Sensitivity Analysis for Biomedical Models

This article discusses the application of sensitivity analysis (SA) in biomedical models. Sensitivity analysis is widely applied in physics, chemistry, economics, social sciences and other areas where models are developed. By assigning a prior probability distribution to each model variable, the SA framework appeals to the posterior probabilities of the model to evaluate the relative importance of these variables on the output distribution based on the principle of general variance decomposition. Within this framework, the SA paradigm serves as an objective platform to quantify the contributions of each model factor relative to their empirical range. We present statistical derivations of variance-based SA in this context and discuss its detailed properties through some practical examples. Our emphasis is on the application of SA in the biomedical field. As we show, it may provide a useful tool for model quality assessment, model reduction and factor prioritization, and improve our understanding of the model structure and underlying mechanisms. When usual approaches for calculating sensitivity index involve the employment of Monte Carlo analysis, which is computationally expensive in the large-sampling paradigm, we develop two effective numerical approximate methods for quick SA evaluations based on the unscented transformation (UT) that utilize a deterministic sampling approach in place of random sampling to calculate posterior statistics. We show that these methods achieve an excellent compromise between computational burden and calculation precision. In addition, a clear guideline is absent to evaluate the importance of variable for model reduction, we also present an objective statistical criterion to quantitatively decide whether or not a descriptive parameter is nominal and may be discarded in ensuing model-based analysis without significant loss of information on model behavior.