Development Classifications using Polynomial Regression
Step-down Polynomial Regression
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 jth gene: Yij
= β0j + β1j*x + β2j*x2 + β3j*x3
+ εij where yij denotes the expression of the jth
gene at the ith replication, x denotes time, β0j is the mean
expression of the jth gene at x = 0, β1j is the linear effect
parameter of the jth gene, β2j is the quadratic effect parameter
of the jth gene, and, εij is the random error associated with
the expression of the jth gene at the ith replication and
is assumed to be an independently distributed normal with mean 0 and variance.
If the overall model(1) p-value > α0, the jth 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 ≤ α0, the jth 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.
- If the p-value of the linear effect ≤ 0.05 and the p-values of the quadratic and
cubic effects are > 0.05, the jth 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 p-value of the quadratic effect ≤ 0.05 and the p-values of linear and cubic
effects > 0.05, the jth gene is considered to be significant only
in the quadratic term. The expression pattern of the gene is uniquely quadratic.
- If the p-value of cubic effect ≤ 0.05 and p-values of the linear and cubic effects
> 0.05, the jth gene is considered to be significant only in the cubic
term. The expression pattern of the gene is uniquely cubic.
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