The additive hazards model with high-dimensional regressors

TY - JOUR

T1 - The additive hazards model with high-dimensional regressors

AU - Martinussen, Torben

AU - Scheike, Thomas

N1 - Keywords: Algorithms; Breast Neoplasms; Data Interpretation, Statistical; Female; Gene Expression Profiling; Humans; Kaplan-Meiers Estimate; Least-Squares Analysis; Liver Cirrhosis, Biliary; Oligonucleotide Array Sequence Analysis; Proportional Hazards Models; Regression Analysis

PY - 2009

Y1 - 2009

N2 - This paper considers estimation and prediction in the Aalen additive hazards model in the case where the covariate vector is high-dimensional such as gene expression measurements. Some form of dimension reduction of the covariate space is needed to obtain useful statistical analyses. We study the partial least squares regression method. It turns out that it is naturally adapted to this setting via the so-called Krylov sequence. The resulting PLS estimator is shown to be consistent provided that the number of terms included is taken to be equal to the number of relevant components in the regression model. A standard PLS algorithm can also be constructed, but it turns out that the resulting predictor can only be related to the original covariates via time-dependent coefficients. The methods are applied to a breast cancer data set with gene expression recordings and to the well known primary biliary cirrhosis clinical data.

AB - This paper considers estimation and prediction in the Aalen additive hazards model in the case where the covariate vector is high-dimensional such as gene expression measurements. Some form of dimension reduction of the covariate space is needed to obtain useful statistical analyses. We study the partial least squares regression method. It turns out that it is naturally adapted to this setting via the so-called Krylov sequence. The resulting PLS estimator is shown to be consistent provided that the number of terms included is taken to be equal to the number of relevant components in the regression model. A standard PLS algorithm can also be constructed, but it turns out that the resulting predictor can only be related to the original covariates via time-dependent coefficients. The methods are applied to a breast cancer data set with gene expression recordings and to the well known primary biliary cirrhosis clinical data.

U2 - 10.1007/s10985-009-9111-y

DO - 10.1007/s10985-009-9111-y

M3 - Journal article

C2 - 19184421

SN - 1380-7870

VL - 15

SP - 330

EP - 342

JO - Lifetime Data Analysis

JF - Lifetime Data Analysis

IS - 3

ER -