APR Sept/Oct 2023 - 56

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FORMULATION AND DEVELOPMENT
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R Code to Estimate Probability of Passing
USP Dissolution Test
Prasanth Sambaraju
Independent Researcher
Abstract
considered pass if all six units are ≥ Q + 5%. The probability of passing
can be directly computed P{Pass S1
one unit greater than Q + 5%. In case of S2 and S3, no exact formulas
Dissolution testing is required by the United State Pharmacopeia (USP)
to ensure that the drug products meet the established standards of
strength, quality and stability. A manufacturing process is considered
to be in compliance only if it meets the respective acceptance criteria
for tests like content uniformity and dissolution at different times
during the process. The article proposes a custom written code in R
based on a reported method to estimate the probability of passing the
multistage USP dissolution test.
Keywords Dissolution, USP<711>, Acceptance criteria, Simulation,
Introduction
Dissolution testing for solid oral drug formulations was introduced
in the 1960s and is used to predict the in vivo drug release.
Dissolution testing provides useful information during the entire
drug development process. It is used to select the most suitable
formulation, test for batch-to-batch reproducibility and performance
throughout its shelf life. USP <711>1
provides guidance for acceptance
criteria for immediate-release dosage forms, which consists of three
stages of testing. In the case of S1
testing six units are tested and are
Table 1. USP <711> dissolution test acceptance criteria for
immediate-release dosage forms
Stage of
dissolution
S1
S2
Numbers
tested
6
6
Acceptance criteria
(1)
Each unit is not less than Q + 5%
For 12 units
a) Average of (S1
b) No unit (S1
S3
12
For 24 units
a) Average of (S1
+ S2
+ S2) is equal to or greater than Q
) is less than Q - 15%
T1, T2 and T3 represent the events which meet the criteria for S1, S2 and
+ S2+ S3) is equal to or greater than Q
b) No more than 2 units are less than Q - 15 %
c) No unit is less than Q - 25 %
S3 stage respectively. The event of passing the USP dissolution test is
given by T1
T2
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| September/October 2023
T3
.
are available due to the conditional nature of the test.2
A Monte Carlo simulation method was employed to estimate the
probability of passing the dissolution test. It was observed that the
probability of passing is dependent on mean and standard deviation
(expressed as percentage of labelled content) of the representative
samples tested from the manufactured batch. Normal distribution
was considered a suitable model, since the amount of drug dissolved
from each unit tested is dependent on a large number of variables.3
A parametric bootstrap method in combination with Monte
Carlo simulation was proposed to obtain sampling distribution
of estimated probabilities of passing USP dissolution test and its
confidence intervals.4
Method
Wang proposed a close-form approximation to estimate the
probability of passing the USP dissolution test, under the assumption
that the results of dissolution follow normal distribution with known
mean and standard deviation.5
If yi
, i = 1, 2, . . . , 24 represent the sample dissolution results and ȳk
represent the average of y1
, y2, . . .,yk. The events of passing three stages
for USP dissolution test are expressed as
} = p6, where p is the probability of
С
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