Mathematical and statistical model misspecifications in modelling immune response in renal transplant recipients

We examine uncertainty in clinical data from a kidney transplant recipient infected with BK virus and investigate mathematical model and statistical model misspecifications in the context of least squares methodology. A difference-based method is directly applied to data to determine the correct statistical model that represents the uncertainty in data. We then carry out an inverse problem with the corresponding iterative weighted least squares technique and use the resulting modified residual plots to detect mathematical model discrepancy. This process is implemented using both clinical and simulated data. Our results demonstrate mathematical model misspecification when both simpler and more complex models are assumed compared to data dynamics.