Functional modeling of recurrent events on time‐to‐event processes

Abstract

In clinical practice, it is often the case where the association between the occurrence of events and time‐to‐event outcomes is of interest; thus, it can be modeled within the framework of recurrent events. The purpose of our study is to enrich the information available for modeling survival with relevant dynamic features, properly taking into account their possibly time‐varying nature, as well as to provide a new setting for quantifying the association between time‐varying processes and time‐to‐event outcomes. We propose an innovative methodology to model information carried out by time‐varying processes by means of functional data, modeling each time‐varying variable as the compensator of marked point process the recurrent events are supposed to derive from. By means of Functional Principal Component Analysis, a suitable dimensional reduction of these objects is carried out in order to plug them into a Cox‐type functional regression model for overall survival. We applied our methodology to data retrieved from the administrative databases of Lombardy Region (Italy), related to patients hospitalized for Heart Failure (HF) between 2000 and 2012. We focused on time‐varying processes of HF hospitalizations and multiple drugs consumption and we studied how they influence patients' overall survival. This novel way to account for time‐varying variables allowed to model self‐exciting behaviors, for which the occurrence of events in the past increases the probability of a new event, and to quantify the effect of personal behaviors and therapeutic patterns on survival, giving new insights into the direction of personalized treatment.

Joint frailty modeling of time-to-event data to elicit the evolution pathway of events: a generalized linear mixed model approach

“…Alternatively, multistate survival models may be adopted to account for competing events at each transition between disease states; see Crowther and Lambert (2017) , Williams and others (2020) and the review by Hougaard (1999) . This approach formulates multiple states via a stochastic process (e.g., Spreafico and Ieva (2020) ) and emphasizes on modeling transition probabilities between states using Markov or semi-Markov models. Multistate survival models are particularly important in studies where covariate effects for each specific transition between disease states are the primary interest.…”

Modelling time-varying covariates effect on survival via functional data analysis: application to the MRC BO06 trial in osteosarcoma

“…Starting from the customized functional datum, the FDA approach also allows to reconstruct its derivative dx Kong et al (2018) to the case of multiple functional predictors (Spreafico and Ieva 2021). Let X ð1Þ i ; .…”

“…During the past two decades, Functional Data Analysis (FDA) has been increasingly used to analyse, model and predict dynamic processes (Ramsay andSilverman 2002, 2005;Müller 2005;Yao et al 2005;Ferraty and Vieu 2006;Liu and Yang 2009;Ullah and Finch 2013;Ieva et al 2013;Ieva and Paganoni 2016;Martino et al 2019;Spreafico and Ieva 2021). The idea behind FDA and functional models is to express discrete observations arising from time series, i.e., longitudinal timevarying observations, in the form of functions (Ramsay andSilverman 2002, 2005).…”

“…FPCA is one of the most popular dimensionality reduction method in FDA and it is used to summarise each function to a finite set of covariates through FPC scores, while losing a minimum part of the information. An extended version of the FLCRM by Kong et al (2018) to the case of multiple functional predictorsnamed Multivariate FLCRM (MFLCRM)-was introduced by Spreafico and Ieva (2021) to model recurrent events effect on long-term survival. However, since the main focus of the work was to develop a methodology for effectively modelling time-varying recurrent events in terms of the functional compensators underlying the processes of interest, the authors have neither compared MFLCRM with other survival models, nor considered its predictive performances over time.…”

Functional Multivariable Logistic Regression With an Application to HIV Viral Suppression Prediction

“…Another issue that is worth noticing is that the time‐dependent HIV infection measures are endogenous (Kalbfleisch and Prentice 2011), and one needs to be really careful when modeling it with the outcomes defined in the same time domain. Therefore, in our research, we focus only on the scalar binary outcome at a future time point outside of the domain of the functional predictors, similar to the idea of Spreafico and Ieva (2021).…”