UMBC High Performance Computing Facility
Please note that this page is under construction. We are documenting the
240-node cluster maya that will be available after Summer 2014.
Currently, the 84-node cluster tara still operates independently,
until it becomes part of maya at the end of Summer 2014.
Please see the 2013 Resources Pages under the Resources tab for tara information.
Comparing drug dissolution profiles: proposals based on tolerance intervals
Dr. Yi Huang, Dept of Math and Stat, UMBC
Dr. Thomas Mathew, Dept of Math and Stat, UMBC
Shuyan Zhai, Dept of Math and Stat, UMBC
Drug dissolution is defined as the amount of drug substance that goes
into solution, per unit time, under standardized conditions. In other
words, dissolution measures the in-vitro drug release, as a function of
time. Availability of a drug in solution is usually essential for drug
absorption and appearance in the blood, in order to eventually provide
therapeutic benefits. The sample dissolution profile is the recorded
percentage amount dissolved at prespecified time points. The
corresponding population dissolution profile is the curve representing
the mean dissolution rate over time.
Dissolution tests are performed to compare prototype formulations of a
drug product. For example, after a drug product has been approved, for
post-approval changes such as equipement changes, process changes,
changes in component and composition, scale up etc., the U.S. FDA
requires a comparison of dissolution profiles between pre-change and
post-change products, and establish similarity between the two profiles
based on suitable criteria.
An easy to use measure for checking the similarity of two dissolution
profiles is a similarity factor (denotedby f2), recommended by the FDA.
The similarity factor f2 is an inverse function of the sum of the
squares of a suitably scaled difference between the percentage amount
dissolved at prespecified time points. The factor takes values between 0
and 100, with the value 100 indicating perfect similarity. According to
FDA guidance, values between 50 and 100 are taken to be evidence for
The use of factors such as f2 has been criticized by various
researchers, since the decision based on such a similarity factor does
not take into account the variability among dissolution profiles, or the
correlation among the percentage amount dissolved at different time
points. In other words, even though f2 is a random variable, this fact
is not taken into account in the decision making process. Motivated by
this, researchers have suggested various alternative criteria, and have
developed statistical inference methodology based on them. However, the
factor f2 continues to be a popular criterion, and a statistically
rigorous approach based on f2 is currently unavailable.
In our research, we propose to develop a lower tolerance limit for the
distribution of f2. A lower tolerance limit is such that a specified
proportion (say, 0.90) or more of the distribution will be above the
limit, with a specified confidence level (say, 0.95). The confidence
level reflects sampling variability, since the limit will be computed
using a sample of dissolution profiles. If such a lower tolerance limit
is large (say, more than 50), we are 95% confident that at least 90% of
the f2 distribution is above 50. This could be taken as strong
indication of similarity between the profiles. Note that such a
tolerance limit does take into account the variability among the
dissolution profiles. A major challenge in developing such a tolerance
limit is the lack of a tractable analytic expression for the
distribution of f2, even if we assume multivariate normality for the
profile data.Nevertheless, it is possible to use non-parametric methods
to derive the tolerance limit; however, a bootstrap calibration is
necessary to obtain an accurate limit. An added complication is that the
mean of the multivariate normal distribution is usually a non-linear
function of unknown parameters, and closed form expressions are not
available for the maximum likelihood estimates. In the area of
dissolution profile testing, a two-parameter Weibull model is very often
used for the mean. All these features make the tolerance limit
computation, and the Monte Carlo estimation of its coverage probability,
very computationally intensive. We could obtain only very limited
numerical results, and they indicate excellent accuracy. Our request for
an account on tara is to speed up this computation.
We also plan to investigate the tolerance limit approach to various
other criteria suggested in the literature.While we won't be able to
recommend one specific criterion for dissolution profile comparison
(this could as well be a regulatory issue), our work will put the
existing criteria on a firm statistical footing.
The work described above is the doctoral work of the graduate student