Download PROC QRPT: Procedure for the Estimation of ED50, Relative Potency and Their Fiducial Limits in Quantal Response Assays

PROC QRPT:
Procedure for the Estimation of EDSO,
Relative Potency and Their Fiducial Limits
in Quantal Response Assays
Ronald G. Fleming
Squibb Corporation
Sue Huang and Nguyen V. Dat
Ortho Phanmaceutical Corporation
1.
ABSTRACT
The frequency counts must be sorted by
preparation and dose (BY VARIABLES also
require sorting. if they are being used).
PROC QRPT procedure is a SAS procedure which
provides estimations for ED50 and Relative
Potency and their fiducial limits in a
PROC SORT; BY PREP DOSE;
convenience of the user in the SAS
PROC QRPT; CLASS PREP DOSE;
VAR RESP; TOTAL TOT;
Quantal Response Assay_ This SAS procedure
is written in FORTRAN and is geared to the
enviroment.
Exampl e I:
This program estimates a 50~ effective dose
(ED50) and relative potency with their 95%
fi duci aI lim; ts wi thi n the framework qf
Fieller's Theorem from a joint probit X2
statistics for testing the similarity of the
probit regression lines required for
Drug
JfBm
Dose
(DOSE)
A
I
attaining parallelism.
A
A
2
PROC QRPT is very user-oriented and can be
tun easily by usi ng SAS data sets.
B
B
B
INTR DOUeT! ON
Responded
Total Animal s
RESP
TOT
(Freg count) (Freq count)
3
I
2
44
24
6
47
34
3
6
50
46
50
50
48
50
where the overa 11 sampl e si ze is 294
We would like to thank Dr. Richard Lam for
2. The preparation values must
contributing the original FORTRAN program in
be eight characters or less.
Dose values ~ be numeric.
Which this PROC is founded.
If you would like a copy of thi s PROC, please
3. Each VAR variable must have a
corresponding TOTALYariable.
Ronald Fleming at Squibb Corporation.
'Princeton. NJ.
~ontact
4.
Class statement must conta; n
two vari abIes only. VAR
statement contains 50
variables maximum. The
pROCEDURE QRPT
The response counts and total counts for each
maximum number of dose 5 or
dose within preparation (e.g. drug) must be
input into PROC QRPT (sooetimes using an
output dataset from PROC FREQ and
responses (per preparation)
are 20 and 50 respectively.
transposed). The original progr~ has been
altered to reduce the n~ber or required
input para~eters. For e~ample, the n~ber
of levels of the preparation and dose are
detemined within the procedure. However,
-the user r.tust coraply wi th certain constraints:
"pROCEDURE SYNTAX
,he PROC QRPT stateoent
'PROC QRPT options;
The options below may appear in
-n'e PROC QRPT statement.
STANDARD: 'value' or S: 'value'
BOO
The STANDARD = option allows the
user to specify the standard data
set against which all othe~ data
sets wi 11 be compared. Th, s
value Will be compared agal nst
the preparation values (PREP) in
the CLASS statement.
Note: The STANDARD value and the
preparation values both must be
eight characters or less.
CMEAN
=
value or eM
=
Example: PROC SORT; BY PROOECT
DRUG DOSE;
PROC QRPT; CLASS DRUG
DOSE; BY PRnJECT;
Where DRUG is the
preparation, DOSE is the dose
and PRWECT is the BY
VARIABLE.
3.
VAR variable names; (required)
The VAR statement wi 11 defi ne
the response variables.
These vari abIes contai n the
frequency counts for each
comb1 nation of level s of the
CLASS variables.
4-.
TOTAL variable names;
(opti onall
TOTAL is a statement that
defines the total population
of each VAR variable. The
order of variables 1 n the
TOTAL statement corresponds
di rectly to that of the
variables in the VAR
statement as illustrated
below.
value.
This constant; s applicable when
a threshold response exists and
the control value represent this
thre sho 1d.
Default val ue i s zero.
CctlSTANT = value or C = value.
This constant; 5 applicable when
a dose equals zero. The log of
this value cannot be calculated,
therefore a constant should be
added. If this constant is not
specified, the followi ng
-procedure will be used: S2 is
the second lowest dose and 53
is the third lowest dose.
CctlSTANT=(S2-0 )X(S2/S3)'
DilTA =
Use DATA= to give the name of the
EXAWLE 2: Dose 0 or .1 or .01 is
assigned at random to 70
anfmals. Tne response
categories are eye. nose
and ear. The response is
either yes or no to whether
or not an i nflar.mation
occurred. The tota 1 s may
look like RSTI - RST3 for
the response variables in
the follOwing data set.
SAS data set to be used by QRPT.
If it is omitted, the most
recently created data set wi 11 be
used.
Statements used with QRPT
1..
BY variable names; (optional)
2.
CLASS preparation name dose
~ame;
(required)
The CLASS statement indicates
the names of the preparati on
and dose variables. in that
order. The data must be
sorted by "BY VARIABLES' (if
any), preparation and dose.
80'
i.
I'ROC SORT; BY PROJECT DRUG DOSE
PROC QRPT: CLASS DRUG DOSE: BY PROJECT:
VAR EYE NOSE EAR:
TOTAL RSTl RST2 RST3;
PROJECT DRUG DOSE EYE
(freq)
1
1
1
2
1
2
2
2
10
7
9
8
9
2
3
2
EAR
RST1
NOSE
RST2
(freq) (freq) (freq) (freq)
1
2
5
3
5
3
10
10
3
5
9
8
10
1
3
8
3
7
2
5
5
9
10
10
RST3
(freq)
10
8
9
10
9
2
2
9
Area of Application
The probit line is then used to estimate the
E050:
Quantal response assay is a qualitative
indirect bioassay. It is examp1ified by
experiements in which a dose of a dru9 (or
preparation) is applied to a total of n
animals and r of them response to the drug.
if yl=probit (.5)=0 then m, the estimator
Of log E050, is:
Investigators may be interested in estimating
the 50% effective dose (ED50) of a
----r-a _-- a
m - yI
preparation and its confidence limits.
-
~
The estimated E050 f s the antilog of m.
Confi dence 1imit for thf s estimate can be
A way to estimate the E050 ; s based on the
probit transformation which transforms p=r/n
into its probit Y, Y=(probit(p», Y is then
used to regress a line on the dose or its log
calculated using the weighted standard error
of the esti~ator m:
transformation (X=log dose):
Y = probit (p) = a
+
S =! 1
bx.
m
Where a and b are estimated us; n9 the
least square method;
b_
-
where
1
tXY -
z
L..J.rl
pq
d EX LY
1\ = J:nwX
tow
ZX2 -} (u)2
a= ~
w=
b tnw
(1: Y -
b EX)
where dis number of doses.
802
+m
"_-_-"'X_.....,,.
Enw(X _ 10 2
(f(y) =
z
1 e -Y )
ff
2'
When one or more (KI preparations are being
compared with. standard one, parallel probit
lines are assumed. A coman slope is estimated
for overall data:
REFERENCES;
1.
Estimation.
ci Zj
i=l
Where Zi is the Indicator variables:
Yj = a + bX + 1: k
Z
i
=
{I otherwi
preparation I
se.
if
Fie1ler, E. C., M. A. Creasy and S. r.
David (1954). Symposium on Interval
16:
2.
J. Roy.
Finney, D. J., (1971). Probit
Analysis, 3rd Ed. New York:
Cambridge U. Press.
=j
0
3.
Regular F-test is used to test the
non-parallel co~ponents (the test is
equivalent to the test of Interactions
Finney, D. J., (1978). Statistical
Method in Biological Assay, 3rd Ed.
London, Charles Griffin & Co.
between Zi 's and Xl.
95% confidence limits for the slope are al so
given using the regular least square oethod
to calculate the standard error of the slope:
A
A
S(Y - a - b XI
2
(d - 2 I 1: (X - )0
2
The relative potency is calculated as the
ratio of the ED50 values. Confidence limits
of the relative potency is evaluated using
Fieller's Theorem as applied by Finney (1978).
SAf4?LE OUTPUT
See data from Example 1.
TH,
CONTROL
•.z.ooocooo
1.0000001)
3.00000()O
THE
B
NU:~9ER
!-IE.\~j
TH'
0.0
50
OF
••50
NUf16Eit OF
.•
Z4
.,
~OSES
IS:
)
.0
1.0000000
Z.OI)OOOOO
3 ••JOOOJ03
[s
Doses•• IS:
3
47
3•
18
REGRESSl'JN ANALYSIS
EFFECT
IJF
CHI-SOU,
~O~I-II
1
Z
0.6115
2.601
PESIO.
SLOPE
-4.4zal
95 PC
VA~IANCC
A
B
~ELATlvE
0.0
PROBIF)
0.0
LI~ITS
-).4515
~=IT¢S:,JRTCVbll¢eZ/Se*z",
POTENCY
F-RATIO
0.0
CQ~FIOENCE
-5.404S
statist. Soc. B.
175-222
D.04S64S0
TO A
QS pc CO/l;f:IOEIIICE LI"'tITS
POTENCY
Q5?C CONFIOENCE LIMIT
0.1861D+01 0.1642D+Ol 0.21050.01
O.ZS31~+Ol 0.22390+0t 0.29200+01 0.73310+00 0.60570+00 0.37290+00
803