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Operating Characteristics of Partial Least Squares in Right-Censored Data Analysis and Its Application in Predicting the Change of HIV-I RNA

Jie Huang1 and David Harrington2

1 Department of Preventive Medicine, Feinberg School of Medicine, Northwestern University, 680 N. Lake Shore Drive Suite 1102, Chicago, Illinois 60611, U.S.A. [email protected]

2 Department of Biostatistics, Harvard School of Public Health, and Department of Biostatistical Science, Dana-Farber Cancer Institute, 44 Binney Street, Boston, Massachusetts 02115, U.S.A. [email protected]

Abstract. It is often of interest to effectively use the information on a large number of covariates in predicting response or outcome. Various statistical tools have been developed to overcome the difficulties caused by the high-dimensionality of the covariate space in the setting of a linear regression model. This paper focuses on the situation where the outcomes of interest are subjected to right censoring. We implement the extended partial least squares method along with other commonly used approaches for analyzing the high dimensional covariates to a data set from AIDS clinical trials (ACTG333). Predictions were computed on the covariate effect and the response for a future subject with a set of covariates. Simulation studies were conducted to compare our proposed methods with other prediction procedures for different numbers of covariates, different correlations among the covariates and different failure time distributions. Mean squared prediction error and mean absolute distance were used to measure the accuracy of prediction on the covariate effect and the response, respectively. We also compared the prediction performance of different approaches using numerical studies. The results show that the Buckley-James based partial least squares, stepwise subset model selection and principal components regression have similar predictive power and the partial least squares method has several advantages in terms of inter-pretability and numerical computation.

Keywords: Dimension reduction, partial least squares, accelerative failure time model, cross-validation, prediction

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