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On the robustness of the adaptive lasso to model misspecification.

ABSTRACT: Penalization methods have been shown to yield both consistent variable selection and oracle parameter estimation under correct model specification. In this article, we study such methods under model misspecification, where the assumed form of the regression function is incorrect, including generalized linear models for uncensored outcomes and the proportional hazards model for censored responses. Estimation with the adaptive least absolute shrinkage and selection operator, lasso, penalty is proven to achieve sparse estimation of regression coefficients under misspecification. The resulting estimators are selection consistent, asymptotically normal and oracle, where the selection is based on the limiting values of the parameter estimators obtained using the misspecified model without penalization. We further derive conditions under which the penalized estimators from the misspecified model may yield selection consistency under the true model. The robustness is explored numerically via simulation and an application to the Wisconsin Epidemiological Study of Diabetic Retinopathy.

SUBMITTER: Lu W

PROVIDER: S-EPMC4188068 | biostudies-literature | 2012 Sep

REPOSITORIES: biostudies-literature

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On the robustness of the adaptive lasso to model misspecification.

Lu W W Goldberg Y Y Fine J P JP

Biometrika 20120711 3

Penalization methods have been shown to yield both consistent variable selection and oracle parameter estimation under correct model specification. In this article, we study such methods under model misspecification, where the assumed form of the regression function is incorrect, including generalized linear models for uncensored outcomes and the proportional hazards model for censored responses. Estimation with the adaptive least absolute shrinkage and selection operator, lasso, penalty is prov ...[more]

PMID: 25294946

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Project description:BackgroundThe genetic etiology of complex diseases in human has been commonly viewed as a complex process involving both genetic and environmental factors functioning in a complicated manner. Quite often the interactions among genetic variants play major roles in determining the susceptibility of an individual to a particular disease. Statistical methods for modeling interactions underlying complex diseases between single genetic variants (e.g. single nucleotide polymorphisms or SNPs) have been extensively studied. Recently, haplotype-based analysis has gained its popularity among genetic association studies. When multiple sequence or haplotype interactions are involved in determining an individual's susceptibility to a disease, it presents daunting challenges in statistical modeling and testing of the interaction effects, largely due to the complicated higher order epistatic complexity.ResultsIn this article, we propose a new strategy in modeling haplotype-haplotype interactions under the penalized logistic regression framework with adaptive L1-penalty. We consider interactions of sequence variants between haplotype blocks. The adaptive L1-penalty allows simultaneous effect estimation and variable selection in a single model. We propose a new parameter estimation method which estimates and selects parameters by the modified Gauss-Seidel method nested within the EM algorithm. Simulation studies show that it has low false positive rate and reasonable power in detecting haplotype interactions. The method is applied to test haplotype interactions involved in mother and offspring genome in a small for gestational age (SGA) neonates data set, and significant interactions between different genomes are detected.ConclusionsAs demonstrated by the simulation studies and real data analysis, the approach developed provides an efficient tool for the modeling and testing of haplotype interactions. The implementation of the method in R codes can be freely downloaded from http://www.stt.msu.edu/~cui/software.html.

Dataset Information

On the robustness of the adaptive lasso to model misspecification.

Publications

On the robustness of the adaptive lasso to model misspecification.

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