One of the major topics in survival analysis is analyzing the effect covariates have on the survival time. Frequently, these covariate effects are observed to be either time-varying, heterogeneous, i.e. patient, treatment or subgroup specific, or even both. While the standard model, the Cox proportional hazards model, allows neither time-varying nor heterogeneous effects, several extensions to the Cox model as well as alternative modeling frameworks have been introduced. However, none of these studies includes heterogeneously time-varying effects of covariates. Such effects occur if a covariate influences the survival time not only in a heterogeneous and time-varying manner, but this time-variation is heterogeneous, too.

In this talk we propose to model such effects by introducing heterogeneously time-varying coefficients to piece-wise exponential additive mixed models. We deploy functional random effects, also known as factor smooths, to model such coefficients as the interaction effect of heterogeneity and time-variation. Our approach allows for non-linear time-effects due to being based on penalized splines and uses an efficient random effects basis to model the heterogeneity. Using a penalized basis prevents overfitting in case of absence of such effects. In addition, the penalization mostly solves the problem of choosing the number of intervals which is usually present in piece-wise exponential approaches. The practical relevance is outlined by presenting a brain tumor case study. Finally, we demonstrate the superiority of our approach in comparison to competitors by means of a simulation study.

Liver transplantation provides the best survival outcomes for patients with early hepatocellular carcinoma (HCC). However, as the demand far exceeds the number of available organs, it is crucial to identify the patients who will benefit most from liver transplantation. The α-fetoprotein (AFP) level, the radiographic tumour burden score (TBS), and the model for end-stage liver disease (MELD) score are routinely measured to monitor HCC progression and liver dysfunction to inform transplantation decisions. The transplant-related survival benefit has been proposed as a comprehensive metric combining post-transplant and waiting list life expectancies. Despite recent advances, existing methods of estimating this metric disregard the full longitudinal information, the observational nature of the data, and the influence of time-varying confounders.

Our primary goal is to dynamically predict the individualized transplant-related survival benefit in HCC patients to improve transplant prioritization. We analyse data from 7,471 waitlisted and 4,786 transplanted HCC patients listed in the US Scientific Registry for Transplant Recipients (SRTR) between March 2002 and March 2022.

We propose a Bayesian joint model that associates the risk of death, before and after transplantation, with the pre-transplant AFP level, TBS, and MELD score trajectories. We establish the necessary assumptions to unbiasedly estimate the causal transplantation effects from the observational data at hand. Using the postulated joint model we predict the pre- and post-transplant five-year survival probabilities for each patient at risk at a given time. From these, we derive the posterior distribution of the causal transplantation benefit. This distribution captures the full range of potential benefits, helping to identify patients most likely to derive the greatest benefit from an available organ. The individual benefits can be dynamically updated as new marker measurements become available. The model is implemented in the R package JMbayes2.

Our results demonstrate that AFP, TBS, and MELD each have distinct associations with the risk of death before and after transplantation, confirming the value of the new approach. Despite the observational nature of the SRTR data, our model can unbiasedly estimate the causal effect of transplantation on survival, leading to unbiased individualized transplant-related benefit distributions.

Our modelling strategy ensures a fair allocation of the limited number of liver transplants, optimizing the use of available organs and improving the overall survival of all waitlisted patients.

Longitudinal and high-dimensional data are nowadays common in biomedical research. Repeated measurements data carry important information about ageing and disease progression, and this information can be used to dynamically update predictions of survival outcomes, such as the onset of dementia, cancer relapses, and death. Traditional approaches to dynamic prediction include joint modelling, which becomes computationally burdensome as the number of longitudinal predictors increases, and LOCF landmarking, which is computationally straightforward but only uses data from the last available observation.

In this talk I will introduce penalized regression calibration (PRC) [1,2], a new statistical method that strives to strike a balance between the mathematical elegance of joint models, and the simplicity of landmarking.

In short, PRC specifies a conditional model for the probability of experiencing an event in the future, given that a subject has not experienced the event up until a given landmark time l. PRC allows flexible modelling of the longitudinal data gathered up to the landmark through mixed-effects models, and it models the conditional survival function S(t | l) using appropriate summaries of the longitudinal covariates as predictors (alongside relevant baseline / time-constant covariates) in a Cox model. Estimation of the Cox model can be performed using penalized likelihood: this allows to reduce the risk of overfitting the available data, and makes it possible to handle a large number of predictors, both in low- and high-dimensional settings.

After illustrating how PRC works, I will show how it can be easily implemented using the R package pencal [2], and discuss how to properly validate the predicted performance of the fitted models. I will present the results of applications that show that PRC can achieve a predictive performance that is comparable to that of joint models, but in a much more computationally-efficient way. I will conclude by presenting our ongoing work to enhance the flexibility of PRC so that it can better handle discrete longitudinal predictors, interval censoring, and competing risks.