Risk Prediction for Prostate Cancer Recurrence Through Regularized Estimation with Simultaneous Adjustment for Nonlinear Clinical Effects

Deep Learning and Machine Learning with Grid Search to Predict Later Occurrence of Breast Cancer Metastasis Using Clinical Data

Background: It is important to be able to predict, for each individual patient, the likelihood of later metastatic occurrence, because the prediction can guide treatment plans tailored to a specific patient to prevent metastasis and to help avoid under-treatment or over-treatment. Deep neural network (DNN) learning, commonly referred to as deep learning, has become popular due to its success in image detection and prediction, but questions such as whether deep learning outperforms other machine learning methods when using non-image clinical data remain unanswered. Grid search has been introduced to deep learning hyperparameter tuning for the purpose of improving its prediction performance, but the effect of grid search on other machine learning methods are under-studied. In this research, we take the empirical approach to study the performance of deep learning and other machine learning methods when using non-image clinical data to predict the occurrence of breast cancer metastasis (BCM) 5, 10, or 15 years after the initial treatment. We developed prediction models using the deep feedforward neural network (DFNN) methods, as well as models using nine other machine learning methods, including naïve Bayes (NB), logistic regression (LR), support vector machine (SVM), LASSO, decision tree (DT), k-nearest neighbor (KNN), random forest (RF), AdaBoost (ADB), and XGBoost (XGB). We used grid search to tune hyperparameters for all methods. We then compared our feedforward deep learning models to the models trained using the nine other machine learning methods. Results: Based on the mean test AUC (Area under the ROC Curve) results, DFNN ranks 6th, 4th, and 3rd when predicting 5-year, 10-year, and 15-year BCM, respectively, out of 10 methods. The top performing methods in predicting 5-year BCM are XGB (1st), RF (2nd), and KNN (3rd). For predicting 10-year BCM, the top performers are XGB (1st), RF (2nd), and NB (3rd). Finally, for 15-year BCM, the top performers are SVM (1st), LR and LASSO (tied for 2nd), and DFNN (3rd). The ensemble methods RF and XGB outperform other methods when data are less balanced, while SVM, LR, LASSO, and DFNN outperform other methods when data are more balanced. Our statistical testing results show that at a significance level of 0.05, DFNN overall performs comparably to other machine learning methods when predicting 5-year, 10-year, and 15-year BCM. Conclusions: Our results show that deep learning with grid search overall performs at least as well as other machine learning methods when using non-image clinical data. It is interesting to note that some of the other machine learning methods, such as XGB, RF, and SVM, are very strong competitors of DFNN when incorporating grid search. It is also worth noting that the computation time required to do grid search with DFNN is much more than that required to do grid search with the other nine machine learning methods.

Variable selection for high-dimensional partly linear additive Cox model with application to Alzheimer's disease

Variable selection has been discussed under many contexts and especially, a large literature has been established for the analysis of right-censored failure time data. In this article, we discuss an interval-censored failure time situation where there exist two sets of covariates with one being low-dimensional and having possible nonlinear effects and the other being high-dimensional. For the problem, we present a penalized estimation procedure for simultaneous variable selection and estimation, and in the method, Bernstein polynomials are used to approximate the involved nonlinear functions. Furthermore, for implementation, a coordinate-wise optimization algorithm, which can accommodate most commonly used penalty functions, is developed. A numerical study is performed for the evaluation of the proposed approach and suggests that it works well in practical situations. Finally the method is applied to an Alzheimer's disease study that motivated this investigation.

Assessing predictive accuracy of survival regressions subject to nonindependent censoring

Survival regression is commonly applied in biomedical studies or clinical trials, and evaluating their predictive performance plays an essential role for model diagnosis and selection. The presence of censored data, particularly if informative, may pose more challenges for the assessment of predictive accuracy. Existing literature mainly focuses on prediction for survival probabilities with limitation work for survival time. In this work, we focus on accuracy measures of predicted survival times adjusted for a potentially informative censoring mechanism (ie, coarsening at random (CAR); non-CAR) by adopting the technique of inverse probability of censoring weighting. Our proposed predictive metric can be adaptive to various survival regression frameworks including but not limited to accelerated failure time models and proportional hazards models. Moreover, we provide the asymptotic properties of the inverse probability of censoring weighting estimators under CAR. We consider the settings of high-dimensional data under CAR or non-CAR for extensions. The performance of the proposed method is evaluated through extensive simulation studies and analysis of real data from the Critical Assessment of Microarray Data Analysis.

Addressing issues associated with evaluating prediction models for survival endpoints based on the concordance statistic

Prediction models for disease risk and prognosis play an important role in biomedical research, and evaluating their predictive accuracy in the presence of censored data is of substantial interest. The standard concordance (c) statistic has been extended to provide a summary measure of predictive accuracy for survival models. Motivated by a prostate cancer study, we address several issues associated with evaluating survival prediction models based on c-statistic with a focus on estimators using the technique of inverse probability of censoring weighting (IPCW). Compared to the existing work, we provide complete results on the asymptotic properties of the IPCW estimators under the assumption of coarsening at random (CAR), and propose a sensitivity analysis under the mechanism of noncoarsening at random (NCAR). In addition, we extend the IPCW approach as well as the sensitivity analysis to high-dimensional settings. The predictive accuracy of prediction models for cancer recurrence after prostatectomy is assessed by applying the proposed approaches. We find that the estimated predictive accuracy for the models in consideration is sensitive to NCAR assumption, and thus identify the best predictive model. Finally, we further evaluate the performance of the proposed methods in both settings of low-dimensional and high-dimensional data under CAR and NCAR through simulations.

A novel artificial neural network method for biomedical prediction based on matrix pseudo-inversion

Biomedical prediction based on clinical and genome-wide data has become increasingly important in disease diagnosis and classification. To solve the prediction problem in an effective manner for the improvement of clinical care, we develop a novel Artificial Neural Network (ANN) method based on Matrix Pseudo-Inversion (MPI) for use in biomedical applications. The MPI-ANN is constructed as a three-layer (i.e., input, hidden, and output layers) feed-forward neural network, and the weights connecting the hidden and output layers are directly determined based on MPI without a lengthy learning iteration. The LASSO (Least Absolute Shrinkage and Selection Operator) method is also presented for comparative purposes. Single Nucleotide Polymorphism (SNP) simulated data and real breast cancer data are employed to validate the performance of the MPI-ANN method via 5-fold cross validation. Experimental results demonstrate the efficacy of the developed MPI-ANN for disease classification and prediction, in view of the significantly superior accuracy (i.e., the rate of correct predictions), as compared with LASSO. The results based on the real breast cancer data also show that the MPI-ANN has better performance than other machine learning methods (including support vector machine (SVM), logistic regression (LR), and an iterative ANN). In addition, experiments demonstrate that our MPI-ANN could be used for bio-marker selection as well.

A general binomial regression model to estimate standardized risk differences from binary response data

Estimates of absolute risks and risk differences are necessary for evaluating the clinical and population impact of biomedical research findings. We have developed a linear-expit regression model (LEXPIT) to incorporate linear and nonlinear risk effects to estimate absolute risk from studies of a binary outcome. The LEXPIT is a generalization of both the binomial linear and logistic regression models. The coefficients of the LEXPIT linear terms estimate adjusted risk differences, whereas the exponentiated nonlinear terms estimate residual odds ratios. The LEXPIT could be particularly useful for epidemiological studies of risk association, where adjustment for multiple confounding variables is common. We present a constrained maximum likelihood estimation algorithm that ensures the feasibility of risk estimates of the LEXPIT model and describe procedures for defining the feasible region of the parameter space, judging convergence, and evaluating boundary cases. Simulations demonstrate that the methodology is computationally robust and yields feasible, consistent estimators. We applied the LEXPIT model to estimate the absolute 5-year risk of cervical precancer or cancer associated with different Pap and human papillomavirus test results in 167,171 women undergoing screening at Kaiser Permanente Northern California. The LEXPIT model found an increased risk due to abnormal Pap test in human papillomavirus-negative that was not detected with logistic regression. Our R package blm provides free and easy-to-use software for fitting the LEXPIT model.

VARIABLE SELECTION IN PARTLY LINEAR REGRESSION MODEL WITH DIVERGING DIMENSIONS FOR RIGHT CENSORED DATA

Recent biomedical studies often measure two distinct sets of risk factors: low-dimensional clinical and environmental measurements, and high-dimensional gene expression measurements. For prognosis studies with right censored response variables, we propose a semiparametric regression model whose covariate effects have two parts: a nonparametric part for low-dimensional covariates, and a parametric part for high-dimensional covariates. A penalized variable selection approach is developed. The selection of parametric covariate effects is achieved using an iterated Lasso approach, for which we prove the selection consistency property. The nonparametric component is estimated using a sieve approach. An empirical model selection tool for the nonparametric component is derived based on the Kullback-Leibler geometry. Numerical studies show that the proposed approach has satisfactory performance. Application to a lymphoma study illustrates the proposed method.