dx.doi.org/10.14227/DT110304P25
`Statistical Properties of the
`Dissolution Test of USP
`Carlos D. Saccone1,3, Julio Tessore1, Silvino A. Olivera2,
`and Nora S. Meneces1
`
`email: csaccone@fing.edu.uy
`
`Abstract
`The Monte Carlo simulation method is used to study statistical properties of the USP dissolution test. Some interesting
`aspects of immediate release dissolution are presented, including:
`
`a. A unified operating curve that allows estimation of the probability of acceptance (Pa) of a lot as a function of its sta-
`tistical parameters.
`b. Verification that the statistical behavior is only slightly affected by the underlying distribution of the individual
`amounts dissolved.
`The average number of samples required to reach a decision is presented as a function of parameters of the lot.
`The relative influence of the three stages of the test in the probability of acceptance.
`
`c.
`d.
`
`IntroductionThe dissolution test as defined in the United States Phar-
`
`macopoeia (1) is used in judging the quality of pharma-
`ceutical products. Dissolution testing is a method for
`evaluating physiological availability that depends upon
`having the drug in a dissolved state. The USP Dissolution
`testing involves three stages and the acceptance criteria are
`defined for each stage as a function of a quantity Q,a
`percentage of the label value that is established for each
`drug product in its monograph. Acceptance criteria are
`shown in Table 1.
`These acceptance criteria are complex and the behavior
`of the test for samples of varying quality levels is not easily
`predictable from the knowledge of its drug properties.
`Pharmaceutical manufacturers are interested in many of
`
`Table 1. USP Acceptance Criteria
`
`Stage
`
`Number
`units
`
`Acceptance Criteria
`
`the statistical properties of the dissolution test. The follow-
`ing aspects of immediate release dissolution were studied:
`
`•
`
`•
`
`•
`
`•
`
`Probability of acceptance of the dissolution test (Pa), e.
`g. probability of passing the test, as a function of the
`dissolution population parameters (mean and standard
`deviation expressed as a percentage of label content),
`Influence of the shape of the population distribution
`on the probability of acceptance.
`Average sample number needed for reaching a deci-
`sion when the test is applied.
`Contribution of each stage of the test to the probabili-
`ty of acceptance.
`
`Methodology
`The Monte Carlo simulation method was used to study
`statistical properties of the dissolution test. Amounts dis-
`solved, expressed as a percentage of the label value of each
`unit (tablet, capsules, etc.), were obtained through the use
`of Visual Basic-Excel statistical routines. In Figure 8, a flow-
`chart (similar to the flowchart presented by PHEATT (2) of
`the simulation is provided. More than 100 million dissolu-
`tion values were generated in order to assure uncertainty
`values of less than 0.01 in the probability of acceptance.
`Probability of acceptance, (Pa), and average sample num-
`ber (ASN) were studied in the range of conditions of inter-
`est for the objectives of this study, as shown in Table 2.
`
`Results and Discussion
`Operating Characteristic Curves
`The operating characteristic curves of the dissolution
`test are defined in this paper as Probability of acceptance
`
`6
`
`6
`
`12
`
`S1
`
`S2
`
`S3
`
`Each unit is not less than Q* +5%
`Average of the 12 (S1+S2) units is ≥
`Q and no uni is less than Q−15%
`Average of 24 (S1+S2+S3) units is ≥
`Q and not more than 2 units are
`less than Q−15% and no unit is less
`than Q−25%
`*Q is the amount of dissolved active ingredient specified in the individ-
`ual monograph, expressed as a percentage of the labeled content.
`
`1 University of the Republic of Uruguay, Faculty of Engineering, Industrial
`Production Department, Montevideo, Uruguay
`2 University of the Republic of Uruguay, Faculty of Chemistry, Estrella
`Campos Department, Montevideo, Uruguay
`
`3 Corresponding author, Facultad de Ingeniería, Instituto de Ingeniería
`Mecánica y Producción Industrial, Julio Herrera y Reissig 565, Montevideo,
`Uruguay
`
`Dissolution Technologies | AUGUST 2004
`
`25
`
`MYLAN - EXHIBIT 1033
`
`

`

`Figure 1. Operating curves for Q = 80, RSD 1 to 10%, Normal distribution.
`
`Table 2. Operation Conditions for studying probability of
`acceptance (Pa) and the average sample number (ASN)
`
`Q = 75
`
`Q = 80
`
`Pa
`
`ASN
`
`Pa
`
`ASN
`
`70–90
`
`50–90
`
`75-95
`
`55–95
`
`Mean (%)
`
`RSD (%)*
`
`1–10
`
`1–15
`
`N, LN
`
`1–10
`
`N, LN
`
`1–15
`
`N, LN
`
`Less than
`0.01
`
`Distributions
`
`N, LN**
`
`Uncertainty
`in Pa
`
`Less than
`0.01
`
`Figure 2. Plot of Probability of acceptance of dissolution test as a function of
`(Mean-Q)/Std. Deviation. Unified curve made by using all the values
`obtained for Q = 75 and Q = 80 and RSD 1 to 10%.
`
`Figure 3. Plot of the differences between Probabilities of acceptance in disso-
`lution test (Normal minus lognormal), assuming Normal and Lognormal dis-
`tributions as a function of Mean, Q=75 and RSD 1 to 10%. Solid dots were
`obtained for RSD between 1 and 8 %, empty dots were obtained for RSD 9
`and 10%.
`
`(Pa) vs. mean of dissolution values expressed as a percent-
`age of the label content. They have a characteristic S shape,
`and are shown in Figure 1.
`All the curves, in the range of RSD studied, intercept at a
`mean value equal to Q. This means that at this point, the
`Probability of acceptance does not depend on RSD and its
`value is Pa = 0.62. For Q=75 a similar behavior is obtained
`in the shape of the curves and in the intercept value
`(Pa=0.62, mean=Q).
`
`26 Dissolution Technologies | AUGUST 2004
`
`*RSD: Relative standard deviation
`**N, LN: Normal and lognormal distribution.
`
`Unified Characteristic Curve
`As Murphy and Sampson (3) suggested, the curves may
`be unified representing Pa as a function of a parameter
`that eliminates the influence of Q and RSD. The results
`obtained for Pa as a function of (Mean=Q)/Standard devia-
`tion are shown in Figure 2. The curve was made by using all
`the values obtained for Q=75 and Q=80 and RSD 1 to 10%.
`This curve thus built allows us to easily estimate Pa as a
`function of dissolution parameters (mean, standard devia-
`tion). The thickness of the curve indicates the maximum
`observed variations in the Pa obtained in the simulations
`performed. These variations observed represent less than
`approximately ±0.02 in the Pa in all the ranges studied.
`It can be observed that when the mean value is Q-0.6
`standard deviation and less, the Pa is insignificant, and
`when the mean value is Q+0.6 standard deviation and
`more, the Pa is almost 1.
`
`Robustness
`There is no agreement (2) about the shape of the distrib-
`ution of the dissolved amounts and therefore it was con-
`sidered important to study how the curves shown above
`depend on the distribution assumed. Particularly, for nor-
`mal and lognormal distributions the different Pa have been
`evaluated. These distributions were chosen for the follow-
`ing reasons:
`
`•
`
`•
`
`Normal distribution was considered a good model of
`the distribution since the amount dissolved by each
`unit is a function of a large number of variables.
`Lognormal distribution seems suitable to simulate a
`physical limit to the amount dissolved due to the
`amount of drug product in the pharmaceutical dosage
`form. If the underlying distribution of amount dis-
`solved is lognormal, a large slope is observed towards
`the right (where the physical limit exists) and a low
`slope towards the left.
`
`The observed influence on probability of acceptance is
`shown in Figure 3, and it can be seen that there are not rele-
`
`

`

`Figure 4. Ideal curve. Average Sample Number as a function of Mean, Q=75
`and RSD=0%.
`
`vant differences between normal and lognormal distribu-
`tions. The probability of passing the test when the data were
`normally distributed differs less than 0.03 from that of log-
`normal distribution for population RSD values of 8% or less.
`As expected, in the range in which the rejections are due
`to the non-compliance of the requirements on the average
`value (stages 2 and 3), the central limit theorem assures
`insensitivity to the distribution shape. When non-compli-
`ances are due to individual values (clauses Q-25% and Q-
`15%), the probability of acceptance is more dependent on
`the assumed distribution of amount dissolved. This occurs
`for larger RSDs, 9 and 10%.
`
`Average Sample Number
`The average sample number of units required to arrive at
`a decision about the test was studied. This number (ASN) is
`a function of the mean and standard deviation.
`Ideally, if it is considered that the variability is zero
`(RSD=0), when the dissolution values increase (Figure 4) it
`should be expected that:
`
`a.
`
`b.
`
`Rejection of tests in the first stage if dissolution is less
`than Q-15% (tested units = 6)
`Three stages are required to reach a decision with dis-
`solution values less than Q and more than Q-15%
`(tested units = 24)
`c. Acceptance in the second stage for dissolution values
`that are more than Q and less than Q+5% (tested units
`= 12)
`d. Acceptance in the first stage for dissolution values that
`are more than Q +5% (tested units = 6)
`
`Figure 5. Plot of Average Sample Number as a function of Mean, Q=75 and
`RSD 1 to 15%.
`
`The curves obtained with variability different to zero,
`(RSD 1 to 15%) present the four steps described, but they
`separate from the ideal curve and differences are larger as
`the RSD increases (Figure 5).
`Additionally, it must be said that the point with a
`mean=Q shows a behavior that is practically independent
`of RSD in the ranges studied: it requires 18 samples as an
`average. Also the behavior is almost independent of RSD
`when the mean is equal to Q+5% or Q-15% when RSD is
`less than 8%.
`
`Contribution of each stage
`to the acceptance of the test
`In order to understand the operation of the dissolution
`test, contributions to the total probability of acceptance
`were studied for each stage of the test.
`The following results were obtained:
`
`•
`
`In all the other situations, the acceptance decisions are
`produced in the second stage.
`
`For Q=80 a similar behavior to the above explained for
`Q=75 is obtained.
`
`•
`
`•
`
`The first stage begins to contribute to the Pa when the
`mean is more than Q+5%. As the mean increases and it
`approaches the label value this contribution becomes
`larger than those of other stages. See Figures 6 and 7.
`The third stage only contributes to the Pa when the
`mean is close to Q. For RSD 1 to 10% and when stan-
`dard deviation is eight or less, the maximum contribu-
`tion found for the third stage to the Pa was about 20%.
`
`Conclusions
`a. A unified operating curve is presented that allows esti-
`mating the probability of acceptance (Pa) of the disso-
`lution test as a function of the dissolution parameters
`that characterize it. This curve can be used to evaluate
`the probability of passing the test by the authority
`and, therefore, the risks of releasing lots of varying
`quality levels and its possible consequences.
`
`Dissolution Technologies | AUGUST 2004
`
`27
`
`

`

`Figure 6. Plot of probability of acceptance of the dissolution test at Stage 1,
`Stage 2 and Stage 3 as a function of Mean, Q=75 and RSD=5%.
`
`Figure 8. Flowchart of dissolution test simulation
`
`Figure 7. Plot of probability of acceptance of the dissolution test at Stage 1,
`Stage 2 and Stage 3 as a function of Mean, Q=75 and RSD=10%.
`
`c.
`
`d.
`
`b.
`
`For means less than Q-0.6σ, the probability of accep-
`tance is practically zero. A mean value larger than Q+
`0.6σ assures the acceptance of tests. This value
`(Q+0.6σ) could be the release criteria used by the man-
`ufacturer, to minimize risk of rejection by the authority.
`The statistical behavior does not depend on the shape
`of the distribution of the amounts dissolved, at least
`for standard deviation less than 7, considered custom-
`ary by Hofer and Gray (4) in the dissolution test.
`The number of tests required to reach a test decision
`depends on the population’s dissolution parameters.
`As usual with double or multiple sampling plans, with
`very bad or very good lots, the decision of acceptance
`or rejection of the test is reached quickly and the num-
`ber of units tested is minimum (6, only first stage).
`e. Although the test involves three stages, the behavior is
`dominated by the first and second stage.
`
`2.
`
`References
`1.
`The United Stated Pharmacopoeia XXVI,The U. S.
`Pharmacopeial Convention, Inc., Board of Trustees,
`Webcom Limited,Toronto, Ontario, 2155–2156, 2003.
`Pheatt, Charles B., ”Evaluation of U.S. Pharmacopeia
`Sampling Plans for Dissolution”, Journal of Quality
`Technology, 12 (3, July), 158–164, 1980.
`Buncher, Ralph C.,Tsay, Jia-Yeong, Statistics in the
`Pharmaceutical Industry, Statistics:Textbooks and
`Monographs, Marcel Dekker, Inc., 140, 402–406, 1994.
`4. Hofer, Jeffrey D., Gray Vivian A,“Examination of selec-
`tion of Immediate Release Dissolution Acceptance
`Criteria”, Dissolution Technologies, 10 (1, February),
`16–20, 2003.
`
`3.
`
`28 Dissolution Technologies | AUGUST 2004
`
`