Variable selection approach for zero-inflated count data via adaptive lasso

This article proposes a variable selection approach for zero-inflated count data analysis based on the adaptive lasso technique. Two models including the zero-inflated Poisson and the zero-inflated negative binomial are investigated. An efficient algorithm is used to minimize the penalized log-likelihood function in an approximate manner. Both the generalized cross-validation and Bayesian information criterion procedures are employed to determine the optimal tuning parameter, and a consistent sandwich formula of standard errors for nonzero estimates is given based on local quadratic approximation. We evaluate the performance of the proposed adaptive lasso approach through extensive simulation studies, and apply it to analyze real-life data about doctor visits.     

On the grouped selection and model complexity of the adaptive elastic net

Lasso proved to be an extremely successful technique for simultaneous estimation and variable selection. However lasso has two major drawbacks. First, it does not enforce any grouping effect and secondly in some situation lasso solutions are inconsistent for variable selection. To overcome this inconsistency adaptive lasso is proposed where adaptive weights are used for penalizing different coefficients. Recently a doubly regularized technique namely elastic net is proposed which encourages grouping effect i.e. either selection or omission of the correlated variables together. However elastic net is also inconsistent. In this paper we study adaptive elastic net which does not have this drawback. In this article we specially focus on the grouped selection property of adaptive elastic net along with its model selection complexity. We also shed some light on the bias-variance tradeoff of different regularization methods including adaptive elastic net. An efficient algorithm was proposed in the line of LARS-EN, which is then illustrated with simulated as well as real life data examples.     

Gibbs sampling method for the Bayesian adaptive elastic net

This article considers the adaptive elastic net estimator for regularized mean regression from a Bayesian perspective. Representing the Laplace distribution as a mixture of Bartlett–Fejer kernels with a Gamma mixing density, a Gibbs sampling algorithm for the adaptive elastic net is developed. By introducing slice variables, it is shown that the mixture representation provides a Gibbs sampler that can be accomplished by sampling from either truncated normal or truncated Gamma distribution. The proposed method is illustrated using several simulation studies and analyzing a real dataset. Both simulation studies and real data analysis indicate that the proposed approach performs well.     

Regularization and variable selection via the elastic net

Summary.  We propose the elastic net, a new regularization and variable selection method. Real world data and a simulation study show that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation. In addition, the elastic net encourages a grouping effect, where strongly correlated predictors tend to be in or out of the model together. The elastic net is particularly useful when the number of predictors ( p ) is much bigger than the number of observations ( n ). By contrast, the lasso is not a very satisfactory variable selection method in the p ≫ n case. An algorithm called LARS-EN is proposed for computing elastic net regularization paths efficiently, much like algorithm LARS does for the lasso.     

Variable selection for high-dimensional generalized linear model with block-missing data

In modern scientific research, multiblock missing data emerges with synthesizing information across multiple studies. However, existing imputation methods for handling block-wise missing data either focus on the single-block missing pattern or heavily rely on the model structure. In this study, we propose a single regression-based imputation algorithm for multiblock missing data. First, we conduct a sparse precision matrix estimation based on the structure of block-wise missing data. Second, we impute the missing blocks with their means conditional on the observed blocks. Theoretical results about variable selection and estimation consistency are established in the context of a generalized linear model. Moreover, simulation studies show that compared with existing methods, the proposed imputation procedure is robust to various missing mechanisms because of the good properties of regression imputation. An application to Alzheimer's Disease Neuroimaging Initiative data also confirms the superiority of our proposed method.     

Variable selection for longitudinal data with high-dimensional covariates and dropouts

A new variable selection approach utilizing penalized estimating equations is developed for high-dimensional longitudinal data with dropouts under a missing at random (MAR) mechanism. The proposed method is based on the best linear approximation of efficient scores from the full dataset and does not need to specify a separate model for the missing or imputation process. The coordinate descent algorithm is adopted to implement the proposed method and is computational feasible and stable. The oracle property is established and extensive simulation studies show that the performance of the proposed variable selection method is much better than that of penalized estimating equations dealing with complete data which do not account for the MAR mechanism. In the end, the proposed method is applied to a Lifestyle Education for Activity and Nutrition study and the interaction effect between intervention and time is identified, which is consistent with previous findings.     

Variable selection for semiparametric errors-in-variables regression model with longitudinal data

In this paper, we focus on the variable selection for the semiparametric regression model with longitudinal data when some covariates are measured with errors. A new bias-corrected variable selection procedure is proposed based on the combination of the quadratic inference functions and shrinkage estimations. With appropriate selection of the tuning parameters, we establish the consistency and asymptotic normality of the resulting estimators. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedure. We further illustrate the proposed procedure with an application.     

Variable selection strategies in survival models with multiple imputations

In this paper, the variable selection strategies (criteria) are thoroughly discussed and their use in various survival models is investigated. The asymptotic efficiency property, in the sense of Shibata Ann Stat 8: 147-164, 1980, of a class of variable selection strategies which includes the AIC and all criteria equivalent to it, is established for a general class of survival models, such as parametric frailty or transformation models and accelerated failure time models, under minimum conditions. Furthermore, a multiple imputations method is proposed which is found to successfully handle censored observations and constitutes a competitor to existing methods in the literature. A number of real and simulated data are used for illustrative purposes.     

A class of semiparametric transformation models for survival data with a cured proportion

We propose a new class of semiparametric regression models based on a multiplicative frailty assumption with a discrete frailty, which may account for cured subgroup in population. The cure model framework is then recast as a problem with a transformation model. The proposed models can explain a broad range of nonproportional hazards structures along with a cured proportion. An efficient and simple algorithm based on the martingale process is developed to locate the nonparametric maximum likelihood estimator. Unlike existing expectation-maximization based methods, our approach directly maximizes a nonparametric likelihood function, and the calculation of consistent variance estimates is immediate. The proposed method is useful for resolving identifiability features embedded in semiparametric cure models. Simulation studies are presented to demonstrate the finite sample properties of the proposed method. A case study of stage III soft-tissue sarcoma is given as an illustration.     

A Bayesian adaptive design for two-stage clinical trials with survival data

A randomized two-stage adaptive Bayesian design is proposed and studied for allocation and comparison in a phase III clinical trial with survival time as treatment response. Several exact and limiting properties of the design and the follow-up inference are studied, both numerically and theoretically, and are compared with a single-stage randomized procedure. The applicability of the proposed methodology is illustrated by using some real data.     

Variable selection in robust semiparametric modeling for longitudinal data

This paper considers robust variable selection in semiparametric modeling for longitudinal data with an unspecified dependence structure. First, by basis spline approximation and using a general formulation to treat mean, median, quantile and robust mean regressions in one setting, we propose a weighted M-type regression estimator, which achieves robustness against outliers in both the response and covariates directions, and can accommodate heterogeneity, and the asymptotic properties are also established. Furthermore, a penalized weighted M-type estimator is proposed, which can do estimation and select relevant nonparametric and parametric components simultaneously, and robustly. Without any specification of error distribution and intra-subject dependence structure, the variable selection method works beautifully, including consistency in variable selection and oracle property in estimation. Simulation studies also confirm our method and theories.     

Variable selection in discrete survival models including heterogeneity

Several variable selection procedures are available for continuous time-to-event data. However, if time is measured in a discrete way and therefore many ties occur models for continuous time are inadequate. We propose penalized likelihood methods that perform efficient variable selection in discrete survival modeling with explicit modeling of the heterogeneity in the population. The method is based on a combination of ridge and lasso type penalties that are tailored to the case of discrete survival. The performance is studied in simulation studies and an application to the birth of the first child.     

Variable selection in heterogeneous panel data models with cross-sectional dependence

This paper studies the Bridge estimator for a high-dimensional panel data model with heterogeneous varying coefficients, where the random errors are assumed to be serially correlated and cross-sectionally dependent. We establish oracle efficiency and the asymptotic distribution of the Bridge estimator, when the number of covariates increases to infinity with the sample size in both dimensions. A BIC-type criterion is also provided for tuning parameter selection. We further generalise the marginal Bridge estimator for our model to asymptotically correctly identify the covariates with zero coefficients even when the number of covariates is greater than the sample size under a partial orthogonality condition. The finite sample performance of the proposed estimator is demonstrated by simulated data examples, and an empirical application with the US stock dataset is also provided.     

Sample size re-estimation for survival data in clinical trials with an adaptive design

In clinical trials with survival data, investigators may wish to re-estimate the sample size based on the observed effect size while the trial is ongoing. Besides the inflation of the type-I error rate due to sample size re-estimation, the method for calculating the sample size in an interim analysis should be carefully considered because the data in each stage are mutually dependent in trials with survival data. Although the interim hazard estimate is commonly used to re-estimate the sample size, the estimate can sometimes be considerably higher or lower than the hypothesized hazard by chance. We propose an interim hazard ratio estimate that can be used to re-estimate the sample size under those circumstances. The proposed method was demonstrated through a simulation study and an actual clinical trial as an example. The effect of the shape parameter for the Weibull survival distribution on the sample size re-estimation is presented.     

Variable screening for survival data in the presence of heterogeneous censoring

Variable screening for censored survival data is most challenging when both survival and censoring times are correlated with an ultrahigh-dimensional vector of covariates. Existing approaches to handling censoring often make use of inverse probability weighting by assuming independent censoring with both survival time and covariates. This is a convenient but rather restrictive assumption which may be unmet in real applications, especially when the censoring mechanism is complex and the number of covariates is large. To accommodate heterogeneous (covariate-dependent) censoring that is often present in high-dimensional survival data, we propose a Gehan-type rank screening method to select features that are relevant to the survival time. The method is invariant to monotone transformations of the response and of the predictors, and works robustly for a general class of survival models. We establish the sure screening property of the proposed methodology. Simulation studies and a lymphoma data analysis demonstrate its favorable performance and practical utility.     

Variable selection for recurrent event data via nonconcave penalized estimating function

Variable selection is an important issue in all regression analysis and in this paper, we discuss this in the context of regression analysis of recurrent event data. Recurrent event data often occur in long-term studies in which individuals may experience the events of interest more than once and their analysis has recently attracted a great deal of attention (Andersen et al., Statistical models based on counting processes, 1993; Cook and Lawless, Biometrics 52:1311–1323, 1996, The analysis of recurrent event data, 2007; Cook et al., Biometrics 52:557–571, 1996; Lawless and Nadeau, Technometrics 37:158-168, 1995; Lin et al., J R Stat Soc B 69:711–730, 2000). However, it seems that there are no established approaches to the variable selection with respect to recurrent event data. For the problem, we adopt the idea behind the nonconcave penalized likelihood approach proposed in Fan and Li (J Am Stat Assoc 96:1348–1360, 2001) and develop a nonconcave penalized estimating function approach. The proposed approach selects variables and estimates regression coefficients simultaneously and an algorithm is presented for this process. We show that the proposed approach performs as well as the oracle procedure in that it yields the estimates as if the correct submodel was known. Simulation studies are conducted for assessing the performance of the proposed approach and suggest that it works well for practical situations. The proposed methodology is illustrated by using the data from a chronic granulomatous disease study.     

Variable selection and collinearity processing for multivariate data via row-elastic-net regularization

AStA Advances in Statistical Analysis - Multivariate data is collected in many fields, such as chemometrics, econometrics, financial engineering and genetics. In multivariate data,...