Highly efficient factorial designs for cDNA microarray experiments: use of approximate theory together with a step-up step-down procedure

Abstract

A general method for obtaining highly efficient factorial designs of relatively small sizes is developed for cDNA microarray experiments. The method allows the main effects and interactions of successive orders to be of possibly unequal importance. First, the approximate theory is employed to get an optimal design measure which is then discretized. It is, however, observed that a naïve discretization may fail to yield an exact design of the stipulated size and, even when it yields such an exact design, there is often scope for improvement in efficiency. To address these issues, we propose a step-up/down procedure which is seen to work very well. The resulting highly efficient designs are found to remain almost free from possible dye-color effects under a suitable dye-color assignment. They are also seen to be quite robust to heteroscedasticity as may be caused by biological variability. We focus on the baseline and all-to-next parametrizations but our method works equally well also for hybrids of the two and other parametrizations.

Optimal design measures under asymmetric errors, with application to binary design points

“…However, multiplicative algorithms (cf. Zhang and Mukerjee, 2013) can be employed conveniently for their numerical determination. The D-optimality algorithm starts with the uniform measure which assigns a mass 1/n to each design point and, in view of Lemma 3(a), finds = ,…”

Optimal designs for regression models using the second-order least squares estimator

“…Bose and Mukerjee (2015) and Gao and Zhou (2015) made further developments, including the convexity results for the criteria and numerical algorithms. Bose and Mukerjee (2015) applied the multiplicative algorithms in Zhang and Mukerjee (2013) for computing the optimal designs, while Gao and Zhou (2015) used the CVX program in MATLAB (Grant and Boyd (2013)).…”

Approximate theory-aided robust efficient factorial fractions under baseline parametrization

“…Several examples in Section 5 illustrate this point. Our computations suggest thatZhang and Mukerjee's (2013) approach, involving only deletion or only addition of runs,…”

“…Also, in agricultural or industrial experiments, the currently used level of each factor can well constitute the baseline level. Under baseline parametrization, optimal paired comparison designs for full factorials have been studied by several authors in the context of microarray experiments; see Banerjee and Mukerjee (2008), Zhang and Mukerjee (2013), and the references therein. As for designing efficient or optimal factorial fractions under this parametrization, not much work has been reported so far beyond the results in Mukerjee and Tang (2012) and Li, Miller and Tang (2014) on the two-level case.…”