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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.
Project funded by funded by NIH Grant HD052472. Please view our funding & data sharing policy
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