Hello,
So I was first thinking FDOE.
But the hard part is the following
y(ABC, T, t) ~ f(t, k(T,A,B,C), b0(A,B,C))
- A,B,C are coded factors
- k(T,A,B,C) are reaction rate constants they are of the form ln(k) = lnk0(A,B,C) - Ea(A,B,C)/T(kelvin) - deltaR z(T)
z(T) is a nonlinear transformer on the temperature in kelvin.
Ea is the energy of activation.
The tricky part is that the k parameters (kinetic factors) change in an exponential way with the reciprocal of the Temperature, though not necessarily linear (unfortunately, in biologics).
On term those k values can change how fast the y response evolves.
Usually it may be seen as a time scaler.
But sometimes also the curve is changing shape with T (temperature).
The DOE is of the type of central-composite-design.
The factors affect nonlinearly the coefficients of ln(k0
For each run the dataset contains a full stability study.
So the entire dataset can be seen as a kronecker product of a DOE with a stability study at different discrete temperatures.
In the end we want
- a profiler as function of factors, time, temperature
- some way to derive meaningful coefficients and describe how the DOE factors affect them (like the activation energy).
If we go fully mechanistic then JMP wouldn't be the answer since we'd require an ODE solver.
But perhaps we could have the rate factor in nonlinear way affecting the time axis on top of a b-spline or functional DOE
any idea how this could be done without too much manual labor?
