Exploring Pathway-Based Group Lasso for Cancer Survival Analysis: A Special Case of Multi-Task Learning

Motivation: The Cox proportional hazard models are widely used in the study of cancer survival. However, these models often meet challenges such as the large number of features and small sample sizes of cancer data sets. While this issue can be partially solved by applying regularization techniques such as lasso, the models still suffer from unsatisfactory predictive power and low stability.Methods: Here, we investigated two methods to improve survival models. Firstly, we leveraged the biological knowledge that groups of genes act together in pathways and regularized both at the group and gene level using latent group lasso penalty term. Secondly, we designed and applied a multi-task learning penalty that allowed us leveraging the relationship between survival models for different cancers.Results: We observed modest improvements over the simple lasso model with the inclusion of latent group lasso penalty for six of the 16 cancer types tested. The addition of a multi-task penalty, which penalized coefficients in pairs of cancers from diverging too greatly, significantly improved accuracy for a single cancer, lung squamous cell carcinoma, while having minimal effect on other cancer types.Conclusion: While the use of pathway information and multi-tasking shows some promise, these methods do not provide a substantial improvement when compared with standard methods.

Prognostic Genomic Predictive Biomarkers for Early-Stage Lung Cancer Patients

Aims: Our goal is to find predictive genomic biomarkers in order to identify subgroups of early-stage lung cancer patients that are most likely to benefit from adjuvant chemotherapy with surgery (ACT). Background: Receiving ACT appears to have a better prognosis for more severe early-stage non-small cell lung cancer patients than surgical resection only. However, not all patients benefit from chemotherapy. Objective: Preliminary studies suggest that the application of ACT is associated with a better prognosis for more severe NSCLC patients compared to those who only underwent surgical resection. Given the immense personal and financial costs associated with ACT, finding the patients who are most likely to benefit from ACT is paramount. Thus, the purpose of this research is to utilize gene expression and clinical data from lung cancer patients to find treatment-associated genomic biomarkers. Methods: To investigate the treatment effect, a modified-covariate regularized Cox regression model with lasso penalty is implemented using National Cancer Institute gene expression data to find genomic biomarkers. Results: This research utilized an independent validation dataset involving 318 lung cancer patients to validate the models. In the validation set with 318 patients, the modified covariate Cox model with lasso penalty were able to show patients who followed their predicted recommendation (either ACT for low-risk group or OBS for the high-risk group, n = 171) have higher survival benefits than 147 patients who did not follow the recommendations (p < .0001). Conclusion: Based on validation data, patients who follow our predicted recommendation by genomic biomarkers selected from the proposed model will likely benefit from ACT.

Jewel: A Novel Method for Joint Estimation of Gaussian Graphical Models

In this paper, we consider the problem of estimating multiple Gaussian Graphical Models from high-dimensional datasets. We assume that these datasets are sampled from different distributions with the same conditional independence structure, but not the same precision matrix. We propose jewel, a joint data estimation method that uses a node-wise penalized regression approach. In particular, jewel uses a group Lasso penalty to simultaneously guarantee the resulting adjacency matrix’s symmetry and the graphs’ joint learning. We solve the minimization problem using the group descend algorithm and propose two procedures for estimating the regularization parameter. Furthermore, we establish the estimator’s consistency property. Finally, we illustrate our estimator’s performance through simulated and real data examples on gene regulatory networks.

A Bayesian group lasso classification for ADNI volumetrics data

The primary objective of this paper is to develop a statistically valid classification procedure for analyzing brain image volumetrics data obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) in elderly subjects with cognitive impairments. The Bayesian group lasso method thereby proposed for logistic regression efficiently selects an optimal model with the use of a spike and slab type prior. This method selects groups of attributes of a brain subregion encouraged by the group lasso penalty. We conduct simulation studies for high- and low-dimensional scenarios where our method is always able to select the true parameters that are truly predictive among a large number of parameters. The method is then applied on dichotomous response ADNI data which selects predictive atrophied brain regions and classifies Alzheimer’s disease patients from healthy controls. Our analysis is able to give an accuracy rate of 80% for classifying Alzheimer’s disease. The suggested method selects 29 brain subregions. The medical literature indicates that all these regions are associated with Alzheimer’s patients. The Bayesian method of model selection further helps selecting only the subregions that are statistically significant, thus obtaining an optimal model.

Multiple imputation with compatibility for high-dimensional data

Multiple Imputation (MI) is always challenging in high dimensional settings. The imputation model with some selected number of predictors can be incompatible with the analysis model leading to inconsistent and biased estimates. Although compatibility in such cases may not be achieved, but one can obtain consistent and unbiased estimates using a semi-compatible imputation model. We propose to relax the lasso penalty for selecting a large set of variables (at most n). The substantive model that also uses some formal variable selection procedure in high-dimensional structures is then expected to be nested in this imputation model. The resulting imputation model will be semi-compatible with high probability. The likelihood estimates can be unstable and can face the convergence issues as the number of variables becomes nearly as large as the sample size. To address these issues, we further propose to use a ridge penalty for obtaining the posterior distribution of the parameters based on the observed data. The proposed technique is compared with the standard MI software and MI techniques available for high-dimensional data in simulation studies and a real life dataset. Our results exhibit the superiority of the proposed approach to the existing MI approaches while addressing the compatibility issue.

RAMRSGL: A Robust Adaptive Multinomial Regression Model for Multicancer Classification

In view of the challenges of the group Lasso penalty methods for multicancer microarray data analysis, e.g., dividing genes into groups in advance and biological interpretability, we propose a robust adaptive multinomial regression with sparse group Lasso penalty (RAMRSGL) model. By adopting the overlapping clustering strategy, affinity propagation clustering is employed to obtain each cancer gene subtype, which explores the group structure of each cancer subtype and merges the groups of all subtypes. In addition, the data-driven weights based on noise are added to the sparse group Lasso penalty, combining with the multinomial log-likelihood function to perform multiclassification and adaptive group gene selection simultaneously. The experimental results on acute leukemia data verify the effectiveness of the proposed method.

LASSO type penalized spline regression for binary data

Background Generalized linear mixed models (GLMMs), typically used for analyzing correlated data, can also be used for smoothing by considering the knot coefficients from a regression spline as random effects. The resulting models are called semiparametric mixed models (SPMMs). Allowing the random knot coefficients to follow a normal distribution with mean zero and a constant variance is equivalent to using a penalized spline with a ridge regression type penalty. We introduce the least absolute shrinkage and selection operator (LASSO) type penalty in the SPMM setting by considering the coefficients at the knots to follow a Laplace double exponential distribution with mean zero. Methods We adopt a Bayesian approach and use the Markov Chain Monte Carlo (MCMC) algorithm for model fitting. Through simulations, we compare the performance of curve fitting in a SPMM using a LASSO type penalty to that of using ridge penalty for binary data. We apply the proposed method to obtain smooth curves from data on the relationship between the amount of pack years of smoking and the risk of developing chronic obstructive pulmonary disease (COPD). Results The LASSO penalty performs as well as ridge penalty for simple shapes of association and outperforms the ridge penalty when the shape of association is complex or linear. Conclusion We demonstrated that LASSO penalty captured complex dose-response association better than the Ridge penalty in a SPMM.

A Regularized Mixture of Linear Experts for Quality Prediction in Multimode and Multiphase Industrial Processes

This paper proposes the use of a regularized mixture of linear experts (MoLE) for predictive modeling in multimode-multiphase industrial processes. For this purpose, different regularized MoLE were evaluated, namely, through the elastic net (EN), Lasso, and ridge regression (RR) penalties. Their performances were compared when trained with different numbers of samples, and in comparison to other nonlinear predictive models. The models were evaluated on real multiphase polymerization process data. The Lasso penalty provided the best performance among all regularizers for MoLE, even when trained with a small number of samples.