On the calibration of survival models with competing risks

Survival analysis deals with modeling the time until an event occurs, and accurate probability estimates are crucial for decision-making, particularly in the competing-risks setting where multiple events are possible. While recent work has addressed calibration in standard survival analysis, the competing-risks setting remains under-explored as it is harder (the calibration applies to both probabilities across classes and time horizon). We show that existing calibration measures are not suited to the competing-risk setting and that recent models do not give well-behaved probabilities. To address this, we introduce a dedicated framework with two novel calibration measures that are minimized for oracle estimators (i.e., both measures are proper). We also introduce some methods to estimate, test, and correct the calibration. Our recalibration methods yield good probabilities while preserving discrimination.

Survival Models: Proper Scoring Rule and Stochastic Optimization with Competing Risks

When dealing with right-censored data, where some outcomes are missing due to a limited observation period, survival analysis -- known as time-to-event analysis -- focuses on predicting the time until an event of interest occurs. Multiple classes of outcomes lead to a classification variant: predicting the most likely event, a less explored area known as competing risks. Classic competing risks models couple architecture and loss, limiting scalability.To address these issues, we design a strictly proper censoring-adjusted separable scoring rule, allowing optimization on a subset of the data as each observation is evaluated independently. The loss estimates outcome probabilities and enables stochastic optimization for competing risks, which we use for efficient gradient boosting trees. SurvivalBoost not only outperforms 12 state-of-the-art models across several metrics on 4 real-life datasets, both in competing risks and survival settings, but also provides great calibration, the ability to predict across any time horizon, and computation times faster than existing methods.

Teaching Models To Survive: Proper Scoring Rule and Stochastic Optimization with Competing Risks

When data are right-censored, i.e. some outcomes are missing due to a limited period of observation, survival analysis can compute the "time to event". Multiple classes of outcomes lead to a classification variant: predicting the most likely event, known as competing risks, which has been less studied. To build a loss that estimates outcome probabilities for such settings, we introduce a strictly proper censoring-adjusted separable scoring rule that can be optimized on a subpart of the data because the evaluation is made independently of observations. It enables stochastic optimization for competing risks which we use to train gradient boosting trees. Compared to 11 state-of-the-art models, this model, MultiIncidence, performs best in estimating the probability of outcomes in survival and competing risks. It can predict at any time horizon and is much faster than existing alternatives.

Development and external validation of a lung cancer risk estimation tool using gradient-boosting

Lung cancer is a significant cause of mortality worldwide, emphasizing the importance of early detection for improved survival rates. In this study, we propose a machine learning (ML) tool trained on data from the PLCO Cancer Screening Trial and validated on the NLST to estimate the likelihood of lung cancer occurrence within five years. The study utilized two datasets, the PLCO (n=55,161) and NLST (n=48,595), consisting of comprehensive information on risk factors, clinical measurements, and outcomes related to lung cancer. Data preprocessing involved removing patients who were not current or former smokers and those who had died of causes unrelated to lung cancer. Additionally, a focus was placed on mitigating bias caused by censored data. Feature selection, hyper-parameter optimization, and model calibration were performed using XGBoost, an ensemble learning algorithm that combines gradient boosting and decision trees. The ML model was trained on the pre-processed PLCO dataset and tested on the NLST dataset. The model incorporated features such as age, gender, smoking history, medical diagnoses, and family history of lung cancer. The model was well-calibrated (Brier score=0.044). ROC-AUC was 82% on the PLCO dataset and 70% on the NLST dataset. PR-AUC was 29% and 11% respectively. When compared to the USPSTF guidelines for lung cancer screening, our model provided the same recall with a precision of 13.1% vs. 9.3% on the PLCO dataset and 3.2% vs. 3.1% on the NLST dataset. The developed ML tool provides a freely available web application for estimating the likelihood of developing lung cancer within five years. By utilizing risk factors and clinical data, individuals can assess their risk and make informed decisions regarding lung cancer screening. This research contributes to the efforts in early detection and prevention strategies, aiming to reduce lung cancer-related mortality rates.