Method and system for the analysis of variance of microarray data
OwnerM. Kathleen Kerr, Gary A. Churchillinventors
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Abstract
A method for estimating the factor and interaction effects for gene expression microarray experiments is disclosed. The method requires the inversion of two square matrices of size p and p′, respectively, instead of a matrix of size q where q>>p≈p′. The invention also includes implementation of the methods in computer software, computer readable media comprising these software instructions, and computer systems for performing the methods.
Claims34
A method for estimating the effects of a plurality of factors and at least one of a plurality of interactions between the factors in a gene expression microarray experiment generating a microarray dataset wherein the factors include a gene factor and at least one non-gene factor and the interactions include at least one gene interaction, the gene factor being orthogonal to the other factors, the method comprising the steps of:
- (a) estimating the factor effects based on a plurality of averages of the microarray dataset;
- and
- (b) estimating the at least one gene interaction effects based on a plurality of averages of the microarray dataset and on the estimated factor effects from step (a).
A method for estimating at least one gene-variety interaction in a gene expression microarray experiment having an experimental design characterized by a number of degrees of freedom, q, and defined by a gene factor, a plurality of non-gene factors, a plurality of two-factor interactions wherein a full replication of genes is present for every combination of the plurality of non-gene factors, the method comprising the steps of:
- (a) inverting a first square matrix characterized by a size, p, wherein p<q;
- (b) estimating at least one of a plurality of non-gene factor effect from the first square matrix inverse;
- (c) constructing a second square matrix based in part on the estimated non-gene factor, the second square matrix characterized by size, p′, wherein p′<q;
- (d) inverting a second square matrix;
- and
- (e) estimating at least one gene-variety interaction from the inverted second square matrix.
A method for estimating at least one gene-variety interaction in a gene expression microarray experiment generating a dataset and having a design characterized by a arrays, v varieties, n genes, and d dyes wherein a full replication of genes is present for every combination of arrays, varieties and dyes, the method comprising the steps of:
- (a) constructing a global data vector, d, based on a plurality of averages of the dataset;
- (b) constructing a square matrix, T, characterized by a size, p, wherein p=a+v+d−3;
- (c) inverting the square matrix, T;
- (d) estimating the global effects, τ, wherein τ=T d;
- (e) constructing a square matrix, Tg, characterized by a size, p′, wherein p′=p−1;
- (f) constructing a gene-specific data vector, dg, based on a plurality of averages of the dataset;
- (g) inverting the square matrix, Tg;
- and
- (g) estimating the gene-variety interaction, τg, wherein τg=Tgdg.
A system for estimating the effects of a plurality of factors and at least one of a plurality of interactions between the factors in a gene expression microarray experiment generating a microarray dataset wherein the factors include a gene factor and a variety factor and the interactions include a variety-gene interaction, the gene factor being orthogonal to the other factors, the system comprising:
- (a) a processor;
- (b) a memory in signal communication with the processor;
- (c) a program stored in the memory, the program capable of being executed by the processor, the program including the steps of:
- (i) estimating the main effects based on a plurality of averages of the microarray dataset;
- and
- (ii) estimating the interaction effects based on a plurality of averages of the microarray dataset and on the estimated factor effects from step (i).
A method for estimating the effects of a plurality of factors and at least one of a plurality of interactions between the factors in a gene expression microarray experiment generating a microarray dataset wherein the factors include a gene factor and a plurality of non-gene factors and the interactions include at least one of a gene-non-gene interaction, the gene factor being orthogonal to the non-gene factors, the method comprising the steps of:
- (a) constructing a first data model including only non-gene factors and non-gene interactions;
- (b) estimating the effects of the non-gene factors and non-gene interactions based on the first data model and on a plurality of averages of the microarray dataset;
- (b) creating a transformed dataset from the microarray dataset and the factor and interaction effects estimated in step (a);
- (c) constructing a second data model including the gene factors and the gene interactions;
- and
- (d) estimating the gene-non-gene interaction effects based on the second data model and a plurality of averages of the transformed dataset.
Dependencies are inferred from the claim text.