• Journal of the Korean Data and Information Science Society
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• v.20 no.5
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• pp.895-903
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• 2009

The penalized partial likelihood based on restricted maximum likelihood method has been widely used for the inference of frailty models. However, the standard-error estimate for frailty parameter estimator can be downwardly biased. In this paper we show that such underestimation can be corrected by using hierarchical likelihood. In particular, the hierarchical likelihood gives a statistically efficient procedure for various random-effect models including frailty models. The proposed method is illustrated via a numerical example and simulation study. The simulation results demonstrate that the corrected standard-error estimate largely improves such bias.

• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1513-1521
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• 2015

Selecting relevant variables for a statistical model is very important in regression analysis. Recently, variable selection methods using a penalized likelihood have been widely studied in various regression models. The main advantage of these methods is that they select important variables and estimate the regression coefficients of the covariates, simultaneously. In this paper, we propose a simple procedure based on a penalized h-likelihood (HL) for variable selection in Poisson hierarchical generalized linear models (HGLMs) for correlated count data. For this we consider three penalty functions (LASSO, SCAD and HL), and derive the corresponding variable-selection procedures. The proposed method is illustrated using a practical example.

• Journal of the Korean Data and Information Science Society
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• v.27 no.2
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• pp.499-510
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• 2016

It is very important to select relevant variables in regression models for survival analysis. In this paper, we introduce a penalized variable-selection procedure in multi-level frailty models based on the "frailtyHL" R package (Ha et al., 2012). Here, the estimation procedure of models is based on the penalized hierarchical likelihood, and three penalty functions (LASSO, SCAD and HL) are considered. The proposed methods are illustrated with multi-country/multi-center bladder cancer survival data from the EORTC in Belgium. We compare the results of three variable-selection methods and discuss their advantages and disadvantages. In particular, the results of data analysis showed that the SCAD and HL methods select well important variables than in the LASSO method.

• The Korean Journal of Applied Statistics
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• v.34 no.3
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• pp.411-425
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• 2021

Accelerated failure time (AFT) model represents a linear relationship between the log-survival time and covariates. We are interested in the inference of covariate's effect affecting the variation of survival times in the AFT model. Thus, we need to model the variance as well as the mean of survival times. We call the resulting model mean and variance AFT (MV-AFT) model. In this paper, we propose a variable selection procedure of regression parameters of mean and variance in MV-AFT model using penalized likelihood function. For the variable selection, we study four penalty functions, i.e. least absolute shrinkage and selection operator (LASSO), adaptive lasso (ALASSO), smoothly clipped absolute deviation (SCAD) and hierarchical likelihood (HL). With this procedure we can select important covariates and estimate the regression parameters at the same time. The performance of the proposed method is evaluated using simulation studies. The proposed method is illustrated with a clinical example dataset.

• The Korean Journal of Applied Statistics
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• v.28 no.6
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• pp.1121-1131
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• 2015

Logistic models with a random intercept are useful to analyze longitudinal binary data. Traditionally, the random intercept of the logistic model is assumed to be parametric (such as normal distribution) and is also assumed to be independent to variables. Such assumptions are very strong and restricted for application to real data. Recently, Garcia and Ma (2015) derived semiparametric efficient estimators for logistic model with a random intercept without these assumptions. Their estimator shows the consistency where we do not assume any parametric form for the random intercept. In addition, the method is computationally simple. In this paper, we apply this method to analyze toenail infection data. We compare the semiparametric estimator with maximum likelihood estimator, penalized quasi-likelihood estimator and hierarchical generalized linear estimator.

• The Korean Journal of Applied Statistics
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• v.28 no.5
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• pp.965-976
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• 2015

Determining relevant variables for a regression model is important in regression analysis. Recently, a variable selection methods using a penalized likelihood with various penalty functions (e.g. LASSO and SCAD) have been widely studied in simple statistical models such as linear models and generalized linear models. The advantage of these methods is that they select important variables and estimate regression coefficients, simultaneously; therefore, they delete insignificant variables by estimating their coefficients as zero. We study how to select proper variables based on penalized hierarchical likelihood (HL) in semi-parametric frailty models that allow three penalty functions, LASSO, SCAD and HL. For the variable selection we develop a new function in the "frailtyHL" R package. Our methods are illustrated with breast cancer survival data from the Medical Center at Chonnam National University in Korea. We compare the results from three variable-selection methods and discuss advantages and disadvantages.