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A Bayesian approach for inducing sparsity in generalized linear models with multi-category response.

Madahian B, Roy S, Bowman D, Deng LY, Homayouni R - BMC Bioinformatics (2015)

Bottom Line: Several approaches exist to reduce the number of variables with respect to small sample sizes.Importantly, using Geneset Cohesion Analysis Tool, we found that the top 100 genes produced by SBGG had an average functional cohesion p-value of 2.0E-4 compared to 0.007 to 0.131 produced by the other methods.Using GDP in a Bayesian GLM model applied to cancer progression data results in better subclass prediction.

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ABSTRACT

Background: The dimension and complexity of high-throughput gene expression data create many challenges for downstream analysis. Several approaches exist to reduce the number of variables with respect to small sample sizes. In this study, we utilized the Generalized Double Pareto (GDP) prior to induce sparsity in a Bayesian Generalized Linear Model (GLM) setting. The approach was evaluated using a publicly available microarray dataset containing 99 samples corresponding to four different prostate cancer subtypes.

Results: A hierarchical Sparse Bayesian GLM using GDP prior (SBGG) was developed to take into account the progressive nature of the response variable. We obtained an average overall classification accuracy between 82.5% and 94%, which was higher than Support Vector Machine, Random Forest or a Sparse Bayesian GLM using double exponential priors. Additionally, SBGG outperforms the other 3 methods in correctly identifying pre-metastatic stages of cancer progression, which can prove extremely valuable for therapeutic and diagnostic purposes. Importantly, using Geneset Cohesion Analysis Tool, we found that the top 100 genes produced by SBGG had an average functional cohesion p-value of 2.0E-4 compared to 0.007 to 0.131 produced by the other methods.

Conclusions: Using GDP in a Bayesian GLM model applied to cancer progression data results in better subclass prediction. In particular, the method identifies pre-metastatic stages of prostate cancer with substantially better accuracy and produces more functionally relevant gene sets.

No MeSH data available.


Related in: MedlinePlus

Posterior mean of θs associated with gene 1 to gene 398. The x-axis represents the list of 398 differentially expressed genes obtained after Benjamini and Hochberg FDR correction of the results of single gene analysis using classical multi-category logistic regression. The y-axis represents the posterior mean of θ associated with each gene. While some signals are reduced toward zero, other signals stand out which turn out to be biologically more relevant to prostate cancer progression subtypes.
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Figure 2: Posterior mean of θs associated with gene 1 to gene 398. The x-axis represents the list of 398 differentially expressed genes obtained after Benjamini and Hochberg FDR correction of the results of single gene analysis using classical multi-category logistic regression. The y-axis represents the posterior mean of θ associated with each gene. While some signals are reduced toward zero, other signals stand out which turn out to be biologically more relevant to prostate cancer progression subtypes.

Mentions: We derived the fully conditional posterior distributions for all parameters in a multi-level hierarchical model in order to perform the fully Bayesian treatment of the problem. The Gibbs sampling algorithm was used to estimate all the parameters of the model [35,36], taking into account the progressive levels of the response variable. The top 398 genes ranked base on p-values obtained in initial feature selection step were used as input to our model. The posterior mean of θs for each gene is represented in Figure 2. This result shows that there is no relationship between θ and the p-value ranking from the initial feature selection methodology.


A Bayesian approach for inducing sparsity in generalized linear models with multi-category response.

Madahian B, Roy S, Bowman D, Deng LY, Homayouni R - BMC Bioinformatics (2015)

Posterior mean of θs associated with gene 1 to gene 398. The x-axis represents the list of 398 differentially expressed genes obtained after Benjamini and Hochberg FDR correction of the results of single gene analysis using classical multi-category logistic regression. The y-axis represents the posterior mean of θ associated with each gene. While some signals are reduced toward zero, other signals stand out which turn out to be biologically more relevant to prostate cancer progression subtypes.
© Copyright Policy - open-access
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4597416&req=5

Figure 2: Posterior mean of θs associated with gene 1 to gene 398. The x-axis represents the list of 398 differentially expressed genes obtained after Benjamini and Hochberg FDR correction of the results of single gene analysis using classical multi-category logistic regression. The y-axis represents the posterior mean of θ associated with each gene. While some signals are reduced toward zero, other signals stand out which turn out to be biologically more relevant to prostate cancer progression subtypes.
Mentions: We derived the fully conditional posterior distributions for all parameters in a multi-level hierarchical model in order to perform the fully Bayesian treatment of the problem. The Gibbs sampling algorithm was used to estimate all the parameters of the model [35,36], taking into account the progressive levels of the response variable. The top 398 genes ranked base on p-values obtained in initial feature selection step were used as input to our model. The posterior mean of θs for each gene is represented in Figure 2. This result shows that there is no relationship between θ and the p-value ranking from the initial feature selection methodology.

Bottom Line: Several approaches exist to reduce the number of variables with respect to small sample sizes.Importantly, using Geneset Cohesion Analysis Tool, we found that the top 100 genes produced by SBGG had an average functional cohesion p-value of 2.0E-4 compared to 0.007 to 0.131 produced by the other methods.Using GDP in a Bayesian GLM model applied to cancer progression data results in better subclass prediction.

View Article: PubMed Central - HTML - PubMed

ABSTRACT

Background: The dimension and complexity of high-throughput gene expression data create many challenges for downstream analysis. Several approaches exist to reduce the number of variables with respect to small sample sizes. In this study, we utilized the Generalized Double Pareto (GDP) prior to induce sparsity in a Bayesian Generalized Linear Model (GLM) setting. The approach was evaluated using a publicly available microarray dataset containing 99 samples corresponding to four different prostate cancer subtypes.

Results: A hierarchical Sparse Bayesian GLM using GDP prior (SBGG) was developed to take into account the progressive nature of the response variable. We obtained an average overall classification accuracy between 82.5% and 94%, which was higher than Support Vector Machine, Random Forest or a Sparse Bayesian GLM using double exponential priors. Additionally, SBGG outperforms the other 3 methods in correctly identifying pre-metastatic stages of cancer progression, which can prove extremely valuable for therapeutic and diagnostic purposes. Importantly, using Geneset Cohesion Analysis Tool, we found that the top 100 genes produced by SBGG had an average functional cohesion p-value of 2.0E-4 compared to 0.007 to 0.131 produced by the other methods.

Conclusions: Using GDP in a Bayesian GLM model applied to cancer progression data results in better subclass prediction. In particular, the method identifies pre-metastatic stages of prostate cancer with substantially better accuracy and produces more functionally relevant gene sets.

No MeSH data available.


Related in: MedlinePlus