Penalized estimation of frailty-based illness-death models for semi-competing risks

An augmented illness-death model for semi-competing risks with clinically immediate terminal events

Preeclampsia is a pregnancy-associated condition posing risks of both fetal and maternal mortality and morbidity that can only resolve following delivery and removal of the placenta. Because in its typical form preeclampsia can arise before delivery, but not after, these two events exemplify the time-to-event setting of "semi-competing risks" in which a non-terminal event of interest is subject to the occurrence of a terminal event of interest. The semi-competing risks framework presents a valuable opportunity to simultaneously address two clinically meaningful risk modeling tasks: (i) characterizing risk of developing preeclampsia, and (ii) characterizing time to delivery after onset of preeclampsia. However, some people with preeclampsia deliver immediately upon diagnosis, while others are admitted and monitored for an extended period before giving birth, resulting in two distinct trajectories following the non-terminal event, which we call "clinically immediate" and "non-immediate" terminal events. Though such phenomena arise in many clinical contexts, to-date there have not been methods developed to acknowledge the complex dependencies between such outcomes, nor leverage these phenomena to gain new insight into individualized risk. We address this gap by proposing a novel augmented frailty-based illness-death model with a binary submodel to distinguish risk of immediate terminal event following the non-terminal event. The model admits direct dependence of the terminal event on the non-terminal event through flexible regression specification, as well as indirect dependence via a shared frailty term linking each submodel. We develop an efficient Bayesian sampler for estimation and corresponding model fit metrics, and derive formulae for dynamic risk prediction. In an extended example using pregnancy outcome data from an electronic health record, we demonstrate the proposed model's direct applicability to address a broad range of clinical questions.

Exploring the impact of stage and tumor site on colorectal cancer survival: Bayesian survival modeling

Colorectal cancer is a prevalent malignancy with global significance. This retrospective study aimed to investigate the influence of stage and tumor site on survival outcomes in 284 colorectal cancer patients diagnosed between 2001 and 2017. Patients were categorized into four groups based on tumor site (colon and rectum) and disease stage (early stage and advanced stage). Demographic characteristics, treatment modalities, and survival outcomes were recorded. Bayesian survival modeling was performed using semi-competing risks illness-death models with an accelerated failure time (AFT) approach, utilizing R 4.1 software. Results demonstrated significantly higher time ratios for disease recurrence (TR = 1.712, 95% CI 1.489-2.197), mortality without recurrence (TR = 1.933, 1.480-2.510), and mortality after recurrence (TR = 1.847, 1.147-2.178) in early-stage colon cancer compared to early-stage rectal cancer. Furthermore, patients with advanced-stage rectal cancer exhibited shorter survival times for disease recurrence than patients with early-stage colon cancer. The interaction effect between the disease site and cancer stage was not significant. These findings, derived from the optimal Bayesian log-normal model for terminal and non-terminal events, highlight the importance of early detection and effective management strategies for colon cancer. Early-stage colon cancer demonstrated improved survival rates for disease recurrence, mortality without recurrence, and mortality after recurrence compared to other stages. Early intervention and comprehensive care are crucial to enhance prognosis and minimize adverse events in colon cancer patients.

Surrogacy validation for time-to-event outcomes with illness-death frailty models

A common practice in clinical trials is to evaluate a treatment effect on an intermediate outcome when the true outcome of interest would be difficult or costly to measure. We consider how to validate intermediate outcomes in a causally-valid way when the trial outcomes are time-to-event. Using counterfactual outcomes, those that would be observed if the counterfactual treatment had been given, the causal association paradigm assesses the relationship of the treatment effect on the surrogate outcome with the treatment effect on the true, primary outcome. In particular, we propose illness-death models to accommodate the censored and semicompeting risk structure of survival data. The proposed causal version of these models involves estimable and counterfactual frailty terms. Via these multistate models, we characterize what a valid surrogate would look like using a causal effect predictiveness plot. We evaluate the estimation properties of a Bayesian method using Markov chain Monte Carlo and assess the sensitivity of our model assumptions. Our motivating data source is a localized prostate cancer clinical trial where the two survival outcomes are time to distant metastasis and time to death.

High-Dimensional Survival Analysis: Methods and Applications

In the era of precision medicine, time-to-event outcomes such as time to death or progression are routinely collected, along with high-throughput covariates. These high-dimensional data defy classical survival regression models, which are either infeasible to fit or likely to incur low predictability due to over-fitting. To overcome this, recent emphasis has been placed on developing novel approaches for feature selection and survival prognostication. We will review various cutting-edge methods that handle survival outcome data with high-dimensional predictors, highlighting recent innovations in machine learning approaches for survival prediction. We will cover the statistical intuitions and principles behind these methods and conclude with extensions to more complex settings, where competing events are observed. We exemplify these methods with applications to the Boston Lung Cancer Survival Cohort study, one of the largest cancer epidemiology cohorts investigating the complex mechanisms of lung cancer.