In clinical research, time-varying covariates are of great interest since they represent the way dynamic patterns evolve, affecting patient’s health status and disease progression. In literature such data are usually considered using a piecewise-constant or fixed-baseline approach, losing the potential information content they may provide if the association between time-varying and time-to-event data is properly captured. Due to the complexity of the phenomena, an advanced analytical framework is required to adequately model disease evolution and characterise its relationship to the dynamic nature of time-dependent features. These aspects are rarely addressed and may provide new insights for medical research, representing a challenge of both clinical relevance and statistical interest. This dissertation focuses on developing mathematical and statistical methods to properly represent time-varying processes and model them within the context of time-to-event analysis by means of appropriate Cox-type survival models. The main purpose is to enrich the knowledge available for modelling survival with relevant features related to the time-varying covariates of interest. The efforts of this work address the complexities of both (i) developing adequate dynamic characterizations of the processes under study (i.e., the representation problem) and (ii) identifying and quantifying the association between time-varying processes and patient survival (i.e., the time-to-event modelling problem). In both cases, the main issue is dealing with complex data sources while taking into account the nature of the processes and their particular aspects (such as temporal dynamics, categorical levels or recurring events) and managing the complex trade-off between clinical interpretability and mathematical formulation. Depending on the context of the study, different approaches are proposed. In terms of representations, on one hand complex data integration and functional data analysis are exploited to propose new longitudinal or functional features capable of incorporating trends and variations in the evolution of processes over time. On the other, novel statistical methodologies are introduced to extract additional information in terms of longitudinal or functional data from different data sources. Stochastic process theory, latent Markov models and compositional data analysis are exploited, among others, to address the research questions. In terms of time-to-event modelling, advanced versions of Cox-type regression are proposed to include the dynamic covariates in the survival analysis. Subject to the type of study and data, joint models, functional survival models exploiting dimensionality reduction techniques or marginal structural models are employed. By solving the aforementioned statistical complexities, this work is not only impacting the community of researchers in mathematics and statistics, but it aims at providing useful tools to support doctors and clinicians in their work. All research topics are motivated by specific clinical questions aimed at gaining insights into personalised treatments for cardiological and oncological patients. Part I of this thesis focuses on the study of the processes of drug consumption, adherence to medications and re-hospitalizations in heart failure patients. Part II deals with the investigation of the time-varying aspects of chemotherapy treatment, such as dose modifications, biomarkers and accumulation of toxicities, in patients affected by osteosarcoma. In conclusion, the development of novel tailored methodologies capable of enhancing time-to-event modelling with time-varying characteristics may represent a significant step forward in the definition of new customized and flexible monitoring tools, which could then be applied to the study of different pathologies characterised by complex data sources.
Nella ricerca clinica, le covariate tempo-dipendenti sono di grande interesse in quanto racchiudono informazioni sull'evoluzione di elementi dinamici che possono avere un impatto sullo stato di salute del paziente e sulla progressione della malattia. In letteratura, queste caratteristiche vengono solitamente analizzate utilizzando un approccio di “baseline" o “costante a tratti", perdendo così il potenziale contenuto informativo che potrebbero fornire se l'associazione tra i dati tempo-dipendenti e quelli di tempo all’evento venisse catturata in maniera appropriata. Data la complessità dei fenomeni, è necessario formulare adeguatamente i modelli per l'evoluzione della malattia e caratterizzare in un contesto analitico avanzato la relazione tra di essa e la natura dinamica delle caratteristiche tempo-varianti. Questi aspetti sono raramente affrontati e possono fornire nuovi spunti per la ricerca medica, rappresentando una sfida sia di rilevanza clinica che di interesse statistico. Questa tesi si concentra sullo sviluppo di metodi matematici e statistici per rappresentare appropriatamente i processi tempo-dipendenti ed includerli in un contesto di analisi di tempo all'evento, mediante modelli di sopravvivenza di tipo “Cox”. Lo scopo principale è quello di arricchire le informazioni disponibili per studiare la sopravvivenza con caratteristiche rilevanti legate alle covariate tempo-varianti di interesse. Questo lavoro affronta quindi le difficoltà sia di (i) sviluppare adeguate caratterizzazioni dinamiche dei processi oggetto di studio (ovvero il problema di rappresentazione), sia di (ii) identificare e quantificare l'associazione tra i processi tempo-dipendenti e la sopravvivenza dei pazienti (ovvero il problema della modellazione del tempo all'evento). In entrambi i casi, la sfida principale consiste nel trattare fonti di dati complesse, sia tenendo conto della natura dei processi e dei loro aspetti peculiari (come le dinamiche temporali, i livelli categorici o gli eventi ricorrenti), sia bilanciando in modo adeguato l'interpretabilità clinica e la formulazione matematica. Lungo il corso della tesi vengono proposti approcci diversificati a seconda del contesto dello studio. In termini di rappresentazione, grazie all'integrazione di fonti di dati complesse e all'utilizzo di tecniche di analisi dei dati funzionali, vengono elaborate nuove covariate tempo-dipendenti (longitudinali o funzionali) in grado di riflettere l'evoluzione dei processi nel tempo. Inoltre, vengono introdotte nuove metodologie statistiche per estrarre dai dati informazioni aggiuntive, impiegando, tra gli altri, la teoria dei processi stocastici, i modelli di Markov latenti e l'analisi dei dati composizionali. In termini di modellazione del tempo all'evento, i modelli di regressione di tipo “Cox" vengono estesi al fine di includere le covariate dinamiche nell'analisi di sopravvivenza. Le tecniche di riduzione della dimensionalità ed i modelli proposti (“joint" o “marginal structural") sono implementati a secondo del tipo di studio e di dati a disposizione. Oltre ad avere un impatto sulla comunità dei ricercatori in matematica e statistica, questo lavoro mira a fornire strumenti utili per supportare i medici nella pratica clinica. Tutti i temi di ricerca che vengono affrontati sono motivati da domande cliniche specifiche riguardanti i trattamenti personalizzati in pazienti cardiologici ed oncologici. La parte I di questa tesi si concentra sullo studio dei processi di re-ospedalizzazione, consumo ed aderenza ai farmaci in pazienti con scompenso cardiaco. La parte II tratta lo studio degli aspetti tempo-varianti della chemioterapia, come le modifiche del dosaggio, i biomarcatori o l'accumulo di tossicità, in pazienti affetti da osteosarcoma. In conclusione, lo sviluppo di nuove metodologie per dati di tempo all'evento che includano informazioni dinamiche può rappresentare un significativo passo avanti nella definizione di nuovi strumenti di monitoraggio personalizzati, che potrebbero poi essere applicati allo studio di diverse patologie caratterizzate da fonti di dati complesse.
Statistical modelling of time-varying covariates for survival data
Spreafico, Marta
2021/2022
Abstract
In clinical research, time-varying covariates are of great interest since they represent the way dynamic patterns evolve, affecting patient’s health status and disease progression. In literature such data are usually considered using a piecewise-constant or fixed-baseline approach, losing the potential information content they may provide if the association between time-varying and time-to-event data is properly captured. Due to the complexity of the phenomena, an advanced analytical framework is required to adequately model disease evolution and characterise its relationship to the dynamic nature of time-dependent features. These aspects are rarely addressed and may provide new insights for medical research, representing a challenge of both clinical relevance and statistical interest. This dissertation focuses on developing mathematical and statistical methods to properly represent time-varying processes and model them within the context of time-to-event analysis by means of appropriate Cox-type survival models. The main purpose is to enrich the knowledge available for modelling survival with relevant features related to the time-varying covariates of interest. The efforts of this work address the complexities of both (i) developing adequate dynamic characterizations of the processes under study (i.e., the representation problem) and (ii) identifying and quantifying the association between time-varying processes and patient survival (i.e., the time-to-event modelling problem). In both cases, the main issue is dealing with complex data sources while taking into account the nature of the processes and their particular aspects (such as temporal dynamics, categorical levels or recurring events) and managing the complex trade-off between clinical interpretability and mathematical formulation. Depending on the context of the study, different approaches are proposed. In terms of representations, on one hand complex data integration and functional data analysis are exploited to propose new longitudinal or functional features capable of incorporating trends and variations in the evolution of processes over time. On the other, novel statistical methodologies are introduced to extract additional information in terms of longitudinal or functional data from different data sources. Stochastic process theory, latent Markov models and compositional data analysis are exploited, among others, to address the research questions. In terms of time-to-event modelling, advanced versions of Cox-type regression are proposed to include the dynamic covariates in the survival analysis. Subject to the type of study and data, joint models, functional survival models exploiting dimensionality reduction techniques or marginal structural models are employed. By solving the aforementioned statistical complexities, this work is not only impacting the community of researchers in mathematics and statistics, but it aims at providing useful tools to support doctors and clinicians in their work. All research topics are motivated by specific clinical questions aimed at gaining insights into personalised treatments for cardiological and oncological patients. Part I of this thesis focuses on the study of the processes of drug consumption, adherence to medications and re-hospitalizations in heart failure patients. Part II deals with the investigation of the time-varying aspects of chemotherapy treatment, such as dose modifications, biomarkers and accumulation of toxicities, in patients affected by osteosarcoma. In conclusion, the development of novel tailored methodologies capable of enhancing time-to-event modelling with time-varying characteristics may represent a significant step forward in the definition of new customized and flexible monitoring tools, which could then be applied to the study of different pathologies characterised by complex data sources.| File | Dimensione | Formato | |
|---|---|---|---|
|
PhD thesis final Spreafico PoliMi.pdf
accessibile in internet solo dagli utenti autorizzati
Descrizione: PhD Thesis Spreafico Marta
Dimensione
16.48 MB
Formato
Adobe PDF
|
16.48 MB | Adobe PDF | Visualizza/Apri |
I documenti in POLITesi sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
https://hdl.handle.net/10589/191852