Principal Component Analysis in Linear Regression Survival Model with Microarray Data

As a useful alternative to the Cox proportional hazards model, the linear regression survival model assumes a linear relationship between the covariates and a known monotone transformation, for example logarithm, of an event time of interest. In this article, we study the linear regression survival model with right censored survival data, when high-dimensional microarray measurements are present. Such data may arise in studies investigating the statistical influence of molecular features on survival risk. We propose using the principal component regression (PCR) technique for model reduction based on the weight least squared Stute estimate. Compared with other model reduction techniques, the PCR approach is relatively insensitive to the number of covariates and hence suitable for high dimensional microarray data. Component selection based on the nonparametric bootstrap, and model evaluation using the time-dependent ROC (receiver operating characteristic) technique are investigated. We demonstrate the proposed approach with datasets from two microarray gene expression profiling studies of lymphoma cancers.