Multi-state models are used to describe how individuals transition through different states over time. The distribution of the time spent in different states, referred to as 'length of stay', is... Show moreMulti-state models are used to describe how individuals transition through different states over time. The distribution of the time spent in different states, referred to as 'length of stay', is often of interest. Methods for estimating expected length of stay in a given state are well established. The focus of this paper is on the distribution of the time spent in different states conditional on the complete pathway taken through the states, which we call 'conditional length of stay'. This work is motivated by questions about length of stay in hospital wards and intensive care units among patients hospitalised due to Covid-19. Conditional length of stay estimates are useful as a way of summarising individuals' transitions through the multi-state model, and also as inputs to mathematical models used in planning hospital capacity requirements. We describe non-parametric methods for estimating conditional length of stay distributions in a multi-state model in the presence of censoring, including conditional expected length of stay (CELOS). Methods are described for an illness-death model and then for the more complex motivating example. The methods are assessed using a simulation study and shown to give unbiased estimates of CELOS, whereas naive estimates of CELOS based on empirical averages are biased in the presence of censoring. The methods are applied to estimate conditional length of stay distributions for individuals hospitalised due to Covid-19 in the UK, using data on 42,980 individuals hospitalised from March to July 2020 from the COVID19 Clinical Information Network. Show less
Multi-state models provide an extension of the usual survival/event-history analysis setting. In the medical domain, multi-state models give the possibility of further investigating intermediate... Show moreMulti-state models provide an extension of the usual survival/event-history analysis setting. In the medical domain, multi-state models give the possibility of further investigating intermediate events such as relapse and remission. In this work, a further extension is proposed using relative survival, where mortality due to population causes (i.e. non-disease-related mortality) is evaluated. The objective is to split all mortality in disease and non-disease-related mortality, with and without intermediate events, in datasets where cause of death is not recorded or is uncertain. To this end, population mortality tables are integrated into the estimation process, while using the basic relative survival idea that the overall mortality hazard can be written as a sum of a population and an excess part. Hence, we propose an upgraded non-parametric approach to estimation, where population mortality is taken into account. Precise definitions and suitable estimators are given for both the transition hazards and probabilities. Variance estimating techniques and confidence intervals are introduced and the behaviour of the new method is investigated through simulations. The newly developed methodology is illustrated by the analysis of a cohort of patients followed after an allogeneic hematopoietic stem cell transplantation. The work has been implemented in the R package mstate. Show less
The main objective of this thesis was to develop clinically relevant survival models for patients with high-grade soft tissue sarcoma of the extremities, in particular the development and... Show moreThe main objective of this thesis was to develop clinically relevant survival models for patients with high-grade soft tissue sarcoma of the extremities, in particular the development and validation of prediction models for use in clinical practice. The interdisciplinary collaboration between the Mathematical Institute of Leiden University and the Leiden University Medical Center resulted in important contributions to the care of soft tissue sarcoma patients. Show less
The effect of donor lymphocyte infusions (DLI) after allogeneic stem cell transplantation is difficult to determine and currently unknown. The thesis describes different statistical methods the... Show moreThe effect of donor lymphocyte infusions (DLI) after allogeneic stem cell transplantation is difficult to determine and currently unknown. The thesis describes different statistical methods the determine the effect of DLI after T-cell depleted allogeneic stem cell transplantation for ALL, AML, MDS, relapse AML and multiple myeloma. The effect on bone marrow disease appears strong as compared to extramudullary disease. Show less
