Gaussian Process Modeling in Conjunction with Individual Patient Simulation Modeling: A Case Study Describing the Calculation of Cost-Effectiveness Ratios for the Treatment of Established Osteoporosis

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Abstract
Individual patient-level models can simulate more complex disease processes than cohort-based approaches. However, large numbers of patients need to be simulated to reduce 1storder uncertainty, increasing the computational time required and often resulting in the inability to perform extensive sensitivity analyses. A solution, employing Gaussian process techniques, is presented using a case study, evaluating the cost-effectiveness of a sample of treatments for established osteoporosis. The Gaussian process model accurately formulated a statistical relationship between the inputs to the individual patient model and its outputs. This model reducedthe time required for future runs from 150 min to virtually-instantaneous, allowing probabilistic sensitivity analyses-to be undertaken. This reduction in computational time was achieved with minimal loss in accuracy. The authors believe that this case study demonstrates the value of this technique in handling 1st- and 2nd-order uncertainty in the context of health economic modeling, particularly when more widely used techniques are computationally expensive or are unable to accurately model patient histories.