Gene ranking in survival data analysis assessment of prognostic value of gene expression experiments

The aim of this work was to investigate the ability of gene expression data in predicting survival of colon cancer patients. Considered the net contribution of the gene, we adjusted for other prognostic factors and we estimated the conditional effect of each single gene, given the rest of the genetic information. A popular approach to screening for prognostic markers is first classify patients on the basis of gene expression and second to evaluate if and at which extent the identified subgroups experience different survival , see for example Alizadeh et al. (2000), Winnepenninckx et al. (2003), Gui & Li (2004), Vasselli et al. (2003). While widely used, the previous approach misses the crucial point because there could be difference in gene expressions detected at step 1 which do not relate to prognosis. A more efficient way would classify patients on the basis of predictive ability of gene expression values. Several methods have been proposed, for a complete review see Dupuy & Simon (2007). The Significance Analysis of Microarrays (SAM) (Tusher, Chu, & Tibshirani, 2001) has been generalized to censored survival data (available as the "survival" option in the samr function loaded in R software by Tibshirani, Hastie, Chu, Narasimha). These procedures are usually based on a marginal approach: they investigate the effect of gene expression without taking into account for other potential prognostic variables (e.g. age, gender, stage of disease) and assessing the effect of each gene separately. A relevant issue not addressed is estimating the net contribution of gene expression in predicting survival, once accounted for patient, tumor characteristics and competing candidate genes. In our work the statistical analysis was based on a two-step procedure, to reduce the complexity of penalized regression and to use standard software. First, we specified Cox regression models (Cox, 1972) to evaluate the association between each single gene expression and survival, taking into account for other prognostic variables. We then ranked genes in order of prognostic value, measured by generalized score statistic. Second, we specified a Penalized Cox regression model (Draper & Smith, 1981) to investigate the conditional effect of the selected top genes. In penalized models, a constraint is introduced on the coefficients, so that the effective number of parameters to be estimated is reduced. Ad hoc codes have been written to calculate the generalized score test statistic and to rank genes. The Penalized Cox regression model was fitted using the estimation algorithm implemented in the survival library of R-software, e.g. Gray (1992).