In this study, we propose a multiple comparison procedure for detecting sequentially a lowest dose level having interaction based on two dose sample means on two treatments with increasing dose levels in a dose-response test. We apply a group sequential procedure in order to realize our method that tests sequentially the null hypotheses of no interaction based on tetrad differences. If we can first detect a dose level having interaction at an early stage in the sequential test, since we can terminate the procedure with just the few observations up to that stage, the procedure is useful from an economical point of view. In the procedure, we present an integral formula to determine the repeated confidence boundaries for satisfying a predefined type I familywise error rate. Furthermore,we show how to decide a required sample size in each cell so as to guarantee the power of the test. In the simulation studies, we evaluate the superiority among the procedures based on three alpha spending functions in terms of the power of the test and the required sample size for various configurations of population means.
Over the past decade, a variety of powerful multiple testing procedures have been developed for the analysis of clinical trials with multiple clinical objectives based, for example, on several endpoints, dose-placebo comparisons and patient subgroups. Sample size and power calculations in these complex settings are not straightforward and,in general, simulation-based methods are used. In this paper, we provide an overview of power evaluation approaches in the context of clinical trials with multiple objectives and illustrate the key principles using case studies commonly seen in the development of new therapies.
In this paper, we attempt to build and evaluate several predictive models to predict success of telemarketing calls for selling bank long-term deposits using a publicly available set of data from a Portuguese retail bank collected from 2008 to 2013 (Moro et al., 2014, Decision Support Systems). The data include multiple predictor variables,either numeric or categorical, related with bank client, product and social-economic attributes. Dealing with a categorical predictor variable as multiple dummy variables increases model dimensionality, and redundancy in model parameterization must be of practical concern. This motivates us to assess prediction performance with more parsimonious modeling. We apply contemporary variable selection methods with penalization including lasso, elastic net, smoothly-clipped absolute deviation, minimum concave penalty as well as the smooth-threshold estimating equation. In addition to variable selection, the smooth-threshold estimating equation can achieve automatic grouping of predictor variables, which is an alternative sparse modeling to perform variable selection and could be suited to a certain problem, e.g., dummy variables created from categorical predictor variables. Predictive power of each modeling approach is assessed by repeating cross-validation experiments or sample splitting, one for training and another for testing.
We consider the Bayesian lasso for regression, which can be interpreted as an L1 norm regularization based on a Bayesian approach when the Laplace or doubleexponential prior distribution is placed on the regression coefficients. A crucial issue is an appropriate choice of the values of hyperparameters included in the prior distributions, which essentially control the sparsity in the estimated model. To choose the values of tuning parameters, we introduce a model selection criterion for evaluating a Bayesian predictive distribution for the Bayesian lasso. Numerical results are presented to illustrate the properties of our sparse Bayesian modeling procedure.
Sparse regularization provides solutions in which some parameters are exactly zero and therefore they can be used for selecting variables in regression models and so on. The lasso is proposed as a method for selecting individual variables for regression models. On the other hand, the group lasso selects groups of variables rather than individuals and therefore it has been used in various fields of applications. More recently,penalties that select variables at both the group and individual levels has been considered. They are so called bi-level selection. In this paper we focus on some penalties that aim for bi-level selection. We overview these penalties and estimation algorithms,and then compare the effectiveness of these penalties from the viewpoint of accuracy of prediction and selection of variables and groups through simulation studies.
In this paper, we present stochastic optimization variants of the alternating direction method of multipliers (ADMM). ADMM is a useful method to solve a regularized risk minimization problem where the regularization term is complicated and not easily dealt with in an ordinary manner. For example, structured regularization is one of the typical applications of such regularization in which ADMM is effective. It includes group lasso regularization, low rank tensor regularization, and fused lasso regularization. Since ADMM is a general method and has wide applications, it is intensively studied and refined these days. However, ADMM is not suited to optimization problems with huge data. To resolve this problem, online stochastic optimization variants and a batch stochastic optimization variant of ADMM are presented. All the presented methods can be easily implemented and have wide applications. Moreover, the theoretical guarantees of the methods are given.
A problem of supervised learning in which the data consist of p features and n observations is considered. Each observation is assumed to belong to either one of the two classes. Linear discriminant analysis (LDA) has been widely used for both classification and dimensionality reduction in this setting. However, when the dimensionality p is high and the observations are scarce, LDA does not offer a satisfactory result for classification. Witten & Tibshirani (2011) proposed the penalized LDA based on the Fisher’s discriminant problem with sparsity penalization. In this paper, an elastic-net type penalization is considered for LDA, and the corresponding optimization problem is efficiently solved.
We consider the problem of sparse estimation of undirected graphical models via the L1 regularization. The ordinary lasso encourages the sparsity on all edges equally likely, so that all nodes tend to have small degrees. On the other hand, many real-world networks are often scale-free, where some nodes have a large number of edges. In such cases, a penalty that induces structured sparsity, such as a log penalty, performs better than the ordinary lasso. In practical situations, however, it is difficult to determine an optimal penalty among the ordinary lasso, log penalty, or somewhere in between. In this paper, we introduce a new class of penalty that is based on the exponentiation of the minimax concave penalty. The proposed penalty includes both the lasso and the log penalty, and the gap between these two penalties is bridged by a tuning parameter. We apply cross-validation to select an appropriate value of the tuning parameter. Monte Carlo simulations are conducted to investigate the performance of our proposed procedure. The numerical result shows that the proposed method can perform better than the existing log penalty and the ordinary lasso.
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