On the validity of time-dependent AUC estimation in the presence of cure fraction

A novel nonparametric time-dependent precision-recall curve estimator for right-censored survival data

In order to assess prognostic risk for individuals in precision health research, risk prediction models are increasingly used, in which statistical models are used to estimate the risk of future outcomes based on clinical and nonclinical characteristics. The predictive accuracy of a risk score must be assessed before it can be used in routine clinical decision making, where the receiver operator characteristic curves, precision-recall curves, and their corresponding area under the curves are commonly used metrics to evaluate the discriminatory ability of a continuous risk score. Among these the precision-recall curves have been shown to be more informative when dealing with unbalanced biomarker distribution between classes, which is common in rare event, even though except one, all existing methods are proposed for classic uncensored data. This paper is therefore to propose a novel nonparametric estimation approach for the time-dependent precision-recall curve and its associated area under the curve for right-censored data. A simulation is conducted to show the better finite sample property of the proposed estimator over the existing method and a real-world data from primary biliary cirrhosis trial is used to demonstrate the practical applicability of the proposed estimator.

Time-dependent receiver operating characteristic curve estimator for correlated right-censored time-to-event data

In clinical trials, evaluating the accuracy of risk scores (markers) derived from prognostic models for prediction of survival outcomes is of major concern. The time-dependent receiver operating characteristic curve and the corresponding area under the receiver operating characteristic curve are appealing measures to evaluate the predictive accuracy. Several estimation methods have been proposed in the context of classical right-censored data which assumes the event time of individuals are independent. In many applications, however, this may not hold true if, for example, individuals belong to clusters or experience recurrent events. Estimates may be biased if this correlated nature is not taken into account. This paper is then aimed to fill this knowledge gap to introduce a time-dependent receiver operating characteristic curve and the corresponding area under the receiver operating characteristic curve estimation method for right-censored data that take the correlated nature into account. In the proposed method, the unknown status of censored subjects is imputed using conditional survival functions given the marker and frailty of the subjects. An extensive simulation study is conducted to evaluate and demonstrate the finite sample performance of the proposed method. Finally, the proposed method is illustrated using two real-world examples of lung cancer and kidney disease.

Time-dependent ROC curve estimation for interval-censored data

The receiver-operating characteristic (ROC) curve is the most popular graphical method for evaluating the classification accuracy of a diagnostic marker. In time-to-event studies, the subject's event status is time-dependent, and hence, time-dependent extensions of ROC curve have been proposed. However, in practice, the calculation of this curve is not straightforward due to the presence of censoring that may be of different types. Existing methods focus on the more standard and simple case of right-censoring and neglect the general case of mixed interval-censored data that may involve left-, right-, and interval-censored observations. In this context, we propose and study a new time-dependent ROC curve estimator. We also consider some summary measures (area under the ROC curve and Youden index) traditionally associated with ROC as well as the Youden-based cutoff estimation method. The proposed method uses available data very efficiently. To this end, the unknown status (positive or negative) of censored subjects are estimated from the data via the estimation of the conditional survival function given the marker. For that, we investigate both model-based and nonparametric approaches. We also provide variance estimates and confidence intervals using Bootstrap. A simulation study is conducted to investigate the finite sample behavior of the proposed methods and to compare their performance with a competitor. Globally, we observed better finite sample performances for the proposed estimators. Finally, we illustrate the methods using two data sets one from a hypobaric decompression sickness study and the other from an oral health study. The proposed methods are implemented in the R package cenROC.

XGBLC: an improved survival prediction model based on XGBoost

MOTIVATION

Survival analysis using gene expression profiles plays a crucial role in the interpretation of clinical research and assessment of disease therapy programs. Several prediction models have been developed to explore the relationship between patients' covariates and survival. However, the high-dimensional genomic features limit the prediction performance of the survival model. Thus, an accurate and reliable prediction model is necessary for survival analysis using high-dimensional genomic data.

RESULTS

In this study, we proposed an improved survival prediction model based on XGBoost framework called XGBLC, which used Lasso-Cox to enhance the ability to analyze high-dimensional genomic data. The novel first- and second-order gradient statistics of Lasso-Cox were defined to construct the loss function of XGBLC. We extensively tested our XGBLC algorithm on both simulated and real-world datasets, and estimated the performance of models with 5-fold cross-validation. Based on 20 cancer datasets from The Cancer Genome Atlas (TCGA), XGBLC outperforms five state-of-the-art survival methods in terms of C-index, Brier score and AUC. The results show that XGBLC still keeps good accuracy and robustness by comparing the performance on the simulated datasets with different scales. The developed prediction model would be beneficial for physicians to understand the effects of patient's genomic characteristics on survival and make personalized treatment decisions.

AVAILABILITY AND IMPLEMENTATION

The implementation of XGBLC algorithm based on R language is available at: https://github.com/lab319/XGBLC.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Assessing cure status prediction from survival data using receiver operating characteristic curves

Survival analysis relies on the hypothesis that, if the follow-up is long enough, the event of interest will eventually be observed for all observations. This assumption, however, is often not realistic. The survival data then contain a cure fraction. A common approach to modelling and analysing this type of data consists in using cure models. Two types of information can therefore be obtained: the survival at a given time and the cure status, both possibly modelled as a function of the covariates. The cure status is often of interest to medical practitioners, and one is usually interested in predicting it based on markers. Receiver operating characteristic, Roc, curves are one way to evaluate the predicted performance; however, the classical Roc curve method is not appropriate since the cure status is partially unobserved due to the presence of censoring in survival data. We propose a Roc curve estimator that aims to evaluate the cured/noncured status classification performance from cure survival data. This estimator, which handles the presence of censoring, decomposes sensitivity and specificity by means of the definition of conditional probability, and estimates these two quantities by means of weighted empirical distribution functions. The mixture cure model is used to calculate the weights. Based on simulations, we demonstrate good performance of the proposed method, and compare it with the classical Roc curve nonparametric estimator that would be obtained if the cure status was fully observed. We also compare our proposed method with the Roc curves of Heagerty et al. (2000) for classical survival analysis. Finally, we illustrate the methodology on a breast cancer dataset.