Approximation by Cubic Splines Leads to Highly Specific Discovery by Microarrays

Abstract

Genome-scale microarray datasets are noisy. We have previously reported an algorithm that yields highly spe- cific genome-scale discovery of states of genetic expression. In its original implementation, the algorithm computes pa- rameters by globally fitting data to a function containing a linear combination of elements that are similar to the Hill equa- tion and the Michaelis-Menten differential equation. In this essay, we show that approximation by cubic splines yields curves that are closer to the datasets, but, in general, the first derivatives of the cubic splines are not as smooth as the de- rivatives obtained by global fitting. Nonetheless, little variation of the first derivative is seen in the area of the curve where the Cutoff Rank is computed. The results demonstrate that piece-wise approximation by cubic splines yields sensi- tivity and specificity equal to those obtained by global fitting.