When studying a novel treatment with a survival time outcome, failure can be defined to include a serious adverse event (AE) among the endpoints typically considered, for instance relapse or progression. These events act as competing risks, where the occurrence of relapse as first event and the subsequent treatment change exclude the possibility of observing AE related to the treatment itself. In principle, the analysis of AE could be tackled by two different approaches: 1. the description of the observed occurrence of AE as first event: treatment ability to protect from relapse has an impact on the chance of observing AE due to the competing risks action. 2. the assessment of the treatment impact on the development of AE in patients who are relapse free in time: one should consider the occurrence of AE as if relapse would not exclude the possibility of observing AE related to the treatment itself. In the first part of the thesis we reviewed the strategy of analysis for the two approaches starting from the type of clinical question of interest. Then we identified the suitable quantities and possible estimators (crude proportion, AE rate, crude incidence, Kaplan-Meier and Aalen-Nelson smoothed estimators of the cause-specific hazard) and judge them according to two features, usually needed in a survival context: (i) the estimator should address for the presence of right censoring (ii) the theoretical quantity and estimator should be functions of time. In the second part of the thesis we proposed alternative methods, such as regression models, stratified Kaplan-Meier curves and inverse probability of censoring weighting, to relax the assumption of independence between the potential time to AE and the potential time to relapse. We showed through simulations that these methods overcome the problems related to the use of standard competing risks estimators in the second approach. In particular, we simulated different scenarios setting the hazard of relapse independent from two binary covariates, dependent from X1 only, dependent from both covariates X1 and X2, also through their interaction. We showed that one can handle patients’ selection, and thus obtain conditional independence between the two potential times, adjusting for all the observed covariates. Of note, even adjusting only for few observed covariates as in the reality due to unmeasured covariates, gives less biased estimates with respect to the estimate obtained from the naive Kaplan-Meier censoring by relapse. In fact, we proved that the estimate obtained from the naive Kaplan-Meier is always biased unless the hazard of relapse is independent from the covariates values. In an hypothetical scenario where all the covariates are observed, the weighted average survival estimate obtained either non parametrically or by the Cox model and the survival estimate from the inverse probability of censoring weighting would be unbiased (methods applied adjusting for both covariates). In addition, we point out that with the inverse probability of censoring weighting method one could obtained biased estimates when all the possible interactions between the observed covariates are not included in the model to estimate the weights. However, the inclusion of the interaction is not needed when the weighted Cox model is used, since conditional on the observed covariates, this model is robust in estimating the average survival. Nevertheless, a limitation in the use of the weighted average survival method is given by the fact that it may be applied only in the presence of binary (or categorical) covariates, since if the covariate is continuous it is impossible to identify the subgroups in which the survival function is estimated.

Nello studio di un nuovo trattamento con un tempo di sopravvivenza come outcome, l’insuccesso può essere definito in modo da includere un evento avverso serio (AE) tra gli endpoint tipicamente considerati, come ad esempio ricaduta o progressione. Questi eventi si comportano come rischi competitivi, dove l’occorrenza di una ricaduta come primo evento e il conseguente cambio di trattamento escludono la possibilità di osservare AE legati al trattamento stesso. L’analisi degli AE può essere affrontata mediante due diversi approcci: 1. descrizione dell’occorrenza osservata di AE come primo evento: la capacità del trattamento di proteggere dalla ricaduta ha un impatto sulla possibilità di osservare AE dovuti all’azione dei rischi competitivi. 2. Valutazione dell’impatto del trattamento sullo sviluppo di AE in pazienti che sono liberi da ricaduta nel tempo: si dovrebbe considerare l’occorrenza di AE come se la ricaduta non escludesse la possibilità di osservare AE legati al trattamento stesso. Nella prima parte della tesi abbiamo rivisto la strategia di analisi per i due approcci partendo dal tipo di domanda clinica di interesse. Quindi abbiamo identificato le quantità più adatte e i possibili stimatori (proporzione grezza, tasso di AE, incidenza grezza, stimatori smoothed di Kaplan-Meier e di Aalen-Nelson per l’hazard causa-specifico) e li abbiamo valutati relativamente a due aspetti, solitamente necessari in un contesto di sopravvivenza: (i) Lo stimatore dovrebbe tenere in considerazione la presenza di censura a destra (ii) La quantità teorica e lo stimatore dovrebbero essere funzioni del tempo. Nella seconda parte della tesi abbiamo proposto metodi alternativi, come modelli di regressione, curve di Kaplan-Meier stratificate e inverse probability of censoring weighting, per rilassare l’assunto di indipendenza tra i tempi potenziali di AE e di ricaduta. Abbiamo mostrato attraverso simulazioni che questi metodi superano i problemi legati all’uso dei classici stimatori per i rischi competitivi nel secondo approccio. In particolare, abbiamo simulato differenti scenari fissando l’hazard di ricaduta indipendente da due covariate binarie, dipendente da X1, dipendente da entrambe le covariate X1 e X2 anche attraverso la loro interazione. Abbiamo mostrato che si può gestire la selezione dei pazienti, e quindi ottenere indipendenza condizionata tra i tempi potenziali, aggiustando per tutte le covariate osservate. Si noti che anche aggiustando solo per poche covariate osservate come nella realtà a causa di covariate non misurate, si ottengono stime meno distorte rispetto a quelle che si ottengono dal Kaplan-Meier naive censurando per la ricaduta. Infatti, abbiamo dimostrato che la stima ottenuta con il Kaplan-Meier naive è sempre distorta a meno che l’hazard di ricaduta sia indipendente dalle covariate. In un ipotetico scenario dove tutte le covariate sono osservate, la stima della sopravvivenza media pesata ottenuta sia non parametricamente sia dal modello di Cox e la stima della sopravvivenza dall’inverse probability of censoring weighting dovrebbero essere non distorte (metodi applicati aggiustando per entrambe le covariate). Inoltre, segnaliamo che con l’inverse probability of censoring weighting si possono ottenere stime distorte quando tutte le possibili interazioni tra le covariate osservate non sono incluse nel modello per stimare i pesi. Tuttavia, l’inserimento dell’interazione non è necessario quando si usa il modello di Cox pesato, poiché condizionatamente alle covariate osservate, questo modello è robusto nella stima della sopravvivenza media. Ciò nonostante, una limitazione nell’uso del metodo della sopravvivenza media pesata è dato dal fatto che può essere utilizzato solo in presenza di covariate binarie (o categoriche), poiché se la covariata è continua non è possibile identificare i sottogruppi entro cui la funzione di sopravvivenza è stimata.

(2022). Adverse events in survival data: from clinical questions to methods for statistical analysis. (Tesi di dottorato, Università degli Studi di Milano-Bicocca, 2022).

Adverse events in survival data: from clinical questions to methods for statistical analysis

TASSISTRO, ELENA
2022

Abstract

When studying a novel treatment with a survival time outcome, failure can be defined to include a serious adverse event (AE) among the endpoints typically considered, for instance relapse or progression. These events act as competing risks, where the occurrence of relapse as first event and the subsequent treatment change exclude the possibility of observing AE related to the treatment itself. In principle, the analysis of AE could be tackled by two different approaches: 1. the description of the observed occurrence of AE as first event: treatment ability to protect from relapse has an impact on the chance of observing AE due to the competing risks action. 2. the assessment of the treatment impact on the development of AE in patients who are relapse free in time: one should consider the occurrence of AE as if relapse would not exclude the possibility of observing AE related to the treatment itself. In the first part of the thesis we reviewed the strategy of analysis for the two approaches starting from the type of clinical question of interest. Then we identified the suitable quantities and possible estimators (crude proportion, AE rate, crude incidence, Kaplan-Meier and Aalen-Nelson smoothed estimators of the cause-specific hazard) and judge them according to two features, usually needed in a survival context: (i) the estimator should address for the presence of right censoring (ii) the theoretical quantity and estimator should be functions of time. In the second part of the thesis we proposed alternative methods, such as regression models, stratified Kaplan-Meier curves and inverse probability of censoring weighting, to relax the assumption of independence between the potential time to AE and the potential time to relapse. We showed through simulations that these methods overcome the problems related to the use of standard competing risks estimators in the second approach. In particular, we simulated different scenarios setting the hazard of relapse independent from two binary covariates, dependent from X1 only, dependent from both covariates X1 and X2, also through their interaction. We showed that one can handle patients’ selection, and thus obtain conditional independence between the two potential times, adjusting for all the observed covariates. Of note, even adjusting only for few observed covariates as in the reality due to unmeasured covariates, gives less biased estimates with respect to the estimate obtained from the naive Kaplan-Meier censoring by relapse. In fact, we proved that the estimate obtained from the naive Kaplan-Meier is always biased unless the hazard of relapse is independent from the covariates values. In an hypothetical scenario where all the covariates are observed, the weighted average survival estimate obtained either non parametrically or by the Cox model and the survival estimate from the inverse probability of censoring weighting would be unbiased (methods applied adjusting for both covariates). In addition, we point out that with the inverse probability of censoring weighting method one could obtained biased estimates when all the possible interactions between the observed covariates are not included in the model to estimate the weights. However, the inclusion of the interaction is not needed when the weighted Cox model is used, since conditional on the observed covariates, this model is robust in estimating the average survival. Nevertheless, a limitation in the use of the weighted average survival method is given by the fact that it may be applied only in the presence of binary (or categorical) covariates, since if the covariate is continuous it is impossible to identify the subgroups in which the survival function is estimated.
VALSECCHI, MARIA GRAZIA
ANTOLINI, LAURA
sopravvivenza; eventi avversi; rischi competitivi; censura informativa; IPCW
survival analysis; adverse events; competing risks; dependent censoring; IPCW
MED/01 - STATISTICA MEDICA
English
21-feb-2022
SANITA' PUBBLICA
34
2020/2021
open
(2022). Adverse events in survival data: from clinical questions to methods for statistical analysis. (Tesi di dottorato, Università degli Studi di Milano-Bicocca, 2022).
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Descrizione: PhD Thesis: Adverse events in survival data: from clinical questions to methods for statistical analysis
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/365520
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