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To facilitate comparative treatment selection when there is substantial heterogeneity of treatment effectiveness, it is important to identify subgroups that exhibit differential treatment effects. Existing approaches model outcomes directly and then define subgroups according to interactions between treatment and covariates. Because outcomes are affected by both the covariate-treatment interactions and covariate main effects, direct modeling outcomes can be hard due to model misspecification, especially in presence of many covariates. Alternatively one can directly work with differential treatment effect estimation. We propose such a method that approximates a target function whose value directly reflects correct treatment assignment for patients. The function uses patient outcomes as weights rather than modeling targets. Consequently, our method can deal with binary, continuous, time-to-event, and possibly contaminated outcomes in the same fashion. We first focus on identifying only directional estimates from linear rules that characterize important subgroups. We further consider estimation of comparative treatment effects for identified subgroups. We demonstrate the advantages of our method in simulation studies and in analyses of two real data sets. [ABSTRACT FROM AUTHOR]

In many scientific and engineering applications, covariates are naturally grouped. When the group structures are available among covariates, people are usually interested in identifying both important groups and important variables within the selected groups. Among existing successful group variable selection methods, some methods fail to conduct the within group selection. Some methods are able to conduct both group and within group selection, but the corresponding objective functions are non-convex. Such a non-convexity may require extra numerical effort. In this article, we propose a novel Log-Exp-Sum(LES) penalty for group variable selection. The LES penalty is strictly convex. It can identify important groups as well as select important variables within the group. We develop an efficient group-level coordinate descent algorithm to fit the model. We also derive non-asymptotic error bounds and asymptotic group selection consistency for our method in the high-dimensional setting where the number of covariates can be much larger than the sample size. Numerical results demonstrate the good performance of our method in both variable selection and prediction. We applied the proposed method to an American Cancer Society breast cancer survivor dataset. The findings are clinically meaningful and may help design intervention programs to improve the qualify of life for breast cancer survivors. [ABSTRACT FROM AUTHOR]

Joint models of longitudinal and survival outcomes have been used with increasing frequency in clinical investigations. Correct specification of fixed and random effects is essential for practical data analysis. Simultaneous selection of variables in both longitudinal and survival components functions as a necessary safeguard against model misspecification. However, variable selection in such models has not been studied. No existing computational tools, to the best of our knowledge, have been made available to practitioners. In this article, we describe a penalized likelihood method with adaptive least absolute shrinkage and selection operator (ALASSO) penalty functions for simultaneous selection of fixed and random effects in joint models. To perform selection in variance components of random effects, we reparameterize the variance components using a Cholesky decomposition; in doing so, a penalty function of group shrinkage is introduced. To reduce the estimation bias resulted from penalization, we propose a two-stage selection procedure in which the magnitude of the bias is ameliorated in the second stage. The penalized likelihood is approximated by Gaussian quadrature and optimized by an EM algorithm. Simulation study showed excellent selection results in the first stage and small estimation biases in the second stage. To illustrate, we analyzed a longitudinally observed clinical marker and patient survival in a cohort of patients with heart failure. [ABSTRACT FROM AUTHOR]

Recent advance in biotechnology and its wide applications have led to the generation of many high-dimensional gene expression data sets that can be used to address similar biological questions. Meta-analysis plays an important role in summarizing and synthesizing scientific evidence from multiple studies. When the dimensions of datasets are high, it is desirable to incorporate variable selection into meta-analysis to improve model interpretation and prediction. According to our knowledge, all existing methods conduct variable selection with meta-analyzed data in an 'all-in-or-all-out' fashion, that is, a gene is either selected in all of studies or not selected in any study. However, due to data heterogeneity commonly exist in meta-analyzed data, including choices of biospecimens, study population, and measurement sensitivity, it is possible that a gene is important in some studies while unimportant in others. In this article, we propose a novel method called meta-lasso for variable selection with high-dimensional meta-analyzed data. Through a hierarchical decomposition on regression coefficients, our method not only borrows strength across multiple data sets to boost the power to identify important genes, but also keeps the selection flexibility among data sets to take into account data heterogeneity. We show that our method possesses the gene selection consistency, that is, when sample size of each data set is large, with high probability, our method can identify all important genes and remove all unimportant genes. Simulation studies demonstrate a good performance of our method. We applied our meta-lasso method to a meta-analysis of five cardiovascular studies. The analysis results are clinically meaningful. [ABSTRACT FROM AUTHOR]

The tumor-node-metastasis staging system has been the lynchpin of cancer diagnosis, treatment, and prognosis for many years. For meaningful clinical use, an orderly grouping of the T and N categories into a staging system needs to be defined, usually with respect to a time-to-event outcome. This can be reframed as a model selection problem with respect to features arranged on a partially ordered two-way grid, and a penalized regression method is proposed for selecting the optimal grouping. Instead of penalizing the L1-norm of the coefficients like lasso, in order to enforce the stage grouping, we place L1 constraints on the differences between neighboring coefficients. The underlying mechanism is the sparsity-enforcing property of the L1 penalty, which forces some estimated coefficients to be the same and hence leads to stage grouping. Partial ordering constraints is also required as both the T and N categories are ordinal. A series of optimal groupings with different numbers of stages can be obtained by varying the tuning parameter, which gives a tree-like structure offering a visual aid on how the groupings are progressively made. We hence call the proposed method the lasso tree. We illustrate the utility of our method by applying it to the staging of colorectal cancer using survival outcomes. Simulation studies are carried out to examine the finite sample performance of the selection procedure. We demonstrate that the lasso tree is able to give the right grouping with moderate sample size, is stable with regard to changes in the data, and is not affected by random censoring. [ABSTRACT FROM PUBLISHER]

Variable selection in high-dimensional clustering analysis is an important yet challenging problem. In this article, we propose two methods that simultaneously separate data points into similar clusters and select informative variables that contribute to the clustering. Our methods are in the framework of penalized model-based clustering. Unlike the classical L1-norm penalization, the penalty terms that we propose make use of the fact that parameters belonging to one variable should be treated as a natural “group.” Numerical results indicate that the two new methods tend to remove noninformative variables more effectively and provide better clustering results than the L1-norm approach. [ABSTRACT FROM AUTHOR]