Development Classifications using Polynomial Regression
Stepdown Polynomial Regression
We used a stepdown polynomial regression method for gene discovery and pattern
recognition for short timecourse 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) pvalue > 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) pvalue ≤ α_{0}, the j^{th} gene will be
considered to have significant differential expression over time. The patterns
are then determined based on the pvalues obtained from F tests. All pvalues have
been adjusted for False Discovery Rate using the BH algorithm.
 If the pvalue of the linear effect ≤ 0.05 and the pvalues of the quadratic and
cubic effects are > 0.05, the j^{th} gene is considered to be significant
in the linear term and is uniquely characterized by a linear pattern. The
expression pattern of the gene is linear.
 If the pvalue of the quadratic effect ≤ 0.05 and the pvalues of linear and cubic
effects > 0.05, the j^{th} gene is considered to be significant only
in the quadratic term. The expression pattern of the gene is uniquely quadratic.
 If the pvalue of cubic effect ≤ 0.05 and pvalues of the linear and cubic effects
> 0.05, the j^{th} gene is considered to be significant only in the cubic
term. The expression pattern of the gene is uniquely cubic.
