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Incorporating Biological Natural History in Simulation Models: Empirical Estimates of the Progression of End-Stage Liver Disease

Department of Industrial and Systems Engineering, University of Wisconsin, Madison

Cindy L. Bryce, PhD

Section of Decision Sciences and Clinical Systems Modeling, Division of General Medicine, University of Pittsburgh School of Medicine, Pittsburgh, PA, Center for Research on Health Care, University of Pittsburgh School of Medicine, Pittsburgh, PA, Department of Medicine, University of Pittsburgh School of Medicine, Pittsburgh, PA

Steven Shechter, MS

Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA

Andrew Schaefer, PhD

Section of Decision Sciences and Clinical Systems Modeling, Division of General Medicine, University of Pittsburgh School of Medicine, Pittsburgh, PA, Department of Medicine, University of Pittsburgh School of Medicine, Pittsburgh, PA

Chung-Chou H. Chang, PhD

Center for Research on Health Care, University of Pittsburgh School of Medicine, Pittsburgh, PA, Department of Medicine, University of Pittsburgh School of Medicine, Pittsburgh, PA, Department of Biostatistics, University of Pittsburgh Graduate School of Public Health, Pittsburgh, PA

Derek C. Angus, MD, MPH

Section of Decision Sciences and Clinical Systems Modeling, Division of General Medicine, University of Pittsburgh School of Medicine, Pittsburgh, PA, Center for Research on Health Care, University of Pittsburgh School of Medicine, Pittsburgh, PA, The CRISMA Laboratory, Department of Critical Care Medicine, University of Pittsburgh School of Medicine, Pittsburgh, PA

Mark S. Roberts, MD, MPP

Section of Decision Sciences and Clinical Systems Modeling, Division of General Medicine, University of Pittsburgh School of Medicine, Pittsburgh, PA, Center for Research on Health Care, University of Pittsburgh School of Medicine, Pittsburgh, PA, Department of Medicine, University of Pittsburgh School of Medicine, Pittsburgh, PA, Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA, robertsm{at}upmc.edu

Objective. To develop an empiric natural-history model that can predict quantitative changes in the laboratory values and clinical characteristics of patients with end-stage liver disease (ESLD), to be used to calibrate an individual microsimulation model. Methods. The authors report the development of a stochastic model that uses cubic splines to interpolate between observed laboratory values over time in a cohort of 1997 patients with ESLD awaiting liver transplantation at the University of Pittsburgh Medical Center. The splines were recursively sampled to provide a stochastic, quantitative natural history of each candidate’s disease. Results. The model was able to simulate the types of erratic disease trajectories that occur in individual patients and was able to preserve the statistical properties of the natural history of ESLD in cohorts of real patients. Moreover, the model was able to predict pretransplant survival rates (87% at 1 year), which were statistically similar to rates observed in the authors’ local cohort (92%). Conclusions. Cubic splines can be used to generate quantitative natural histories for individual patients with ESLD and may be useful for developing clinically robust microsimulation models of other diseases.

Key Words: liver disease • spline function • natural history • microsimulation

Medical Decision Making, Vol. 25, No. 6, 620-632 (2005)
DOI: 10.1177/0272989X05282719


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