Approximation by Cubic Splines Leads to Highly Specific Discovery by Microarrays

Genome-scale microarray datasets are noisy. We have previously reported an algorithm that yields highly specific genome-scale discovery of states of genetic expression. In its original implementation, the algorithm computes parameters by globally fitting data to a function containing a linear combination of elements that are similar to the Hill equation 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 derivatives 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 sensitivity and specificity equal to those obtained by global fitting.