Bayesian Additive Regression Trees for Predicting Colon Cancer: Methodological Study (Validity Study)

Abstract

Recent research in biostatistics and bioinformatics focuses on diagnosing diseases using non-clinical approaches that involve machine learning methods. Several algorithmic procedures have been applied to solve various experimental problems that involve simulation and modelling of deoxyribonucleic acid (DNA) and ribonucleic acid (RNA) proteins. [1][2][3][4][5][6] The DNA and RNA are essential biological measurements used to monitor the abnormal cell growth in genetic sequencing, which serves as the bedrocks in non-clinical diagnoses.

A Novel Variable Selection Procedure for Binary Logistic Regression Using Akaike Information Criteria Testing:An Example in Breast Cancer Prediction: Methodological Study (Validity Study)

“…The goal of logistic regression is to find the best-fitting model that can predict the probability of the binary outcome based on the values of the independent variables. [10][11][12][13][14][15] The logistic regression model is formulated using a logistic function, which is a type of sigmoid function that maps any real-valued input to the range [0, 1]. The logistic function is defined as: (1) where also denoted by is the probability of the dependent variable (breast cancer outcomes) being equal to 1 given the values of the independent variables and their associated coefficient , and is the exponential function.…”

“…For example, suppose that the true coefficients are [0, 1, 1, 1, 0] so that the best model would include predictors 2, 3, and 4, but that our model includes only predictors 3 and 4. Then the false deletion rate is 33% (1/3 of the good predictors were lost), so sensitivity is 67% (2/3 were kept) (10). Therefore, where is the number of the selected informative variables, and is the number of true informative variables.…”

“…For example, suppose that the true model would include predictors 2, 3, and 4 (and exclude predictors 1 and 5), but our estimate contains 1, 2, 3, and 4. Then the false inclusion rate and the specificity rate would both be 50%, since of the two inactive predictors, one was included, and one was not (10).…”

“…Correct model rate (Accuracy) is the proportion of simulations in which exactly the correct subset was identified (i.e., in which sensitivity and specificity were both 100%). If a model is not correctly identified, then it is overfit (has too many predictors), underfit (too few), or misfit (the wrong ones) (10).…”

On the Oracle Properties of Bayesian Random Forest for Sparse High-Dimensional Gaussian Regression

“…Several techniques for handling high-dimensional data have been proposed from different areas of research, such as in oncology (modeling and identification of relevant genetic biomarkers for tumorous cancer cells) [1][2][3][4][5]. The methodologies of the techniques differ, but the collective standpoint is to find an efficient way to analyze high-dimensional data [6].…”