N. R. Bohidar

Construction of upper confidence limit of coefficient of variation for content uniformity

AbstractRelative standard deviation (coefficient of variation) plays an important role in meeting the current compendial requirements for content uniformity. Since the sample RSD value would vary from sample to sample in a population (batch), the scientist would need not only the sample estimate of the RSD but also its 95% two-sided upper confidence limit, for making the proper statistical inference as well as for arriving at the appropriate pharmaceutics decisions. The primary purpose of this paper is to depict the five available methods for determining the confidence limit and to discuss their relative merits and similarities in the context of a content uniformity study associated with Product-C. Suitable tables are furnished to facilitate rapid access to the desired RSD confidence limit.

Determination of Geometric Standard Deviation for Dissolution

AbstractThe two important instances in which the scientist converts his/her experimental data to a logarithmic scale prior to computing the mean and standard deviation, are (i) when the distribution of the data is asymmetrical (e.g. percentage data) and (ii) when he/she intends to compare statistically the averages of two or more groups with unequal standard deviations. In either case, the mean is restored to its original scale by taking the antilog of the log mean, which is the geometric mean. However, this procedure cannot be applied for computing the geometric standard deviation. The author of reference(l) erroneously claims that the antilog of log standard deviation is the geometric standard deviation. This paper demonstrates the incorrectness of the procedure in reference (1), exhibits the exact statistical formula and introduces a novel method called “jackknife statistic” to confirm the results, based on the dissolution data associated with Product-C.

Canonical correlation analysis of formulation optimization experiments

AbstractFormulation optimization experiments are primarily composed of two groups of variables, a set of independent variables and a set of dependent variables. Simultaneous consideration of all the variables in a single analysis is desirable since it provides an opportunity to study the interrelationships of all variables, independent as well as dependent at the same time and imparts an in-depth insight into the entire system as a whole. A multivariate statistical analysis, known as canonical correlation analysis, has indeed this capability. In addition, the analysis has the capacity of extracting the maximum possible correlation, called canonical correlation, between the variables of the two sets. The larger the value of the canonical correlation (0.90 or above), the higher is the predictability of one set from the other set. The analysis produces two composite canonical functions, one for each set. They can be used to streamline the subsequent search process associated with the full-fledged optimizatio...

Multivariate Analyses of a Production Formulation Optimization Experiment

AbstractThree prominent multivariate statistical analyses, canonical correlation analysis (CCA), principal component analysis (PCA) and CAS-Regression analysis (CAS-R) are appropriately applied to the formulation optimization data associated with Product-T for determining a set of key excipient/process variables and a set of key response variables to be used in monitoring the future performance of the optimizated formula. CCA which considers both sets of variables simultaneously in a single analysis, successfully delineated two key parameters, one for each set. PCA which considers only the response variables concurred with the CCA results and CAS-R which considers each response variable separately also concurred. Even though CCA is a predominant technique, adjunct results of PCA and CAS-R could be supplemented for a comprehensive interpretation. It is recommended that all three analyses be carried out and interpreted appropriately.

SHORT-TERM STABILITY DETERMINATION USING SAS

AbstractAppropriate statistical procedures are provided for determining the shelf-life of a drug product. Inverse regression analysis is proposed here. However, the formulas associated with the confidence limits are very cumbersome. Complete SAS computer program statements are presented so that they may be used in a computer to accomplish the task. It has been shown that there are situations in which the confidence limits may not exist. The conditions under which such situations arise are discussed and alternate procedures are proposed.

Exact power function of compendial test requirements for content uniformity

AbstractThe exact distributions associated with the current compendial test requirements are generated by resorting to the well known Computer Intensive Algorithm method to establish the exact percentage point (limit) for RSD, corresponding to each selected cut-off probability level (confidence level) for each of the four possible experimental outcomes based on the USP-NF test requirements. A table is constructed to present the two-dimensional power function. The similarities between these tabular values and the current compendial RSD limits for 10 and 30 dosage units are extremely remarkable.Minor differences exist, however. It is suggested that both the theoretical as well as the numerical approaches should be carried out to arrive at a comprehensive solution.

Detection of Discordant Content Uniformity Observations and Compendial Compliance

AbstractA discordant observation is a data point whose value is drastically different from that of the rest of the members in the data set. In the context of content uniformity experiments, however, a discordant observation arises in two ways: (i) when the value of an observation is markedly distant from that of the other data points even though it is within the required compendial range, and (ii) when the value of an observation is outside the permissible compendial range. Several statistical tests for detecting one or more discordant observations are presented. Since discordancy distorts the symmetricity of the data, several tests of symmetricity are provided. Tests for detection of group discordancy induced by discordant samples are also included. The compendial requirements are explained in statistical terms. The impact of discordant observations on compendial compliance requirements is assessed. The statistical basis of the construction of compendial limits as well as the assumptions implicit in the ...

Relative Efficiency of R2 and B2 in Regression Analysis for Calibration and Formulation

AbstractThe assessment of the adequacy of a regression equation, as measured by the degree of closeness of the predicted values and their respective observed values is accomplished by the two contending statistics, R2 and B2. The derivation of the two statistics is presented and their relative performances are examined in the context of several pharmaceutics experiments involving, calibration, validation and formulation. The results strongly indicate that the B2-statistic is much more sensitive and efficient than the R2-statistic which has a tendency to inflate the magnitude irrespective of the data structure.

A Rebuttal to The “Reply”

AbstractAt the outset a brief background from a pharmaceutics perspective is presented here. Pharmaceutical industry is one of the most tightly regulated industries. Statistics naturally plays an important role in the implementation of the compendial, regulatory and in-house requirements. The minimal requirement consists of a set of basic statistics, such as mean and standard deviation (SD), associated with each group of sample experimental data intended for submission. However, not only each statistic is individually subjected to a set of compendial, regulatory and in-house specifications, but also the individual observation is required to be within specific range for compliance (e.g. content uniformity). Hence these basic statistics are often referred to as the stand-alone sample (SAS) statistics, meaning that each statistic has to meet its own requirements. In this context, the geometric mean is indeed a SAS statistic. It is meaningful and interpretable directly from its face value. The geometric stand...

On truncated poisson distribution for determining mean number of defectives in pharmaceutical products

AbstractThe Poisson distribution plays a dominant role in the determination of the mean value of a distribution of the number of defective units (e.g. tablets, capsules) per sample, based on several samples of same size. If, however, the data emanates from samples with at least one defective unit in each sample, involving the absence of the zero-defective category, then the formula of the Poisson distribution as well as of the mean number of defective units are no longer tenable. In this presentation, appropriate formula for the Poisson distribution, called the truncated Poisson distribution, and for the mean, θ, are developed. The maximum likelihood method of estimation of the parameter θ by employing numerical (iterative) analysis methods is depicted, in detail. The procedure for conducting the chi-square test of goodness of fit of the experimental data to the truncated Poisson distribution is demonstrated. The results of the analyses of two recent experiments based on the methods described above are pr...