Time-varying
covariates for
survival models

Background

In clinical research, to study the association between functional time-varying responses (e.g. biomarkers or toxicity) with a time to event outcome (e.g. treatment failure or death) is a challenging task.  Well-known examples are therapies which change during treatment, such as chemotherapy. Depending on patients’ treatment history or development of toxicity, chemotherapy treatment is modified by delaying a course or reducing the dose intensity. Models for time to event able to deal with the dynamic nature of the drug intake during treatment are not well developed. In addition, chemotherapy presents some particular aspects, such as latent accumulation of toxicity. The effect on survival is still unclear. To assess the association of time-varying chemotherapy and toxicity on survival is a difficult problem which involves the use of complex chemotherapy data.

Aims

Statistical models which deal with dynamic functional covariates will be developed to provide personalized prediction of long-term survival for patients with osteosarcoma. In particular, the project focus on the following methodological aspects

• Compare methods to include time-varying covariates into a survival framework. 

• Development of structural equation or latent class models to analyse relationships between unobserved functional factors from observable variables, plugging them into a survival field. 

• Development of hidden Markov models with functional response, focusing on models where the path through states is only observed through some error-prone marker. 

Relevance for cancer research

Within this project, research will be carried out in order to develop methodologies to deal with time-varying functional covariates for survival analysis of cancer data. These methodologies will be applied to provide personalized prediction of long-term survival for osteosarcoma patients. Since time-varying factors are usually measured in clinical research, these methods could be applied to other disease.

Project Outcomes

• Spreafico M, Ieva F & Fiocco M (2023). Causal effect of chemotherapy received dose intensity on survival outcome: a retrospective study in osteosarcoma. arXiv:2307.09405

• Spreafico M, Ieva F & Fiocco M (2023). Longitudinal Latent Overall Toxicity (LOTox) profiles in osteosarcoma: a new taxonomy based on latent Markov models. arXiv:2107.12863 

• Spreafico M, Ieva F & Fiocco M (2023). Modelling time-varying covariates effect on survival via Functional Data Analysis: application to the MRC BO06 trial in osteosarcoma. Statistical Methods & Applications, 32:271-298. doi: 10.1007/s10260-022-00647-0 

• Spreafico M (2022, October 12). Statistical modelling of time-varying covariates for survival data, Part II. [Doctoral Thesis]

• Spreafico M, Ieva F, Arlati F, Capello F, Fatone F, Fedeli F, Genalti G, Anninga JK, Gelderblom H & Fiocco M (2021). Novel longitudinal Multiple Overall Toxicity (MOTox) score to quantify adverse events experienced by patients during chemotherapy treatment: a retrospective analysis of the MRC BO06 trial in osteosarcoma. BMJ Open, 11:e053456. doi: 10.1136/bmjopen-2021-053456