Machine Learning for Survival Analysis: A Survey <s> Uncensoring approach. <s> BACKGROUND ::: ::: The TNM staging system originated as a response to the need for an accurate, consistent, universal cancer outcome prediction system. Since the TNM staging system was introduced in the 1950s, new prognostic factors have been identified and new methods for integrating prognostic factors have been developed. This study compares the prediction accuracy of the TNM staging system with that of artificial neural network statistical models. ::: ::: ::: ::: METHODS ::: ::: For 5-year survival of patients with breast or colorectal carcinoma, the authors compared the TNM staging system's predictive accuracy with that of artificial neural networks (ANN). The area under the receiver operating characteristic curve, as applied to an independent validation data set, was the measure of accuracy. ::: ::: ::: ::: RESULTS ::: ::: For the American College of Surgeons' Patient Care Evaluation (PCE) data set, using only the TNM variables (tumor size, number of positive regional lymph nodes, and distant metastasis), the artificial neural network's predictions of the 5-year survival of patients with breast carcinoma were significantly more accurate than those of the TNM staging system (TNM, 0.720; ANN, 0.770; P < 0.001). For the National Cancer Institute's Surveillance, Epidemiology, and End Results breast carcinoma data set, using only the TNM variables, the artificial neural network's predictions of 10-year survival were significantly more accurate than those of the TNM staging system (TNM, 0.692; ANN, 0.730; P < 0.01). For the PCE colorectal data set, using only the TNM variables, the artificial neural network's predictions of the 5-year survival of patients with colorectal carcinoma were significantly more accurate than those of the TNM staging system (TNM, 0.737; ANN, 0.815; P < 0.001). Adding commonly collected demographic and anatomic variables to the TNM variables further increased the accuracy of the artificial neural network's predictions of breast carcinoma survival (0.784) and colorectal carcinoma survival (0.869). ::: ::: ::: ::: CONCLUSIONS ::: ::: Artificial neural networks are significantly more accurate than the TNM staging system when both use the TNM prognostic factors alone. New prognostic factors can be added to artificial neural networks to increase prognostic accuracy further. These results are robust across different data sets and cancer sites. Cancer 1997; 79:857-62. © 1997 American Cancer Society. <s> BIB001 </s> Machine Learning for Survival Analysis: A Survey <s> Uncensoring approach. <s> Objective:: The prediction of breast cancer survivability has been a challenging research problem for many researchers. Since the early dates of the related research, much advancement has been recorded in several related fields. For instance, thanks to innovative biomedical technologies, better explanatory prognostic factors are being measured and recorded; thanks to low cost computer hardware and software technologies, high volume better quality data is being collected and stored automatically; and finally thanks to better analytical methods, those voluminous data is being processed effectively and efficiently. Therefore, the main objective of this manuscript is to report on a research project where we took advantage of those available technological advancements to develop prediction models for breast cancer survivability. Methods and material:: We used two popular data mining algorithms (artificial neural networks and decision trees) along with a most commonly used statistical method (logistic regression) to develop the prediction models using a large dataset (more than 200,000 cases). We also used 10-fold cross-validation methods to measure the unbiased estimate of the three prediction models for performance comparison purposes. Results:: The results indicated that the decision tree (C5) is the best predictor with 93.6% accuracy on the holdout sample (this prediction accuracy is better than any reported in the literature), artificial neural networks came out to be the second with 91.2% accuracy and the logistic regression models came out to be the worst of the three with 89.2% accuracy. Conclusion:: The comparative study of multiple prediction models for breast cancer survivability using a large dataset along with a 10-fold cross-validation provided us with an insight into the relative prediction ability of different data mining methods. Using sensitivity analysis on neural network models provided us with the prioritized importance of the prognostic factors used in the study. <s> BIB002 </s> Machine Learning for Survival Analysis: A Survey <s> Uncensoring approach. <s> Censoring is a common phenomenon that arises in many longitudinal studies where an event of interest could not be recorded within the given time frame. Censoring causes missing time-to-event labels, and this effect is compounded when dealing with datasets which have high amounts of censored instances. In addition, dependent censoring in the data, where censoring is dependent on the covariates in the data leads to bias in standard survival estimators. This motivates us to develop an approach for pre-processing censored data which calibrates the right censored (RC) times in an attempt to reduce the bias in the survival estimators. This calibration is done using an imputation method which estimates the sparse inverse covariance matrix over the dataset in an iterative convergence framework. During estimation, we apply row and column-based regularization to account for both row and column-wise correlations between different instances while imputing them. This is followed by comparing these imputed censored times with the original RC times to obtain the final calibrated RC times. These calibrated RC times can now be used in the survival dataset in place of the original RC times for more effective prediction. One of the major benefits of our calibration approach is that it is a pre-processing method for censored data which can be used in conjunction with any survival prediction algorithm and improve its performance. We evaluate the goodness of our approach using a wide array of survival prediction algorithms which are applied over crowdfunding data, electronic health records (EHRs), and synthetic censored datasets. Experimental results indicate that our calibration method improves the AUC values of survival prediction algorithms, compared to applying them directly on the original survival data. <s> BIB003
In survival data, incompleteness in the event (outcome) information makes it difficult for standard machine learning methods to learn from such data. The censored observations in survival data might look similar to unlabeled samples in classification or to unknown responses in a regression problem in the sense that the status or time to event is not known for some of these observations. However, unlike unlabeled samples where the labeling information is completely missing, the censored instances actually have partial informative labeling information that indicates the possible range of the corresponding true response (survival time). Such censored data have to be handled with special care within any machine learning method in order to make good predictions. Also, in survival analysis problems, only the information before a certain time point (before censoring occurs) is available for the censored instances, and this information should be integrated into the prediction algorithm to obtain the best results. There are typically two naive ways of handling such censored data. One is to delete the censored instances, which performs well if the number of samples is sufficiently large and the censoring instances are not censored randomly. However, this will provide a suboptimal model because it neglects the information available in the censored instances BIB002 BIB001 . Treating censoring as event-free is another naive and simple choice. This method performs well for data with only a few censored instances but underestimates the true performance of the model. Although both approaches offer simple ways to handle censored data, they ignore useful information present in the data. To address this issue, two other approaches have been proposed in the literature to handle censored data. (1) Group the instances in the given data into three categorizes  : (i) instances which experience the event of interest during the observation will be labeled as events, (ii) instances whose censored time is later than a predefined time point are labeled as event-free, and (iii) instances whose censored time is earlier than a predefined time point will be duplicated, and one will be labeled as an event and the other will be labeled as event-free. All these instances will be weighted by a marginal probability of event occurrence estimated by the KM method. (2) For each censored instance, estimate the probability of the event and the probability of being censored (considering censoring as a new event) using the KM estimator and assign a new class label based on these probability values . For each instance in the data, when the probability of the event exceeds the probability of being censored, it will be labeled as an event; otherwise, it will be labeled as event-free, which indicates that even if there is complete follow-up information for that instance, there is an extremely low chance of event occurrence by the end of the observation time period. 6.2.2 Calibration. Censoring causes missing time-to-event labels, and this effect is compounded when dealing with datasets with high amounts of censored instances. Instead of using uncensoring approaches, calibration for survival analysis can also be used to solve this problem by learning optimal time-to-event labels for the censored instances. Generally, there are mainly two reasons for performing such calibrations. First, survival analysis models are built using a given dataset where the missing time to events for the censored instances are assigned a value such as the duration of the study or the last known follow-up time. However, this approach is not suitable for handling data with many censored instances because these inappropriately labeled censored instances cannot provide much information to survival methods. Calibration methods should instead be used to overcome this missing time-to-event problem in survival analysis. Second, dependent censoring in the data, where censoring depends on covariates, may lead to some bias in standard survival estimators such as the KM method. This is the driving force behind the imputed censoring approach, which calibrates the time-to-event attribute to decrease the bias of the survival estimators. BIB003 proposed a calibration method which uses a regularized inverse covariance-based imputation to overcome the problems just mentioned. This has the ability to capture correlations between censored instances as well as correlations between similar features. In a calibrated survival analysis, imputing an appropriate label value for each censored instance enables a new representation of the original survival data to be learned effectively. This approach fills a gap in the current literature by estimating the calibrated time-to-event values for these censored instances based on row-wise and column-wise correlations among the censored instances.