We used a step-down polynomial regression method for gene discovery and pattern recognition for short time-course microarray experiment. The first step is to fit the following quadratic regression model to the j^{th} gene: Y_{ij} = β_{0j} + β_{1j}*x + β_{2j}*x^{2} + β_{3j}*x^{3} + ε_{ij} where y_{ij} denotes the expression of the j^{th} gene at the i^{th} replication, x denotes time, β_{0j} is the mean expression of the j^{th} gene at x = 0, β_{1j} is the linear effect parameter of the j^{th} gene, β_{2j} is the quadratic effect parameter of the j^{th} gene, and, ε_{ij} is the random error associated with the expression of the j^{th} gene at the i^{th} replication and is assumed to be an independently distributed normal with mean 0 and variance.
If the overall model(1) p-value > α_{0}, the j^{th} gene is considered to have no significant differential expression over time. The expression pattern of the gene is flat.
If the overall model(1) p-value ≤ α_{0}, the j^{th} gene will be considered to have significant differential expression over time. The patterns are then determined based on the p-values obtained from F tests. All p-values have been adjusted for False Discovery Rate using the BH algorithm.