Expression and differential CNA, and prediction of the pCR ofpatients after treatment. A final remark is provided in the discussion section.Motivating ExampleWe consider data in breast Title Loaded From File cancer consisting of 121 patients from three disease subgroups, ER+, HER2+, and triple negative (TN). ER+ patients have present estrogen receptors ?a protein related to hormone and regulation of gene expression ?in their cancer cells. HER2+ patients are instead those whose tumor cells test positive for a protein called human epidermal growth factor receptor 2. Finally TN patients lack three “receptors” in their cancer cells: ER, HER2, and progesterone receptors. ER+ and HER2+ patients were therefore collapsed in the same group, in order to compare TN patients versus others. On a slightly reduced set of 116 patients we have a measure, formalized as a dichotomous variable, on their positive or negative pCR to treatment. Numerosities are specified in 11967625 the table 1. The mRNA expression data was obtained with Affymetrix U133A gene chips. The data was normalized with MAS5 algorithm, scaled to target intensity of 600 and log2 transformed. The expression profiles of the cancers are available at GEO accession number GSE22093 [14]. The DNA copy number data was generated with Agilent 4x44K CGH arrays, processed as log2 ratios of the intensities of the two colors, and is available at ArrayExpress accession number E-TABM-584. ArrayCGH and microarray RNA experiments have been performed using the 121 breast 1315463 samples to obtain the copy number data on 22,944 probes and RNA expression data for 11,306 genes. We then mapped 22,944 probes to the 11,306 genes, which gave us a matching between the probe ids on the aCGH and the gene ids on the microarrays.Materials and Methods Ethics StatementAll the research used public data, published in 2009 in the following paper: “Molecular characterization of breast cancer with high-resolution oligonucleotide comparative genomic hybridization array” written by Andre F. et al. and published in Clinical Cancer Research [14].Sampling model for w and yOn arrayCGH, the Title Loaded From File experimental unit is probe b belonging to gene g. On RNA microarray, the experimental unit is gene g. Denote wbt the log2 intensity ratio for probe b at sample t, and ygt the RNA expression level for gene g at sample t, b 1,:::B g 1,:::,G, and t 1,:::T: Denoting fb [ gg the set of arrayCGH probes corresponding to gene g, the matched copy number and RNA expression data for sample t is then f(wbt )b[g , ygt g: We propose mixture models for w and y and introduce latent variables representing the differential expression status of the DNA and RNA, respectively. We then integrate the two models by constructing a prior probit regression linking the latent variables from both platforms. We use a mixture model [15] to introduce trinary latent indicator variables for the CNA state for each probe and the differential expression (DE) state for each gene. Specifically, let ew bt take values in the set f{1,0:1g , respectively corresponding to the copy-loss (v2 copy number), copy-neutral ( 2 copy number), and copy-gain (w2 copy number) states and ey take values in the gtTable 1. Contingency table to classify patients with respect to subgroup of breast cancer and pathological complete response.Positive to ER, Triple Negative HER2 or both Positive pCR No pCR Missing TOT 20 33 3 56 11 52 2TOT 31 85 5doi:10.1371/journal.pone.0068071.tBayesian Models and Integration Genomic PlatformsFigure 1. Grap.Expression and differential CNA, and prediction of the pCR ofpatients after treatment. A final remark is provided in the discussion section.Motivating ExampleWe consider data in breast cancer consisting of 121 patients from three disease subgroups, ER+, HER2+, and triple negative (TN). ER+ patients have present estrogen receptors ?a protein related to hormone and regulation of gene expression ?in their cancer cells. HER2+ patients are instead those whose tumor cells test positive for a protein called human epidermal growth factor receptor 2. Finally TN patients lack three “receptors” in their cancer cells: ER, HER2, and progesterone receptors. ER+ and HER2+ patients were therefore collapsed in the same group, in order to compare TN patients versus others. On a slightly reduced set of 116 patients we have a measure, formalized as a dichotomous variable, on their positive or negative pCR to treatment. Numerosities are specified in 11967625 the table 1. The mRNA expression data was obtained with Affymetrix U133A gene chips. The data was normalized with MAS5 algorithm, scaled to target intensity of 600 and log2 transformed. The expression profiles of the cancers are available at GEO accession number GSE22093 [14]. The DNA copy number data was generated with Agilent 4x44K CGH arrays, processed as log2 ratios of the intensities of the two colors, and is available at ArrayExpress accession number E-TABM-584. ArrayCGH and microarray RNA experiments have been performed using the 121 breast 1315463 samples to obtain the copy number data on 22,944 probes and RNA expression data for 11,306 genes. We then mapped 22,944 probes to the 11,306 genes, which gave us a matching between the probe ids on the aCGH and the gene ids on the microarrays.Materials and Methods Ethics StatementAll the research used public data, published in 2009 in the following paper: “Molecular characterization of breast cancer with high-resolution oligonucleotide comparative genomic hybridization array” written by Andre F. et al. and published in Clinical Cancer Research [14].Sampling model for w and yOn arrayCGH, the experimental unit is probe b belonging to gene g. On RNA microarray, the experimental unit is gene g. Denote wbt the log2 intensity ratio for probe b at sample t, and ygt the RNA expression level for gene g at sample t, b 1,:::B g 1,:::,G, and t 1,:::T: Denoting fb [ gg the set of arrayCGH probes corresponding to gene g, the matched copy number and RNA expression data for sample t is then f(wbt )b[g , ygt g: We propose mixture models for w and y and introduce latent variables representing the differential expression status of the DNA and RNA, respectively. We then integrate the two models by constructing a prior probit regression linking the latent variables from both platforms. We use a mixture model [15] to introduce trinary latent indicator variables for the CNA state for each probe and the differential expression (DE) state for each gene. Specifically, let ew bt take values in the set f{1,0:1g , respectively corresponding to the copy-loss (v2 copy number), copy-neutral ( 2 copy number), and copy-gain (w2 copy number) states and ey take values in the gtTable 1. Contingency table to classify patients with respect to subgroup of breast cancer and pathological complete response.Positive to ER, Triple Negative HER2 or both Positive pCR No pCR Missing TOT 20 33 3 56 11 52 2TOT 31 85 5doi:10.1371/journal.pone.0068071.tBayesian Models and Integration Genomic PlatformsFigure 1. Grap.
