TY - JOUR
T1 - Integrative weighted group lasso and generalized local quadratic approximation
AU - Pan, Qing
AU - Zhao, Yunpeng
N1 - Funding Information:
This publication was supported by Award Numbers UL1TR000075 and KL2TR000076 from the NIH National Center for Advancing Translational Sciences . Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the National Center for Advancing Translational Sciences or the National Institutes of Health.
Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2016/12/1
Y1 - 2016/12/1
N2 - Longitudinal clinical outcomes are often collected in genomic studies, where selection methods accounting for dynamic effects of biomarkers are desirable. Biomarker effects can be modeled by nonparametric B-splines and selected by group lasso. A novel weight function is proposed based on the extremum of the biomarker effects over time for the penalty. In addition to the common practice treating weights as adaptive functions depending on some first-stage estimates, an integrative group lasso which treats the loss, penalty and weight functions as an integrative whole is proposed, where parameters in all three are jointly estimated in one step. Generalized local quadratic approximations are developed to optimize the integrative group lasso whose guidelines are applicable in a wide range of non-convex optimization problems. The integrative version has theoretical advantages as it requires weaker assumptions in achieving consistency and sparsistency. Both adaptive and integrative procedures show larger areas under the ROC curves as well as smaller biases and mean square prediction errors over unweighted group lasso in simulation studies. Finally, the proposed method is illustrated on the GWAS from the Epidemiology and Intervention of Diabetes Complication trial. To accommodate more candidate markers, 23 chromosomes are analyzed separately with common tuning parameters.
AB - Longitudinal clinical outcomes are often collected in genomic studies, where selection methods accounting for dynamic effects of biomarkers are desirable. Biomarker effects can be modeled by nonparametric B-splines and selected by group lasso. A novel weight function is proposed based on the extremum of the biomarker effects over time for the penalty. In addition to the common practice treating weights as adaptive functions depending on some first-stage estimates, an integrative group lasso which treats the loss, penalty and weight functions as an integrative whole is proposed, where parameters in all three are jointly estimated in one step. Generalized local quadratic approximations are developed to optimize the integrative group lasso whose guidelines are applicable in a wide range of non-convex optimization problems. The integrative version has theoretical advantages as it requires weaker assumptions in achieving consistency and sparsistency. Both adaptive and integrative procedures show larger areas under the ROC curves as well as smaller biases and mean square prediction errors over unweighted group lasso in simulation studies. Finally, the proposed method is illustrated on the GWAS from the Epidemiology and Intervention of Diabetes Complication trial. To accommodate more candidate markers, 23 chromosomes are analyzed separately with common tuning parameters.
KW - Adaptive group lasso
KW - GWAS
KW - Generalized local quadratic approximation
KW - Integrative group lasso
KW - Optimization of non-convex function
KW - Varying-coefficient regression
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U2 - 10.1016/j.csda.2016.06.004
DO - 10.1016/j.csda.2016.06.004
M3 - Article
AN - SCOPUS:84978288638
SN - 0167-9473
VL - 104
SP - 66
EP - 78
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
ER -