The group lasso in the proportional hazards model with an application to multiply imputed high-dimensional data

The increasing dimensionality of data, for example in genetics, requires additional assumptions on the regression models in order to obtain estimates of the regression coefficients, known as regularization. Lasso, one of the regularization methods available, imposes an L1 constraint on the vector of coefficients, leading to the desirable feature of setting some coefficients to zero. This results in sparse, and more importantly, estimable models. However, setting some coefficients becomes problematic when one would want a group of variables to be in or out of the model, e.g. a factor coded as several dummy variables. This problem is solved by the group lasso. This paper presents an extension to the algorithm presented by Goeman for optimizing the penalized log likelihood under the proportional hazards model. This algorithm combines the gradient ascent algorithm and the Newton-Raphson algorithm. This methodology is then applied to data obtained from the Carema case-cohort study, which...Show moreThe increasing dimensionality of data, for example in genetics, requires additional assumptions on the regression models in order to obtain estimates of the regression coefficients, known as regularization. Lasso, one of the regularization methods available, imposes an L1 constraint on the vector of coefficients, leading to the desirable feature of setting some coefficients to zero. This results in sparse, and more importantly, estimable models. However, setting some coefficients becomes problematic when one would want a group of variables to be in or out of the model, e.g. a factor coded as several dummy variables. This problem is solved by the group lasso. This paper presents an extension to the algorithm presented by Goeman for optimizing the penalized log likelihood under the proportional hazards model. This algorithm combines the gradient ascent algorithm and the Newton-Raphson algorithm. This methodology is then applied to data obtained from the Carema case-cohort study, which aim is to assess the additional predict 10-year risk of coronary heart disease.Show less

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The group lasso in the proportional hazards model with an application to multiply imputed high-dimensional data