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Feature Selection for Survival Analysis in Bioinformatics

The development of microarray technology has made it possible to assemble biomedical datasets that measure the expression profile of thousands of genes simultaneously. However, such high-dimensional datasets make computation costly and can complicate the interpretation of a predictive model. To address this, feature selection methods are used to extract biological information from a large amount of data in order to filter the expression dataset down to the smallest possible subset of accurate predictor genes. Feature selection has three main advantages: it decreases computational costs, mitigates the possibility of overfitting due to high intervariable correlations, and allows for an easier clinical interpretation of the model. In this paper we compare three methods of feature selection : iterative Bayesian Model Averaging (BMA), Random Survival Forest (RSF) and Cox Proportional Hazard (CPH) and four methods of survival analysis: Analysis Random Survival Forest (RSF), Cox Proportional Hazard (CPH), Alan Additive Filter (AAF) and Deepsurv (neural network). Feature selection methods permit to extract the most relevant features for survival analysis from the dataset automatically and are compared with a hand selected set of features. Certain survival analysis methods also permit to perform feature selection such as RSF and CPH. All the data we used came from the Metabric breast cancer dataset. For every feature selection method, we compare varied numbers of selected features. Our results indicate that feature selection improves the performance of survival analysis methods. Overall, the best survival analysis performance was obtained by combining RSF for feature selection and Deepsurv for survival prediction. I. PRINCIPLES OF SURVIVAL ANALYSIS Survival analysis is about predicting the time duration until an event occurs [7]. In our case, we are interested in using microarray data to estimate the longevity of a patient diagnosed with breast cancer. However, the approach is generalizable to any highly dimensional data used for survival analysis tasks. A. Modeling Survival Analysis In survival analysis, we do not necessarily know the actual longevity of every individual since the experiment may have stopped within their lifetime. Those individuals who have not been subject to the death event during the study are labeled as right censored. This includes any patient who drops out of the study early. As such, for each individual, we consider either the survival time (if we have the death date) or a censored time (if we do not have the date of the death but instead the date of the last visit to the doctor). An instance in the survival data is usually represented as (xi, ti, δi) where xi is the feature vector, ti is the observed time, and δi is the indicator. An indicator of 1 is used to indicate an uncensored instance (i.e., the death of a patient) while 0 is used to indicate a censored instance. The survival function S(t|x) = P (O > t|x) represents the probability of being alive after time t, where O represent the total survival time and x the data from which is inferred the prediction. B. Concordance Index We cannot evaluate the predictive ability of a survival model using classical loss functions such as L2 because we do not possess the curve which represents the probability of dying for our data [5]. Instead, we only know the time at which a patient actually died. One measure used is the concordance index, or c-index. This measure evaluates the ordering of predicted survival times: 0.5 is the expected result from random predictions, 1.0 is perfect concordance, and 0.0 is perfect anti-concordance (i.e., one must multiply predictions by −1 to get a cindex of 1.0). Throughout this paper, we use the c-index to evaluate the accuracy of our predictions. II. METHODS OF SURVIVAL ANALYSIS