Prognostic Functions Based on Multi-state Models

Multi-state models are models for a process, which at any time occupies one of several possible states. An example of a multi-state process is the life history of an individual, where the states can be different diseases and an absorbing state-death. We applied these methods to study cardiovascular diseases (CVD) and how they affect mortality. With the increasing proportion of elderly people in most developed countries, the burden of CVD on the society is increasing as well. It is estimated that by year 2020 heart disease and stroke will become leading cause of death and disability world wide. The number of fatalities is projected to increase to more than 20 million a year, and more than 24 million by year 2030. (Atlas of Heart Disease and Stroke, WHO, September 2004) Prognostic models have been widely used by clinicians to predict the outcomes for patients free of CVD. These models have been developed mainly using risk functions for the binary outcome (yes=CVD, no=no CVD) in logistic regression or for modelling the failure time (time to death) in survival analysis. In both approaches, the focus is to determine the effect of the covariates (fixed at baseline or time-varying) to mortality. As the population ages and more people experience different diseases or events, such as heart attack or stroke, which do irreversible damage to the heart/brain and change the life expectancy. It is also expected, that factors like high blood pressure or diabetes may have different effects for a person before and after a stroke. The question that we are interested is how to model the event history for individuals who go through different disease states in their lifetime. The goal is to include information for a set of covariates as well as the time and the type of disease people encounter. We approach this problem from a multi-state prospective, where the states describe the progression of the disease, for example healthy state, coronary heart disease (CHD state) cerebral vascular accident (stroke) and death (absorbing state). The problem can be generally divide into steps: The first step is to estimate how transition rates between various states depend on the covariates. This will allow us to compare the role of covariates for different transitions. The second step is to combine the estimated rates for a given set of covariates into appropriate transition rates. This will allow us to calculate a survival probability for a given subject. This can be used as a prognostic function at baseline, as well as at a later time, when information for the event history of the subject is available.