVALUE = 'P-VALUE'T
WEEK;
LEVENEP ='LEVENES *TEST'
=T -STATISTIC'
1 ='R..AcEBO*~N'STO 1 ='STO'
MODEL D!FF =DRUG !NVlD DRUG ~NV1D /5s3;
N 1 ='N'MEAN
LSMEANS DRUG fl'D!FF STOERR OUT=SUGIA.LSM;
N 2 = 'N' MEAN 2 = 'Q:lUG *rvt=AN' STO 2 = 'STO't\Y INVlD;
/*CREATING DATA SETS WITH P.lJALUES AND DEGREES OF FREEDOM
ID INV1D;
*j
FORMAT MEAN
DATA DRUG;SET SUGIASTAT2;
INV.;
1 STO 1 MEAN2sT02 8.2LEVENEP T PVALUE 5.31NVlD
IF _SOURCE_ ='DRUG';
VAR WEEK N 1 MEAN
PVALUE 1 =PROB;
TITLE 6 'TABLE 9.6';
1 STO 1 N2MEAN 2STO2 LEVENEP
KEEP WEEK PVALUE 1;
TITLE 7 'SYSTOUC ROOD R:iESSURE (v1M
DATA DI;SET SUGIASTAT2;
TITLES '.ANALYSIS BY NVESTlGATOR'i
T OF PVALUE;
1-13)';
IF _SOURCE_ ='DRUG*INVID';
ApPENDIX 4: CONRDENCE INTERVALS AND POWER CALCULATlONS:
PVALUE2=PAOB;
KEEP WEEK PVALUE2;
/* calculate confidence intervals * /
diff1 = Ism3-lsm1;
var1 = (se1*se1) + (se3*se3);
stderr1 =sqrt(var1);
diff2 = Ism2-lsm 1;
var2= (se2*se2) + (se1*se1);
stderr2 =sqrt(var2);
t13= (diff1)jstderr1;
t12= (diff2)jstderr2;
P13 = (1-PROBT(ABS(T13),DF))*2;
DATA PVALUES;r..1ERGE DRUG DI,:3Y WEEK;
output statements Q.e.PROC PRINT, PUT ,ETC.)
Appendix 2 - levene's Test:
1*
CALCULATE LEVENE'S TEST FOR HOMOGENBTY OF VARIANCES
*/
1188
Appendix 5: ComblnaUon orug Trial
P12 • (I.PROBT(ABS(T12),0F)"2;
f = finv(O.95,1 ,df);
j*GPOUP I VS 3
t - sqrt(f);
LOW13 ~ OIFFl • T*STOERR1;
UP13 = OIFFl + T*STOERR1;
LOW12 - DlFF2· T*STOERR2;
UP12 _ DlFF2 + T*STOERR2;
1*
LSM3ls
*j
TliE lEAST SQUARES MEAN
OF GROUP 3
j*LSMlIS GPOUP 1 ETC.
'·SElIS THE STANDARD ERROR OF GROUP 1
,*VAR 115 THE VARIANCE OF THE DIFFERENCE OF
1* power caluclationl
*1
I·THE ESTIMAlE OF THE TWO ESTIMATES
f • finv(O.95.1.df)~
I - sqrt(f);
A = 1.21*~·I.06)/df;
A = A +1;
013- 2jSTDERRI;
012- 2/STOERR2;
012=012/A;
013=013/A;
TBETAI2=012· T;
TBETAI3=013· T;
POWER12 = PROBT(TBETAI2,0F);
POWERI3 = PROBT(TBETAI3,0F);
OIFF 1- LSM 3-LsM 1;
DIFF
DIFF
DIFF
Dl FF
DIFF
DIFF
DIFF
DIFF
~E2'SE2)
VAR2=
+
~EI'SE1);
STOERR2~jlAR2);
/toMPUTAT10N OF THE T -6TA"TISTlC
T13- ~FF l)foToERR I;
T 12-"'FF 2)f.;TOERR 2;
/'PJJALUES ARE CALCULATED
•/
*'
p13. (I.pROBT"as(r13)PF»"21'12 = (I.pROBT!las(r12)pF»"2;
ERROR
DRUG
INVID
DRUG*INVID
ERROR
DRUG
INVID
DRUG*INVID
ERROR
160 634.76
2.08
2
5
9.46
10
58.10
143 1023.44
13.29
2
5
57.52
10
46.15
553
553
553
ERROR
553
553
553
PROB
F
0.2617 0.77010
0.4767 0.79324
1.4645 0.15723
0.9286
1.6075
0.6448
0.39748
0.16178
0.m33
TABLE 1
-
T'VIIO-oARM PAAAllEL TRIAL
-12.34
-
1t1.011
190.'7
.... "
• PI""'
....
st"
,... "
,.OJ
"
,... .."
• ,." -H." t.n "
.J
"
.
-U.17
-22.17
1.7.
..
.... '·'.'un
,...
....
.....
,... .....
,...
..... .....
ST"
·tl.7Z
-11.13
-II."
-ZI.U
.
""'*lfIWHt
O.HI
1.71
0.7111
0 ....'
0.102
0.7.
J.tS
TABLE 2
ANAlYSl5 BROI<EN DowN BY INVESnGATOR
.. .• ..
•
"'
.J
IS
IS
I
...
-
PI_
-ll.OJ
IfI.41
-22.71
II
-ZJ.95
"
• ..""
•
-23.46
I
.J
I
I
*/
1*G>,p tvs 2*j
TABLES
r.....u"tor
*1
DlFF2- LSM2uM 1;
55
0
0
0
0
1
1
1
1
*'
*'
VARI= ~EI'SE1) + ~E3'SE3);
STOERRI-saRTjlAR 1);
Appendix 6: Raw ANOVA Results From an OIITSTAT oata set
5
6
7
8
9
10
11
12
*1
..
17
-21.SS
It1.11
-ZZ.44I
-22.04
-12.11
•
,... ••
,... •
•
. ., ••
••
•
STI
....
2.37
-11.17
2.91
-12.89
-12.M
7
IIO.n
•• SO
-21.11
1.12
-24.40
191.20
-U.90
-U.JG
-ZI.5CI
3.91
1.11
1.51
1189
'TO
''ftt
t-.t..ttsuc
1.75
0.617
0.011
1.551
0."5
0.140
1.312
1.101
..'"
2.Zt!
. " ..... .....
.....
,...
2.1t
I."
.....
.....
',nz
,... .....
.....
3.1.
,,......
'.54
0.100
'.551
1 ....
........f
,-..
,-,,,I_
n
"
0.4"
U ••
•. 1_
It
It
"..
.."
"
'.te
'.114
...............
'.01'
'.1.
TABLE 3
lEAST SQUAFES MI:AN ESnMAlES
PI.....,
-
.,"
-3
••
.,"
D.n
190.'
-U.t
0.31
0.30
0.33
-n.'
,~,
-U.8
I.U
-r2.7
.........
.........."
Lent Sqwrn
,~,
-U.3
191.0
-22.3
•,
....
st._rei
....st $qua,,"
....
-u.'
0.0
-fl.O
TABL£ 4
THREE GIO)UPS 011 MOllE
.,,"-.•, " ...-"" .... ....• ""-..... ... ....- ....... . "" ... ..... ""...... ,·,.1...........
..... ....
..... .... ..." ........ . ....
..
..,
"
(OOMBINAllON DRUG STUDY)
•
It
••
.td
St•
-It.S.
Ill.ae
-12.31
-12.'7
-.12.13
-11.n
'.m
-11 .•7
171.00
-II.JS
1.71
170.11
-11.13
-11.13
-11.ZS
1.16
2.11
t
"
S.25
-1l.CS
-11.to
''0000
•• SS
1.11
-0."
'"
'SI
'"
1.15
2.51
1-,.1_
D.57
.. 15
S.'7
'.171
- ,-
_N
....
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~
3.'765
•. 2651
1t.'SII
..034
IIIYID
DInIG·rIlVID
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,
. ..,.,
•
5
10
1.0381
,..
•
J.I9U
5.1'01
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ORtti-lniO
5
10
3.9612
6.5458
11.5046
C.6IU
7.JS69
."'10
ORtJi·tnlO
,·,.1..
0.167
5
10
'.101
2.113
0.471
"4'5
l.tH
1.601
0.645
'43
.........,
I.Ul
0.710
0.193
0.151
0.391
0.161
o.m
TABLE 6
ANALYSIS OF VARIANCE TABLE"'REPEAlBJ MEASURES
.......
..... --
"'"
",
•
•
'r,JI.
:Iwtt
II!It<J
OOUG
nNtlt
DIIUG"INVtD
PAIIDCDRUG"IMVIO'
IC8.195
1'1.899
...........
"''''
.....
IIWID-'€[l
a.uG-INVIO-wtn:
12.1.01'
IS.71S
IS.1«1
7.S8J
2.435
14.640
1.211
3.839
91,S'
3
3
U
"
212
"'1'fIh-F_lll a4Jvst.ftl '-ct.r ..
'_It
36.961
.....
1.693
11.619
'.'13
1.915
'.6].01
3.113
'.]]1
•• tol
c'.tol
'.10.
'.119
'.S94
('.101
'.981
1."
.r ......,...u, .f wlUlt. c....rleM. _trh:":
Ol~.
t
r:!lI.oo
[
31.157
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I ...U • I.... U .. t.r
, (rnr __ ...an .... If f.r I". _"Rl. or"IM ...
Sallerth.. lte ."re.i ..U .. .
I Sall
(rro .. _aft IlIUo're .ncr If f ...
...t .... Ue ."rellt.atl ... .
t (r...r .......-....... If f.r
SaU...t .... Ue ..."lIi ..tI ....
Iltftltl ..t .... "Rl. Df' .......
hW"tt"t.M~""
1190
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'.114
I.ll
'.230
D.lOO
TABLE 5
ANALYSIS OF VAFlANCE TABLE BY \115fT
lIE"
t
-
ell
_"tet. er .......
'.oze