title: Sample size determination in combinatorial chemistry.
abstract: Combinatorial chemistry is gaining wide appeal as a technique for generating molecular diversity. Among the many combinatorial protocols, the split/recombine method is quite popular and particularly efficient at generating large libraries of compounds. In this process, polymer beads are equally divided into a series of pools and each pool is treated with a unique fragment; then the beads are recombined, mixed to uniformity, and redivided equally into a new series of pools for the subsequent couplings. The deviation from the ideal equimolar distribution of the final products is assessed by a special overall relative error, which is shown to be related to the Pearson statistic. Although the split/recombine sampling scheme is quite different from those used in analysis of categorical data, the Pearson statistic is shown to still follow a chi2 distribution. This result allows us to derive the required number of beads such that, with 99% confidence, the overall relative error is controlled to be less than a pregiven tolerable limit L1. In this paper, we also discuss another criterion, which determines the required number of beads so that, with 99% confidence, all individual relative errors are controlled to be less than a pregiven tolerable limit L2 (0 < L2 < 1).
authors.affiliation: Department of Biometrics Research, Merck Research Laboratories, Rahway, NJ 07065, USA.
authors.forename: P L
authors.initials: PL
authors.lastname: Zhao
authors.forename: R
authors.initials: R
authors.lastname: Zambias
authors.forename: J A
authors.initials: JA
authors.lastname: Bolognese
authors.forename: D
authors.initials: D
authors.lastname: Boulton
authors.forename: K
authors.initials: K
authors.lastname: Chapman