In today's drug development industry, establishing the similarity of dissolution profiles is a regulatory requirement. To derive meaningful conclusions, current practice evaluates the entire dissolution profile, compared with the earlier approach that used one time point (for example, the time required for 90% drug dissolution for both reference and test product). The US Food and Drug Administration's (FDA's) guidance for industry on dissolution testing of immediaterelease, solid, oral dosage forms1 describes the modelindependent mathematical approach proposed by Moore and Flanner^{2} for calculating a dissimilarity factor (f_{1}) and a similarity factor (f_{2}) of dissolution across a suitable time interval. The similarity factor f_{2} (where 0<f_{2}<100 and f_{2}>50%, dissolution profiles are defined as similar) is a function of the mean differences and does not take into account the differences in dissolution within the test and reference batches. Hence, careful interpretation is warranted when f_{2} is used as a similarity factor with a large difference in variances between the two profiles. Previous work Previous articles have discussed the more serious deficiencies of using the f_{2} factor for assessing the similarity between two profiles. One of the major drawbacks identified was finding the sampling distribution of the statistic. This statistic has complicated properties, and deriving the distribution of the statistic is not mathematically tractable. Shah et al. proposed a bootstrap method to simulate a confidence interval for the f_{2} factor.^{3} Because the f_{2} is sensitive to the measurements obtained after either the test or reference batch has dissolved more than 85%, Shah and coworkers recommended a limit of one sampling time point after 85% dissolution. Several other authors have discussed defining criteria for dissolution similarity using modeldependent as well as modelindependent approaches. For example, Tsong proposed modelling profiles for individual tablets, and establishing specifications for similarity based on joint confidence regions for level and shape parameters of both reference and test batches.4 The disadvantage of this approach is that such regions are hard to interpret and shrink as a function of the amount of reference material tested. Sathe et al. also discussed a modeldependent approach using Mahalanobis distance,5 and Chow and colleagues proposed dissolution difference measurement and similarity testing based on a time series model in this context.6 However, dissolution data collected for profile comparisons typically have a very limited number of unequally spaced sampling intervals, whereas the intended time series has a large number of equally spaced sampling intervals.Previously, Gohel and coworkers proposed another modelindependent method based on the average absolute value of the log of the ratio of the area under the dissolution curve of both test and reference drugs.7 In the FDA guideline for industry, the procedure (f_{2} factor) allows the use of mean data and recommends that the per cent coefficient of variation at an earlier time point (for example, 15 min) not be more than 20%, and at other time points not more than 10%. In instances in which the per cent coefficient of variation within a batch is more than 15%, the industry guidelines suggest using a multivariate modelindependent procedure. This article examines the use of a multivariate procedure for testing the equivalence of two dissolution profiles through Hotelling's T2 statistic and compares this procedure with the f_{2} closeness criterion for different variancecovariance structures through simulation studies for normal and nonnormal distributions. The two methods were also compared using real data examples. Multivariate approach Suppose xij;Np(mj,S), j 5 1,2 and i = 1,2 . . . n are two independent multivariate normal dissolution profiles, one being a reference batch or a prechange batch and the other being a test batch or a postchange batch. Samples were taken at p different time points; n is the number of vessels, either 6 or 12, which is typical for tablet dissolution for a pharmaceutical product. The dissolution time points (p) for both profiles should be the same. Let ¯x1, ¯x2 be the vector of the sample mean for each of the profiles; S is the sample variance  covariance matrix, and n1, n2 are the number of tablets tested from each batch. To define a closeness of the two dissolution profiles, (12a) 100% confidence region for m_{1}m_{2} is considered, assuming the data follow a multivariate normal distribution. The confidence region for m_{1}m_{2} (5m) with confidence level 12a is the set of vectors m satisfying
where Fp,n2p11 (a) is the (12a) 100% percentile of the central F distribution with p and n2p11 degrees of freedom and n(5 n11n222) is the withinsample degrees of freedom. Assume m 5 dJp, where Jp is a p dimensional column vector of 1's. The maximum mean difference (d 5 max d) for which the equivalent of two given profiles could be concluded with (12a) 100% confidence given the data are the solution of d to equation 2.
