Supervised wavelet method to predict patient survival from gene expression data.

In microarray studies, the number of samples is relatively small compared to the number of genes per sample. An important aspect of microarray studies is the prediction of patient survival based on their gene expression profile. This naturally calls for the use of a dimension reduction procedure together with the survival prediction model. In this study, a new method based on combining wavelet approximation coefficients and Cox regression was presented. The proposed method was compared with supervised principal component and supervised partial least squares methods. The different fitted Cox models based on supervised wavelet approximation coefficients, the top number of supervised principal components, and partial least squares components were applied to the data. The results showed that the prediction performance of the Cox model based on supervised wavelet feature extraction was superior to the supervised principal components and partial least squares components. The results suggested the possibility of developing new tools based on wavelets for the dimensionally reduction of microarray data sets in the context of survival analysis

Least angle regression for time series forecasting with many predictors.

Least Angle Regression(LARS)is a variable selection method with proven performance for cross-sectional data. In this paper, it is extended to time series forecasting with many predictors. The new method builds parsimonious forecast models,taking the time series dynamics into account. It is a exible method that allows for ranking the different predictors according to their predictive content. The time series LARS shows good forecast performance, as illustrated in a simulation study and two real data applications, where it is compared with the standard LARS algorithm and forecasting using diffusion indices.macro-econometrics; model selection; penalized regression; variable ranking;

Development and Validation of Predictive Indices for a Continuous Outcome Using Gene Expression Profiles

There have been relatively few publications using linear regression models to predict a continuous response based on microarray expression profiles. Standard linear regression methods are problematic when the number of predictor variables exceeds the number of cases. We have evaluated three linear regression algorithms that can be used for the prediction of a continuous response based on high dimensional gene expression data. The three algorithms are the least angle regression (LAR), the least absolute shrinkage and selection operator (LASSO), and the averaged linear regression method (ALM). All methods are tested using simulations based on a real gene expression dataset and analyses of two sets of real gene expression data and using an unbiased complete cross validation approach. Our results show that the LASSO algorithm often provides a model with somewhat lower prediction error than the LAR method, but both of them perform more efficiently than the ALM predictor. We have developed a plug-in for BRB-ArrayTools that implements the LAR and the LASSO algorithms with complete cross-validation

Gene Selection using a High-Dimensional Regression Model with Microarrays in Cancer Prognostic Studies

Mining of gene expression data to identify genes associated with patient survival is an ongoing problem in cancer prognostic studies using microarrays in order to use such genes to achieve more accurate prognoses. The least absolute shrinkage and selection operator (lasso) is often used for gene selection and parameter estimation in high-dimensional microarray data. The lasso shrinks some of the coefficients to zero, and the amount of shrinkage is determined by the tuning parameter, often determined by cross validation. The model determined by this cross validation contains many false positives whose coefficients are actually zero. We propose a method for estimating the false positive rate (FPR) for lasso estimates in a high-dimensional Cox model. We performed a simulation study to examine the precision of the FPR estimate by the proposed method. We applied the proposed method to real data and illustrated the identification of false positive genes

Survival models with preclustered gene groups as covariates

<p>Abstract</p> <p>Background</p> <p>An important application of high dimensional gene expression measurements is the risk prediction and the interpretation of the variables in the resulting survival models. A major problem in this context is the typically large number of genes compared to the number of observations (individuals). Feature selection procedures can generate predictive models with high prediction accuracy and at the same time low model complexity. However, interpretability of the resulting models is still limited due to little knowledge on many of the remaining selected genes. Thus, we summarize genes as gene groups defined by the hierarchically structured Gene Ontology (GO) and include these gene groups as covariates in the hazard regression models. Since expression profiles within GO groups are often heterogeneous, we present a new method to obtain subgroups with coherent patterns. We apply preclustering to genes within GO groups according to the correlation of their gene expression measurements.</p> <p>Results</p> <p>We compare Cox models for modeling disease free survival times of breast cancer patients. Besides classical clinical covariates we consider genes, GO groups and preclustered GO groups as additional genomic covariates. Survival models with preclustered gene groups as covariates have similar prediction accuracy as models built only with single genes or GO groups.</p> <p>Conclusions</p> <p>The preclustering information enables a more detailed analysis of the biological meaning of covariates selected in the final models. Compared to models built only with single genes there is additional functional information contained in the GO annotation, and compared to models using GO groups as covariates the preclustering yields coherent representative gene expression profiles.</p