Applications of Bayesian shrinkage prior models in clinical research with categorical responses

Abstract

Background Prediction and classification algorithms are commonly used in clinical research for identifying patients susceptible to clinical conditions such as diabetes, colon cancer, and Alzheimer’s disease. Developing accurate prediction and classification methods benefits personalized medicine. Building an excellent predictive model involves selecting the features that are most significantly associated with the outcome. These features can include several biological and demographic characteristics, such as genomic biomarkers and health history. Such variable selection becomes challenging when the number of potential predictors is large. Bayesian shrinkage models have emerged as popular and flexible methods of variable selection in regression settings. This work discusses variable selection with three shrinkage priors and illustrates its application to clinical data such as Pima Indians Diabetes, Colon cancer, ADNI, and OASIS Alzheimer’s real-world data. Methods A unified Bayesian hierarchical framework that implements and compares shrinkage priors in binary and multinomial logistic regression models is presented. The key feature is the representation of the likelihood by a Polya-Gamma data augmentation, which admits a natural integration with a family of shrinkage priors, specifically focusing on Horseshoe, Dirichlet Laplace, and Double Pareto priors. Extensive simulation studies are conducted to assess the performances under different data dimensions and parameter settings. Measures of accuracy, AUC, brier score, L1 error, cross-entropy, and ROC surface plots are used as evaluation criteria comparing the priors with frequentist methods as Lasso, Elastic-Net, and Ridge regression. Results All three priors can be used for robust prediction on significant metrics, irrespective of their categorical response model choices. Simulation studies could achieve the mean prediction accuracy of 91.6% (95% CI: 88.5, 94.7) and 76.5% (95% CI: 69.3, 83.8) for logistic regression and multinomial logistic models, respectively. The model can identify significant variables for disease risk prediction and is computationally efficient. Conclusions The models are robust enough to conduct both variable selection and prediction because of their high shrinkage properties and applicability to a broad range of classification problems.

Count data models and Bayesian shrinkage priors with real-world data applications

“…With the prior hierarchical structures on the coefficients β from [? ], the posterior distribution for both α and β have similar forms similar to 2.1 [19,20].…”

“…The conditional densities of the hyper-parameters following Horseshoe, DL, and DP priors have the same form and can be referred in [19].…”

Frequency of missed doses and its effects on the regulation of glucose levels in patients with type 2 diabetes: A retrospective analysis

“…In addition to the abovementioned traditional statistical analyses, the impact of potential predictors on medication adherence was further explored using the Bayesian shrinkage prior models implemented in RStan, which is the R interface Stan. This approach was inspired by Bhattacharyya et al’s work, [ 18 ] which discusses the application of shrinkage priors in clinical research settings, particularly for categorical responses. The following parameters were used for sampling: chain = 4, iter = 4000, warmup = 2000, thin = 1, and max_treedepth = 30.…”

Revisiting the complex time-varying effect of non-pharmaceutical interventions on COVID-19 transmission in the United States

“…The Bayesian hierarchical model with shrinkage priors is a compelling method to deal with high-dimensional and correlated structure of predictors ( 35 ). Many simulation and application studies have reported the robustness of the results in high-dimensional regressions by using shrinkage priors ( 36 , 37 ). Depending on the number and forms of prior distribution settings for the coefficients, it could be roughly divided into discrete mixture shrinkage priors, such as the spike-and-slab prior, and global–local (GL) shrinkage priors, including the horseshoe prior and Dirichlet Laplace prior ( 37 , 38 ).…”