Bayesian Bridge Regression

Evaluating the risk of endometriosis based on patients' self-assessment questionnaires

BACKGROUND

Endometriosis is a condition that significantly affects the quality of life of about 10 % of reproductive-aged women. It is characterized by the presence of tissue similar to the uterine lining (endometrium) outside the uterus, which can lead lead scarring, adhesions, pain, and fertility issues. While numerous factors associated with endometriosis are documented, a wide range of symptoms may still be undiscovered.

METHODS

In this study, we employed machine learning algorithms to predict endometriosis based on the patient symptoms extracted from 13,933 questionnaires. We compared the results of feature selection obtained from various algorithms (i.e., Boruta algorithm, Recursive Feature Selection) with experts' decisions. As a benchmark model architecture, we utilized a LightGBM algorithm, along with Multivariate Imputation by Chained Equations (MICE) and k-nearest neighbors (KNN), for missing data imputation. Our primary objective was to assess the model's performance and feature importance compared to existing studies.

RESULTS

We identified the top 20 predictors of endometriosis, uncovering previously overlooked features such as Cesarean section, ovarian cysts, and hernia. Notably, the model's performance metrics were maximized when utilizing a combination of multiple feature selection methods. Specifically, the final model achieved an area under the receiver operator characteristic curve (AUC) of 0.85 on the training dataset and an AUC of 0.82 on the testing dataset.

CONCLUSIONS

The application of machine learning in diagnosing endometriosis has the potential to significantly impact clinical practice, streamlining the diagnostic process and enhancing efficiency. Our questionnaire-based prediction approach empowers individuals with endometriosis to proactively identify potential symptoms, facilitating informed discussions with healthcare professionals about diagnosis and treatment options.

The reciprocal Bayesian LASSO

A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model selection relative to traditional shrinkage methods. Here we consider a fully Bayesian formulation of the rLASSO problem, which is based on the observation that the rLASSO estimate for linear regression parameters can be interpreted as a Bayesian posterior mode estimate when the regression parameters are assigned independent inverse Laplace priors. Bayesian inference from this posterior is possible using an expanded hierarchy motivated by a scale mixture of double Pareto or truncated normal distributions. On simulated and real datasets, we show that the Bayesian formulation outperforms its classical cousin in estimation, prediction, and variable selection across a wide range of scenarios while offering the advantage of posterior inference. Finally, we discuss other variants of this new approach and provide a unified framework for variable selection using flexible reciprocal penalties. All methods described in this article are publicly available as an R package at: https://github.com/himelmallick/BayesRecipe.