Ordinary differential equations (ODEs) provide an attractive framework for modeling temporal dynamics in biological systems. ODEs focus modeling on the rate of change over time rather than directly on the average response. A barrier to the use of ODEs for exploratory and/or confirmatory analysis is the required use of specialized nonlinear optimization software. In
this talk we show how consistent estimation can be obtained by converting a system of ordinary (linear or nonlinear) differential equation into a standard linear statistical model thus allowing simple linear regression techniques for estimation and model assessment. The method
is referred to as the integrated data approach since we integrate both the model and the data to convert estimation into a linear statistical model. Parameter standard errors are easily obtained using parametric or non-parametric bootstrap techniques. The integrated data method offers an alternative to nonlinear least-squares estimation, and in contrast to nonlinear least-squares, does not require analytic or numerical solutions of the defining system of ordinary differential equations. In simulations, the method performs similarly to standard non-linear least squares estimation. Extensions of this method are underway to include the models where the parameters which define the system are distributed across an aggregate population – ie a non-linear random effects model.
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