Indirect estimation of a discrete-state discrete-time model using secondary data analysis of regression data

Multi-state models of chronic disease are becoming increasingly important in medical research to describe the progression of complicated diseases. However, studies seldom observe health outcomes over long time periods. Therefore, current clinical research focuses on the secondary data analysis of the published literature to estimate a single transition probability within the entire model. Unfortunately, there are many difficulties when using secondary data, especially since the states and transitions of published studies may not be consistent with the proposed multi-state model. Early approaches to reconciling published studies with the theoretical framework of a multi-state model have been limited to data available as cumulative counts of progression. This paper presents an approach that allows the use of published regression data in a multi-state model when the published study may have ignored intermediary states in the multi-state model. Colloquially, we call this approach the Lemonade Method since when study data give you lemons, make lemonade. The approach uses maximum likelihood estimation. An example is provided for the progression of heart disease in people with diabetes.