Setting Internal Dissolution Specifications For a Concomitant Variable
Hewa Saranadasa, Ph.D.
R.W.Johnson Pharmaceutical
Sourcing Group of Americas, Raritan, NJ
e-mail: Hsaranad@psgaus.jnj.com
Abstract
The dissolution of solid dosage products needs to meet the USP
three stage acceptance criteria before the products go to the
market. Setting an internal specification for a concomitant variable
that is directly related to the main variable is often implemented
as a supplier test criteria. The classical linear regression approach
may not be appropriate often the variables are then subjected
to random variations. This paper discusses the usage of a bivariate
control region for setting up dissolution specifications for a
concomitant variable. An example of applying the method is also
given.
Introduction
There are situations in the pharmaceutical
industry where setting specification for a variable depends on
the other variables. Consider a situation evaluatin dissolution
of beads and capsules of a pharmaceutical product. The beads are
manufactured in one manufacturing site and shipped to a different
facility for encapsulation. The final products must meet the USP
stage three acceptance criteria [1] before the products are released
to the market. In practice, setting dissolution specifications
for a drug product at pharmaceutical development phase often considers
passing a certain percentage of batches (i.e., 90%) at Stage I
(S1) test.
Such practice will ensure consistency
from one lot to the other and will be useful for quality control.
A lot is considered unacceptable when it fails to meet the specification
at stage 3 of the test. For the two site example offered above,
the pharmaceutical company may need to implement internal specifications
as a supplier test requirement of the bead product prior to its
shipment to the final production site. This practice would guarantee
that the final products would meet the USP 3 Stage 3 test with
a high degree of confidence.
In this context, dissolution of both beads and capsules are subject
to random variation and are normally correlated. A simple linear
regression model may not be appropriate to capture the correlation
between the two variables in the calculation of the specifications
of one of the variables.
This note shows the application of
bivariate 100(1-a)% confidence elliptical control region in
setting the internal specifications for a concomitant or auxiliary
variable. Recently, the author was involved in setting internal
specifications for beads of a capsule product in order to guarantee
that the dissolution of the capsule would pass the S1 test with
a high degree of confidence. This problem is discussed as an illustration
of this method at the end of this paper.
Elliptical Control Region
Suppose 
are
sample vectors from a bivariate normal distribution with mean
µ and variance-covariance matrix
.
Let 
and S are the sample mean vector
and the sample variance-covariance matrix
. The 100(1-µ)% confidence
region consists of the vectors (x) satisfying the inequality (1):
(1)
where 
is
the 100(1-µ)% percentile of the F distribution with
2 and n-2 degrees of freedom. The boundary of the region is an
ellipse whose center is at the point 
.
Let 
be the average dissolution of
the capsules, and let p be the probability of passing S1 of the
USP dissolution test. The expression for p is given in equation
(2):
(2)
where N is the sample size of capsules of all the batches, 
is the intra-batch variability
(vessel to vessel as well as capsule-to-capsule), 
is
the inter-batch variability and n is the number of batches. The
symbol F
denotes the standard normal distribution function. The equation
(2) is being used to establish the Q-specification for a new product
at the drug development phase. In general p=0.90 is used. Then
can be expressed as follows:
(3)
Using equations (1) and (3) the 100(1-a)% confidence lower bound can be calculated
for 
in order to guarantee
passing the dissolution S1 test with 100p% probability.
An Illustration
Dissolution testing for a new capsule product with sprinkle beads
showed that some of the individual dissolution values were out
of S1 test (<Q+5%) for a series of stability and validation
lots. The investigation team on this concluded that the failure
of S1 test was not process related and it may be related to bead
dissolution. For a corrective measure, the team wanted to implement
internal dissolution specifications for the supplier of beads
as an incoming test or as a supplier test requirement prior to
shipment for encapsulation. The internal specification of beads
should guarantee that the capsule dissolution S1 test would pass
with a high degree of confidence.
Twenty-three release lots of individual
dissolution data of S1 test were submitted for the analysis. The
generalized mixed modeling was used to estimate the magnitude
of variability associated with lot-to-lot and analytical variations.
The equation (3) was used to calculate the average capsule dissolution,
which guarantees that S1 of the USP dissolution test would pass
for a given probability with observed inter- and intra-lot variations.
The average of dissolution results of both beads and the capsule
data were used to construct the 95% elliptical confidence bound
for the averages. For the comparison purpose the regression method
was also employed to calculate the specification for beads. The
specification for beads is defined as the 95% elliptical region
and the 95% prediction upper bound that meets the required average
dissolution of capsules to pass S1 test 100p% probability, respectively
for both bivariate and regression approaches.
The parameters of the capsule dissolution
data were; N=138, n=23, a=5% and Q=80%. The average dissolution
estimates were 94.7% and 96.4% for capsules and beads, respectively.
The Pearson's correlation coefficient between the averages of
beads and capsules was 0.834 (p<.0001). The variance-covariance
matrix was, . The estimated analytical and vessel-to-vessel variability
of beads was 7.36 (standard deviation =2.7%) with 115 degree of
freedom. The 95% confidence upper bound for the standard deviation
of 6 capsule beads was 4.4%. Table I gives the specification for
the average beads for given probability of passing S1 dissolution
test for both bivariate and regression approaches. Data plot and
95% confidence elliptical control bounds are given in Figure 1.
Table I: The Average Dissolution Specification of Passing S1 for Given Probability
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Discussion
The method presented in this paper can be applied to a bivariate
situation when both variables are subject to random variations.
The estimates presented in Table I for the example show that the
regression approach gives slightly conservative estimates compared
with the bivariate approach. The recommended criteria for the
bead dissolution for the above problem would be the average of
6 capsule beads not less than 92.5% and the relative standard
deviation (RSD) is not more than 4.5%. Meeting these criteria
for beads guarantee that the USP S1 test would pass the capsule
dissolution with 90% confidence.
References
[1] USP/NF (1990), The United States Pharmacopoeia XXII and the
National Formulary XVII, The United States Pharmacopeal Convention,
Rockville, MD.
Hewa Saranadasa, Ph.D is a senior
statistician at R.W.Johnson Pharmaceutical Sourcing Group
of Americas, 1000 Route 202, P.O.Box 300, Raritan, NJ 08869-0602,
tel. (908)-218-6321, fax (908)-218-6026.