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Il Do HA, Jianxin PAN, Seungyoung OH, and Youngjo LEE Variable selection methods using a penalized likelihood have been widely studied in various statistical models. However, in semiparametric frailty models, these methods have been relatively less studied because the marginal likelihood function involves analytically intractable integrals, particularly when modeling multicomponent or correlated frailties. In this article, we propose a simple but unified procedure via a penalized h-likelihood (HL) for variable selection of fixed effects in a general class of semiparametric frailty models, in which random effects may be shared, nested, or correlated. We consider three penalty functions (least absolute shrinkage and selection operator [LASSO], smoothly clipped absolute deviation [SCAD], and HL) in our variable selection procedure. We show that the proposed method can be easily implemented via a slight modification to existing HL estimation approaches. Simulation studies also show that the procedure using the SCAD or HL penalty performs well. The usefulness of the new method is illustrated using three practical datasets too. Supplementary materials for the article are available online.

In recent years, a growing number of researchers have attempted to overcome the constraints of size and scope in different medical studies to find out the overall treatment effects. As a widespread technique to combine results of multiple studies, commonly used meta-analytic approaches for continuous outcomes demand sample means and standard deviations of primary studies, which are absent sometimes, especially when the outcome is skewed. Instead, the median, the extrema, and/or the quartiles are reported. One feasible solution is to convert the preceding order statistics to demanded statistics to keep effect measures consistent. In this article, we propose new methods based on maximum likelihood estimation for known distributions with unknown parameters. For unknown underlying distributions, the Box–Cox transformation is applied to the reported order statistics so that the techniques for normal distribution can be utilized. Two approaches for estimating the power parameter in Box–Cox transformation are provided. Both simulation studies and real data analysis indicate that in most cases, the proposed methods outperform the existing methods in estimation accuracy.

Efficient estimation of the regression coefficients in longitudinal data analysis requires a correct specification of the covariance structure. Existing approaches usually focus on modeling the mean with specification of certain covariance structures, which may lead to inefficient or biased estimators of parameters in the mean if misspecification occurs. In this paper, we propose a data-driven approach based on semiparametric regression models for the mean and the covariance simultaneously, motivated by the modified Cholesky decomposition. A regression spline based approach using generalized estimating

When modelling longitudinal data generalised estimating equations specify a working structure to the within-subject covariance matrices, aiming to produce efficient parameter estimates. Misspecification of the working covariance structure, however, may lead to a great loss of efficiency of the mean parameter estimates. In this paper we propose an approach for joint modelling of the mean and covariance structures of longitudinal data within the framework of generalised estimating equations. The resulted estimates for the mean and covariance parameters are shown to be consistent and asymptotically Normally distributed. Real data analysis and simulation studies show that the proposed approach yields efficient estimates for both of the mean and covariance parameters.