A boosting first-hitting-time model for survival analysis in high-dimensional settings

Predicting mortality and recurrence in colorectal cancer: Comparative assessment of predictive models

Introduction

Colorectal cancer (CRC), also known as colorectal cancer, is a significant disease marked by high fatality rates, ranking as the third leading cause of global mortality. The main objective of this study was to assess the accuracy of predictive models in predicting both mortality events and the probability of disease recurrence.

Method

A retrospective analysis was conducted on a cohort of 284 individuals diagnosed with colorectal cancer between 2001 and 2017. Demographic and clinical data, including gender, disease stage, age at diagnosis, recurrence status, and treatment details, were meticulously recorded. We rigorously evaluated various predictive models, including Decision Trees, Random Forests, Random Survival Forests (RSF), Gradient Boosting, mboost, Deep Learning Neural Network (DLNN), and Cox regression. Performance metrics, such as sensitivity, positive predictive value (PPV), specificity, area under the receiver operating characteristic curve (ROC area), and overall accuracy, were calculated for each model to predict mortality and disease recurrence. The analysis was performed using R version 4.1.3 software and the Python programming language.

Results

For mortality prediction, the mboost model demonstrated the highest sensitivity at 96.9% (95% CI: 0.83-0.99) and an ROC area of 0.88. It also exhibited high specificity at 80% (95% CI: 0.59-0.93), a positive predictive value of 86.1% (95% CI: 0.70-0.95), and an overall accuracy of 89% (95% CI: 0.78-0.96). Random Forests showed perfect sensitivity of 100% (95% CI: 0.85-1) but had low specificity at 0% (95% CI: 0-0.52) and poor overall accuracy (50%). On the other hand, DLNN had the lowest performance metrics for mortality prediction, with a sensitivity of 24% (95% CI: 0.222-0.268), specificity of 75% (95% CI: 0.73-0.77), and a lower positive predictive value of 42% (95% CI: 0.38-0.45). The Gradient Boosting model showed the best performance in predicting recurrence, achieving perfect sensitivity of 100% (95% CI: 0.87-1) and high specificity at 92.9% (95% CI: 0.76-0.99). It also had a high positive predictive value of 93.3% (95% CI: 0.77-0.99). Gradient Boosting, with an ROC area of 96.4%, and mboost, with an ROC area of 75%, demonstrated remarkable performance. DLNN had the lowest performance metrics for recurrence prediction, with sensitivity at 1.75% (95% CI: 0.01-0.02), specificity at 98% (95% CI: 0.97-0.98), and a lower positive predictive value at 52.6% (95% CI: 0.39-0.65).

Conclusion

In summary, the mboost model demonstrated outstanding performance in predicting mortality, achieving exceptional results across various evaluation metrics. Random Forests exhibited perfect sensitivity but showed poor specificity and overall accuracy. The DLNN model displayed the lowest performance metrics for mortality prediction. In terms of recurrence prediction, the Gradient Boosting model outperformed other models with perfect sensitivity, high specificity, and positive predictive value. The DLNN model had the lowest performance metrics for recurrence prediction. Overall, the results emphasize the effectiveness of the mboost and Gradient Boosting models in predicting mortality and recurrence in colorectal cancer patients.

Semiparametric predictive inference for failure data using first-hitting-time threshold regression

The progression of disease for an individual can be described mathematically as a stochastic process. The individual experiences a failure event when the disease path first reaches or crosses a critical disease level. This happening defines a failure event and a first hitting time or time-to-event, both of which are important in medical contexts. When the context involves explanatory variables then there is usually an interest in incorporating regression structures into the analysis and the methodology known as threshold regression comes into play. To date, most applications of threshold regression have been based on parametric families of stochastic processes. This paper presents a semiparametric form of threshold regression that requires the stochastic process to have only one key property, namely, stationary independent increments. As this property is frequently encountered in real applications, this model has potential for use in many fields. The mathematical underpinnings of this semiparametric approach for estimation and prediction are described. The basic data element required by the model is a pair of readings representing the observed change in time and the observed change in disease level, arising from either a failure event or survival of the individual to the end of the data record. An extension is presented for applications where the underlying disease process is unobservable but component covariate processes are available to construct a surrogate disease process. Threshold regression, used in combination with a data technique called Markov decomposition, allows the methods to handle longitudinal time-to-event data by uncoupling a longitudinal record into a sequence of single records. Computational aspects of the methods are straightforward. An array of simulation experiments that verify computational feasibility and statistical inference are reported in an online supplement. Case applications based on longitudinal observational data from The Osteoarthritis Initiative (OAI) study are presented to demonstrate the methodology and its practical use.

Regression Models for Lifetime Data: An Overview

Two methods dominate the regression analysis of time-to-event data: the accelerated failure time model and the proportional hazards model. Broadly speaking, these predominate in reliability modelling and biomedical applications, respectively. However, many other methods have been proposed, including proportional odds, proportional mean residual life and several other “proportional” models. This paper presents an overview of the field and the concept behind each of these ideas. Multi-parameter modelling is also discussed, in which (in contrast to, say, the proportional hazards model) more than one parameter of the lifetime distribution may depend on covariates. This includes first hitting time (or threshold) regression based on an underlying latent stochastic process. Many of the methods that have been proposed have seen little or no practical use. Lack of user-friendly software is certainly a factor in this. Diagnostic methods are also lacking for most methods.