Estimation of a disease model based on a discrete time Markov model using secondary data with transitions based on multi-dimensional tables

Abstract

The progression of a disease may be affected by many risk factors, such as gender, age, and current disease state. Such information is collected and made publically available by published clinical studies, yet combining this information into a disease model remains a challenge. This paper extends the previously published maximum likelihood estimation technique to estimate model parameters from indirect secondary data. Such information is available in the scientific literature so the modeler can access more data when estimating model parameters. The extension to the estimation procedure allows model transitions that depend on different sets of covariates for which secondary data are available. This extension uses a Markov model with transition probabilities stored in multi-dimensional tables accessed by covariate values. The paper uses a set of cases, including a case of cardiovascular disease in diabetes. The cases demonstrate the proposed method with various model variations. To help cope with model multiplicity, a selection method is demonstrated for picking a preferred model according to likelihood and structure criteria.