The All Possible Comparisons (APC)-criterion for the Analysis of Screening Experiments

Abu Zar Md Shafiullah (University of Dhaka )

Friday 6th May, 2022 15:00-16:00 Zoom

Abstract

An AIC-type model selection criterion, called the APC-criterion (All Possible Comparisons criterion) is proposed for analyzing a variety of screening experiments. The primary focus is on the orthogonal 2-level designs including the Plackett-Burman designs (PBD) where the effects of k factors can be analyzed in only n = k + 1 runs (n is a multiple of 4). The proposed APC procedure has the advantage that it can be designed to maintain strong control of the false positive rates at a specified level for three different definitions of error rate: individual error rate (IER), experiment-wise error rate (EER), and false discovery rate (FDR). The criterion can be used to analyze data from any two level designs that are orthogonal or nearly orthogonal. Extensive simulation studies for a wide range of experimental scenarios demonstrate that the APC-criterion is an effective analysis method in terms of (i) controlling IER, EER or FDR at the specified level while (ii) delivering high values of screening power and accuracy as long as the effects are big enough. The scope of applying the APC-criterion for two-level balanced non-orthogonal designs (NOD’s) is explored. The extensive simulation study reveal that the modified procedure for NOD’s controls the IER, EER and FDR at the specified levels when the design is D-optimal or at least the amount of aliasing is not too large. The procedures of APC-criterion for orthogonal and non-orthogonal designs were adapted with the two step approach of Miller and Sitter (2005) and applied to carry out an initial study for analyzing folded-over 12-run PBD in the presence of few 2-factor interactions. Finally, the R-package APCanalysis which implements the procedure of APC-criterion in R is demonstrated for orthogonal designs using constructed examples and real data sets.

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