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Modeling ApproachThe Joint ModelLet X be the gene expression matrix where Xj is the j^{th} gene expression of the i^{th} compound, i = 1,... ,n and j = 1,... ,m. Let Y denote the measurement for the bioassay data. Both gene expression and bioassay readouts are assumed to be normally distributed. Let Z be the binary chemical structure or fingerprint feature matrix in which the ki^{th} element takes a value of one, z_{ki} = 1, or zero, z_{ki} = 0, if the k^{th} fingerprint feature is respectively present/absent in the i^{th} compound. For a given fingerprint feature, the genespecific joint model that allows testing for which gene is also differentially expressed and which gene is predictive of the response irrespective of the effect of the fingerprint feature is given by where the error terms have a joint zeromean normal distribution with gene specific covariance matrix, Xj:
The parameters aj and в represent the fingerprint feature effects for the j^{th }gene and the response, respectively, and p,j and are genespecific and the responserelated intercepts, respectively. Note that this model is identical to the joint model for a singletrial setting discussed in Chapter 3. Thus, the genespecific association with the response can be obtained using the adjusted association (Buyse and Molenberghs, 1998), a coefficient that is derived from the covariance matrix, Xj, of genespecific joint model (16.2):
Indeed, pj = 1 indicates a deterministic relationship between the gene expression and the response after accounting for the effect of a fingerprint feature. 
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