Nonlinear modeling of serial immunologic data: A case study

This article concerns the analysis of serial immunologic data from a clinical trial of immunosuppressive chemotherapy in the treatment of multiple sclerosis. The goal of the analysis is to relate levels of drug dose to levels of an immunologic outcome variable. I propose a new, nonlinear model for the analysis of such data. The model assumes that the mean function is the solution of an ordinary differential equation in time, parameters of which are related to the dose via a regression function. The defining differential equation is that which gives rise to the generalized logistic function, a flexible form that includes a number of popular growth models. We fit the model, which accounts for random effects and time series autocorrelation, by maximum likelihood. Results suggest strong treatment effects in two active-drug groups and a small but significant effect in a placebo group. These findings agree well with previously reported analyses of clinical outcomes from the trial. An empirical comparison suggests that nonlinear models of this kind can fit better than linear models of comparable complexity.