Fitting multiple dependent variables with time less than zero
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Suppose I have a therapeutic d that modulates an endogenous substance e. I've a pd model of e (for the sake of argument, a constant synthesis rate, and a linear clearance). I've a pk model for d. I have some sort of model that has e interact and bind with d, and the bound complex has a different clearance rate than e alone. My dataset has therapeutic doses applied to subjects at time zero. But I have undosed data for t<0 - perhaps a dataset of a couple months for e leading into the dosing period. The earlier data helps me set the parameters pertaining to e.
But the fitting programs won't accept any data earlier than t=0. Is this correct? Is my workaround to bias all times so that all time values are positive, and to tell SB that the dose is delayed by this bias? Or can I tell SB to accept values of time less than zero?