Hical representation of the model for assessment of gene differential behaviour (A) and the prediction model (B). Boxes refer to variables in the model, where latent variables are represented by dotted line boxes. Circles refere to parameters, where the red ones are the indicators used for posterior inference. doi:10.1371/journal.pone.0068071.gset f{1,0:1g , respectively corresponding to the under-, normal-, and over-expression states. Activity is in keeping with the high structural similarity of the Conditional on ew and ey , the gt bt sampling models for copy number log2 ratios wbt and for gene expression ygt are given by 8 { > U({wb ,0) > > < N(0,n2 ) b fw (wbt Dew ) d bt z > > U(0,wb ) > : if ew {1 bt if ew 0 bt if ew 1 bt8 { > U({yg ,0) > > > < N(0,s2 ) g fy (ygt {mg {at Dey ) d gt > U(0,yz ) > g > > :if ey {1 gt if ey 0 gt if ey 1 gt ????In (2), the mixture model for gene expression data ygt includes a gene effect mg and a sample effect at . This is not the case in the mixture model for aCGH data wbt . The main reason is because wbt is already a log ratio between the cancer sample copy number and the reference sample copy number and therefore theBayesian Models and Integration Genomic PlatformsFigure 2. Posterior probabilities of positive interaction between the two platforms (A), differential CNA (B) and differential joint behaviour (C) after simulation 2. The red dots highlight posterior probabilities of genes which are claimed by the model to show respectively positive interaction between the two platforms, differential CNA and differential joint behaviour. doi:10.1371/journal.pone.0068071.gcorresponding effects should have canceled out by taking the ratio. The sampling model is indexed by n2 and s2 representing normal b g ranges of variability in the observed measurements wbt and ygt .z={ and yg define the tail overdispersion The parameters wb with respect to normality, associated with copy losses or gains for aCGH and under- or over-expression for microarrays. z={w CNA status (e.g., a reference subtype) and dg a trinary indicator accounting for differential CNA in the two subtypes, following a prior distribution given byLatent probit scores and probit regressionAnticipating the integration of both platforms using a regression model, we further introduce latent Gaussian variables zw and zy gt bt to define a probit scores for the trinary indicators ew and ey . gt bt Specifically, define8 > {1 > > < 0 w ebt > 1 > > : if zw v{1 bt if {1zw 1 bt if zw w1 bt and 8 > {1 > > < 0 y egt > 1 > > : if zy v{1 gt if {1zy 1 gt if zy w1 gt8 > {1 > > < 0 w dg > 1 > > :with prob: 0:2 with prob: 0:6 with prob: 0:(3) ??The integration of the two platforms is easily done using the latent probit scores and a linear model. First, we introduce a gene1 X z : level score for the aCGH data, defined as zw gt b[g bt mg Keeping in mind that there is a natural Title Loaded From File biological causal relationship between DNA copy number change and altered gene expression for the corresponding RNAs, we assume that zy Dzw *N(ag zxt cd y zzw ld yw ,t2 ), gt gt gtg gBefore we introduce the probit regression for integration, we present a prior for zw that allows for inference of different CNAs bt across different conditions, in our case of breast cancer data, different subtypes of breast cancer. Let xt is a clinical categorical covariate indicating which subgroups the patient belongs to, we assume thatw a zw Dzw *N(zw zxt cdg ,s2 ) bt b bwhere fxt jg,j 1,0 respectively if the patient belongs to TN subgroup or not, zw , a probe-specifi.Hical representation of the model for assessment of gene differential behaviour (A) and the prediction model (B). Boxes refer to variables in the model, where latent variables are represented by dotted line boxes. Circles refere to parameters, where the red ones are the indicators used for posterior inference. doi:10.1371/journal.pone.0068071.gset f{1,0:1g , respectively corresponding to the under-, normal-, and over-expression states. Conditional on ew and ey , the gt bt sampling models for copy number log2 ratios wbt and for gene expression ygt are given by 8 { > U({wb ,0) > > < N(0,n2 ) b fw (wbt Dew ) d bt z > > U(0,wb ) > : if ew {1 bt if ew 0 bt if ew 1 bt8 { > U({yg ,0) > > > < N(0,s2 ) g fy (ygt {mg {at Dey ) d gt > U(0,yz ) > g > > :if ey {1 gt if ey 0 gt if ey 1 gt ????In (2), the mixture model for gene expression data ygt includes a gene effect mg and a sample effect at . This is not the case in the mixture model for aCGH data wbt . The main reason is because wbt is already a log ratio between the cancer sample copy number and the reference sample copy number and therefore theBayesian Models and Integration Genomic PlatformsFigure 2. Posterior probabilities of positive interaction between the two platforms (A), differential CNA (B) and differential joint behaviour (C) after simulation 2. The red dots highlight posterior probabilities of genes which are claimed by the model to show respectively positive interaction between the two platforms, differential CNA and differential joint behaviour. doi:10.1371/journal.pone.0068071.gcorresponding effects should have canceled out by taking the ratio. The sampling model is indexed by n2 and s2 representing normal b g ranges of variability in the observed measurements wbt and ygt .z={ and yg define the tail overdispersion The parameters wb with respect to normality, associated with copy losses or gains for aCGH and under- or over-expression for microarrays. z={w CNA status (e.g., a reference subtype) and dg a trinary indicator accounting for differential CNA in the two subtypes, following a prior distribution given byLatent probit scores and probit regressionAnticipating the integration of both platforms using a regression model, we further introduce latent Gaussian variables zw and zy gt bt to define a probit scores for the trinary indicators ew and ey . gt bt Specifically, define8 > {1 > > < 0 w ebt > 1 > > : if zw v{1 bt if {1zw 1 bt if zw w1 bt and 8 > {1 > > < 0 y egt > 1 > > : if zy v{1 gt if {1zy 1 gt if zy w1 gt8 > {1 > > < 0 w dg > 1 > > :with prob: 0:2 with prob: 0:6 with prob: 0:(3) ??The integration of the two platforms is easily done using the latent probit scores and a linear model. First, we introduce a gene1 X z : level score for the aCGH data, defined as zw gt b[g bt mg Keeping in mind that there is a natural biological causal relationship between DNA copy number change and altered gene expression for the corresponding RNAs, we assume that zy Dzw *N(ag zxt cd y zzw ld yw ,t2 ), gt gt gtg gBefore we introduce the probit regression for integration, we present a prior for zw that allows for inference of different CNAs bt across different conditions, in our case of breast cancer data, different subtypes of breast cancer. Let xt is a clinical categorical covariate indicating which subgroups the patient belongs to, we assume thatw a zw Dzw *N(zw zxt cdg ,s2 ) bt b bwhere fxt jg,j 1,0 respectively if the patient belongs to TN subgroup or not, zw , a probe-specifi.
