A discrete‐state discrete‐time model using indirect observation

Abstract

This research was motivated by a desire to model the progression of a chronic disease through various disease stages when data are not available to directly estimate all the transition parameters in the model. This is a common occurrence when time and expense make it unfeasible to follow a single cohort to estimate all the transition parameters. One difficulty of developing a model of chronic disease progression from such data is that the available studies often do not include the transitions of interest. For example, in our model of diabetic nephropathy, many clinical studies did not differentiate between patients without nephropathy and those who had microalbuminuria (a pre-clinical stage of nephropathy). Another difficulty was a lack of data to directly estimate parameters of interest. We consider models which can accommodate such difficulties. In this paper we consider the problem of estimating parameters of a discrete-time Markov process when longitudinal data describing the entire process are not available. First, we present a likelihood approach to estimate parameters of a discrete-time Markov model. Next, we use simulation to investigate the finite-sample behaviour of our approach. Finally, we present two examples: a model of diabetic nephropathy and a model of cardiovascular disease in diabetes.

State‐space size considerations for disease‐progression models

“…A number of papers in the MDM and healthcare literature examine how to handle various challenges that arise when estimating TPMs in Markov models of disease, including irregular observation times, incomplete data, and censored observations [10][11][12][13][14][15][16][17][18].…”

Deriving Input Parameters for Cost-Effectiveness Modeling: Taxonomy of Data Types and Approaches to Their Statistical Synthesis

“…Although not presented within an evidence synthesis framework, Isaman and colleagues [87][88][89] proposed an approach that allows the use of published regression data to populate a multistate model describing disease natural history, even when the published study may have ignored intermediary states in the multistate model (taxonomy section B1). The authors applied their proposed methodology to model several chronic conditions, including heart disease and diabetes.…”

Use of secondary data to estimate instantaneous model parameters of diabetic heart disease: Lemonade Method

“…In most applications, there is no single study from which all parameters are estimable. Therefore, these chronic disease models are constructed from secondary data analysis of the clinical literature [3]. Summary statistics reported by a variety of studies in the clinical literature are extracted and used as point estimates for transitions in the theoretical model, often one for each transition.…”

“…Although the four parameters are not estimable using the UKPDS alone, we wish to use the UKPDS along with other studies to estimate our disease model. Isaman and colleagues call this valuable, but confounding data as augmentary data [3], and presented a likelihood based method to estimate all parameters in the model simultaneously using secondary data which may or may not match the design of the theoretical model for the complete disease process. We name this estimation approach the Lemonade Method in the spirit of “when study data give you lemons, make lemonade”.…”

“…The following sections will extend the Lemonade Method in [3] to include both instantaneous states and indirect data into our model of heart disease; will use simulation to investigate the finite-sample behavior of our approach using a simple example; and apply this new method for estimating parameters in a model of heart disease in diabetes (Figure 1). …”