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Principal Investigator  
Principal Investigator's Name: Justin Leach
Institution: University of Alabama at Birmingham
Department: Biostatistics
Country:
Proposed Analysis: We are developing statistical methodology to incorporate spatial dependence into (Bayesian) variable selection and are interested in practical applications where a clinical or otherwise scientifically relevant outcome is modeled as a function of subject image values. For example, an outcome could be cognitive test results with subject images as predictors. The objectives for the model are: 1. To identify locations in the image where differences in measured values reliably result in changes in the outcome. 2. For the model to be generalizable; i.e., the prediction error of the model should be as low as possible. We will use standard statistical approaches to test how well the model achieves these stated goals; e.g., cross validation can help assess the second objective. We also provide some details regarding the statistical model under development. We are extending the spike-and-slab Lasso for generalized linear models to incorporate spatial information into variable selection. Spike-and-slab models marry two established approaches to variable selection. Spike-and-slab priors model variables/parameters as arising from a mixture of two distributions: one for variables that belong in the model and one for variables that do not belong in the model (George & McCulloch, 1993). The lasso is a penalized linear model that can shrink many parameter estimates to exactly zero, thus performing variable selection without explicit hypothesis testing (Park & Casella, 2008; Tibshirani, 1996). Combining spike-and-slab priors with lasso allows for assigning more flexible shrinkage penalties to parameter estimates based on their estimated inclusion probabilities. This model was originally introduced in a regression framework, and separately adapted for generalized linear models (GLM) for application in genetic research (Ročková & George, 2018; Tang et al., 2018; Tang, Shen, Zhang, & Yi, 2017). Our work incorporates spatial information into spike-and-slab GLM’s by placing conditional autoregressive priors on the logit of probabilities of inclusion. We expect that using spatial information can improve the ability for these models to predict clinical outcomes based on subject image data, and we hope to use ADNI data to explore the statistical benefits and limitations of the proposed methodology when applied to real-world imaging data. References George, E. I., & McCulloch, R. E. (1993). Variable Selection Via Gibbs Sampling. Journal of the American Statistical Association. https://doi.org/10.2307/2290777 Park, T., & Casella, G. (2008). The Bayesian Lasso. Journal of the American Statistical Association. https://doi.org/10.1198/016214508000000337 Ročková, V., & George, E. I. (2018). The Spike-and-Slab LASSO. Journal of the American Statistical Association. https://doi.org/10.1080/01621459.2016.1260469 Tang, Z., Shen, Y., Li, Y., Zhang, X., Wen, J., Qian, C., … Yi, N. (2018). Group spike-And-slab lasso generalized linear models for disease prediction and associated genes detection by incorporating pathway information. Bioinformatics. https://doi.org/10.1093/bioinformatics/btx684 Tang, Z., Shen, Y., Zhang, X., & Yi, N. (2017). The spike-and-slab lasso generalized linear models for prediction and associated genes detection. Genetics. https://doi.org/10.1534/genetics.116.192195 Tibshirani, R. (1996). Regression Shrinkage and Selection Via the Lasso. Journal of the Royal Statistical Society: Series B (Methodological). https://doi.org/10.1111/j.2517-6161.1996.tb02080.x
Additional Investigators