Comparison of Designs for Response Surface Models with Random Block Effects
Sourish Saha and André I. Khuri
Abstract: The purpose of this article is to compare designs for response surface models with a random block effect. To assess the quality of prediction associated with a given design, the scaled prediction variance is considered as a design criterion. The proposed approach is based on using quantiles of this design criterion on concentric surfaces within the experimental region. The dependence of these quantiles on the unknown value of the ratio of two variance components, namely, the ones for the block effect and the experimental error, is depicted by plotting the so-called quantile dispersion graphs (QDGs). These plots provide a clear assessment of the quality of prediction associated with a given design. A numerical example is presented to illustrate the proposed methodology.
A Bayesian Design Space Approach To Robustness and System Suitability for Pharmaceutical Assays and Other Processes
John J. Peterson and Mohammad Yahyah
Abstract: The ICH Q2 (R1) Guidance on Validation of Analytical Procedures states that a robustness assessment for an analytical method should provide “an indication of its reliability during normal usage.” The concept of “design space” as specified in the ICH Q8 Guidance may be used to create a zone of reliable robustness for an analytical method or pharmaceutical process. A Bayesian approach to design space as outlined by Peterson (2004) accounts for model parameter uncertainty, correlation among the quality responses at each fixed operating condition, and method response multiplicity. Two examples are provided to illustrate the application of a Bayesian design space to assessing reliability/robustness. One example is about assessing the ability of an HPLC analytical method to meet system suitability criteria and the other deals with a crystallization process for an active pharmaceutical ingredient.
A Bayesian Reliability Approach to Multiple Response Optimization with Seemingly Unrelated Regression Models
John J. Peterson, Guillermo Miró-Quesada and Enrique del Castillo
Abstract: This paper presents a Bayesian predictive approach to multiresponse optimization experiments. It generalizes the work of Peterson [33] in two ways that make it more flexible for use in applications. First, a multivariate posterior predictive distribution of seemingly unrelated regression models is used to determine optimum factor levels by assessing the reliability of a desired multivariate response. It is shown that it is possible for optimal mean response surfaces to appear satisfactory yet be associated with unsatisfactory overall process reliabilities. Second, the use of a multivariate normal distribution for the vector of regression error terms is generalized to that of the (heavier tailed) multivariate t-distribution. This provides a Bayesian sensitivity analysis with regard to moderate outliers. The effect of adding design points is also considered through a preposterior analysis. The advantages of this approach are illustrated with two real examples.
Davis TG, Peterson JJ, Kou J-P, Capper-Spudich EA, Ball D, Nials AT, Wiseman J, Solanke YE, Lucas FS, Williamson RA, Ferrari L, Wren P, Knowles RG, Barnette MS, Podolin PL (2009). The identification of a novel PDE4 inhibitor, EPPA-1, with improved therapeutic index using pica feeding in rats as a measure of emetogenicity. Journal of Pharmacology and Experimental Therapeutics, 330(3):922–931.
Burzykowski T, Carpenter J, Coens C, Evans D, France L, Kenward M, Lane P, Matcham J, Morgan D, Phillips A, Roger J, Sullivan B, White I, Yu L-M (2009). Missing data: Discussion points from the PSI missing data expert group. Pharmaceutical Statistics, early view, DOI: 10.1002/pst.391.
Abstract: The Points to Consider Document on Missing Data was adopted by the Committee of Health and Medicinal Products (CHMP) in December 2001. In September 2007 the CHMP issued a recommendation to review the document, with particular emphasis on summarizing and critically appraising the pattern of drop-outs, explaining the role and limitations of the ‘last observation carried forward’ method and describing the CHMP’s cautionary stance on the use of mixed models. In preparation for the release of the updated guidance document, statisticians in the Pharmaceutical Industry held a one-day expert group meeting in September 2008. Topics that were debated included minimizing the extent of missing data and understanding the missing data mechanism, defining the principles for handling missing data and understanding the assumptions underlying different analysis methods. A clear message from the meeting was that at present, biostatisticians tend only to react to missing data. Limited pro-active planning is undertaken when designing clinical trials. Missing data mechanisms for a trial need to be considered during the planning phase and the impact on the objectives assessed. Another area for improvement is in the understanding of the pattern of missing data observed during a trial and thus the missing data mechanism via the plotting of data; for example, use of Kaplan–Meier curves looking at time to withdrawal.
