Thursday 14th April 2016

Multi-State Modelling Workshop

Held jointly with the RSS Young Statisticians Section (https://statsyss.wordpress.com/)

Chaired by Professor Linda Sharples - Leeds Institute of Clinical Trials Research, University of Leeds

Andrew Titman - Department of Mathematics and Statistics, University of Lancaster [Presentation]

Multi-state modelling: An Overview

Multi-state modelling is a technique within event history analysis. Such models are particularly useful for the joint modelling of survival and important ordinal or categorical time dependent covariates. For instance, they have been used extensively to model chronic diseases, where interest may lie both in the rate of progression between clinically defined stages of disease and in the effect of progression on the hazard of death.

The talk will give an overview of the principal methods and key assumptions used in multi-state models. A distinction will be made between continuously observed processes, where much of the machinery from standard survival analysis carries across and there is an emphasis on non- or semi-parametric methods, and interval-censored or panel-observed data where there are additional computational challenges and analysis is usually parametric. The methods will be illustrated through applications such as modelling progression-free and overall survival in cancer studies and modelling the onset of cardiac allograft vasculopathy in post-heart-transplantation patients.

Dr. Aidan O’Keeffe - Department of Statistical Science, University College London [Presentation]

Multi-state models and causal arguments: Application to a study of clinical damage in psoriatic arthritis

In complex chronic diseases, cohorts of patients may be followed longitudinally with information on the development of different processes/outcomes collected at successive points in time for each patient. It may be of interest to consider the causal effect of changes to one patient-specific process earlier in time on another patient-specific process at a later point in time. Multi-state models provide a convenient, intuitive, method for the modelling of processes changing over time and I will discuss multi-state models as a method for assessing a causal effect of one process on another. As an example, I will use data collected over 35 years at the University of Toronto psoriatic arthritis clinic – a large cohort of psoriatic arthritis patients - and consider how multi-state models can be used to assess the causal relationship between disease activity (tenderness and swelling) and clinical joint damage. Within-patient correlation will be considered through the incorporation of patient-specific random effects in the multi-state modelling framework. Emphasis is given to the use of the Bradford Hill criteria for causal inference in observational studies and the concept of local independence between stochastic processes.

Dr Howard Thom - School of Social and Community Medicine, University of Bristol [Presentation]

Using Parameter Constraints to choose State-Structures in Cost-effectiveness Modelling

The research I will present addresses the question of structural uncertainty in cost-effectiveness decision models, in particular the choice of state-structure in a multi-state model. Key model outputs, such as treatment recommendations and identification of future research needs, may be sensitive to choice of state-structure. For example, it may be uncertain whether to consider similar disease severities or similar clinical events as the same state or as separate states. Model structures can be compared on the basis of their fit to the data used to inform them. However, standard statistical methods for comparing models require a common reference dataset. Merging states in a model aggregates the data, rendering these methods invalid. We describe a new method that involves re-expressing a model with merged states as a model on the larger state space in which particular transition probabilities, costs and utilities are assumed to be equal between states. This produces a model which gives identical estimates of cost-effectiveness to the model with merged states, while leaving the data unchanged. The comparison of state structures for transition probabilities, costs and utilities can therefore be achieved using standard methods to compare the constrained and unconstrained models. This formalises the intuitive principle that two states in a model may be merged if the costs and health consequences for a patient in them are the same. These principles generalise so that any set of state structures can be compared and we note that different structures can be used for rates, costs and utilities, as appropriate. We illustrate our method with applications to two recent models evaluating cost-effectiveness of prescribing anti-depressants by depression severity and the cost-effectiveness of diagnostic tests for coronary artery disease.

The meeting will be held 1:30pm until 4:30 pm at Seminar Room Y, Level 8, Worsley Building, University of Leeds. See interactive campus map, (PDF copy available here).