Variable selection for proportional odds model

Abstract

SUMMARYIn this paper we study the problem of variable selection for the proportional odds model, which is a useful alternative to the proportional hazards model and might be appropriate when the proportional hazards assumption is not satisfied. We propose to fit the proportional odds model by maximizing the marginal likelihood subject to a shrinkage-type penalty, which encourages sparse solutions and hence facilitates the process of variable selection. Two types of shrinkage penalties are considered: the LASSO and the adaptive-LASSO penalty. In the adaptive-LASSO penalty, different weights are imposed on different coefficients such that important variables are more protectively retained in the final model while unimportant ones are more likely to be shrunk to zeros. We further provide an efficient computation algorithm to implement the proposed methods, and demonstrate their performance through simulation studies and an application to real data. Numerical results indicate that both methods can produce accurate and interpretable models, and the adaptive-LASSO tends to work better than the usual LASSO.

Variable Selection for Partially Linear Varying Coefficient Transformation Models with Censored Data

“…Details of the study design and method have been given by [23]. The data set has been analyzed by many authors, for example, [5] fitted the proportional hazards model and [8] considered the proportional odds model. In both methods, all covariates were assumed linear, which may not be true, particularly for the age effect.…”

“…Variable selection is therefore of fundamental interest for survival analysis. Variable selection procedures for survival data have been studied extensively in the literature; see [5][6][7] for cox's model; see [8] for proportional odds model.…”

On Sparse Estimation for Semiparametric Linear Transformation Models

“…For each example, we compare our new estimators with the original estimating equation method (EE) of Chen et al (2002). In addition, for the PH models, we also compare with the penalized partial likelihood (PPL) estimator proposed by Zhang and Lu (2007); for the PO models, we compare with the penalized marginal likelihood (PML) estimator of Lu and Zhang (2007). BIC is used for choosing the regularization parameter for each method.…”

H-likelihood approach for variable selection in gamma frailty models

“…In ordinary linear regression models, there are a variety of classical techniques for variable selection such as forward selection, backward elimination and stepwise selection. However, these classical methods can be computationally expensive for large data set and often suffer from high variability (Fan and Li, 2001;Lu and Zhang, 2007). Thus, Tibshirani (1996) proposed a new variable-selection technique in linear models, called "least absolute shrinkage and selection operator".…”