Dear Colleagues,
I am having a few problems expanding upon example 9 in Nonmem 7.2. This is the
one with the SDE plug-in. I have a model with 3 differential equations and two
observation compartments. One of the differential equations is the parameter
that I want the process noise on. The SDEs look like this:
kmet = exp(A(3))
dAdt(1) = kin - kmet*A(1)
dAdt(2) = kmet*A(1) - kel*A(2)
dAdt(3) = 0 + SGW3 * dW ;
Observations are:
F(1) = A(1)/V
F(2) = A(2)/V
Can someone please provide advice on how to code this model with the SDE
plug-in? Here are the points as I understand them:
· I have 3 "base ODE equations" which should be DADT(1,2,3).
· I have 2 "prediction equations" which should be DADT(4,5).
o e.g., DADT(4) = A(1)/V
o the actual derivatives (dF_i / dA_j) required by the EKF will be computed
from these equations entered in the ODEs, or so promises the commentary in the
example
· I need to have 9 additional compartments to house the state
correlation matrix
o Or is it only 6, the upper triangle?
o What happens if I have too many? The integrator just runs more slowly?
o I don't need to code anything for these, the plug-in will do all the work.
· I have 3 "SGW" parameters that get stored in a local array and sent
into the filtering code. One for each state.
o Can I set the first two to zero, so I only have SGW3 as a THETA parameter?
o Shouldn't there be 9 of these? Or does this mechanism only handle a
diagonal scale matrix for the independent Wiener processes?
· I need to pass the number of ODEs and Observations into SDE_DER
o After reviewing the FORTRAN code, it looks like the order of the parameters
is reversed from that in the comments.
CALL SDE_DER(DADT,A,DA,IR,SGW, NDES, NOBS)
§ NDES=3, NOBS=2
§ DADT, A, and DA are reserved variables (derivatives, state variables, and
system jacobian).
§ What is IR?
· I'm unsure how the $ERROR block is working (Y = IPRED+W*EPS(1) +
WS*EPS(2)):
o Is WS a system variable? If not, how does the SDE_CADD routine update it
as promised in the commentary.
o How does EPS(2) enter the fray?
o Does it matter which EPS is assigned as the process noise term? Must it be
the final one, or always the second one? Can there be more than 2 EPS in the
model?
o Is this a red herring since the R matrix is what really matters for the
likelihood computation and that is being constructed by SDE_CADD?
Thanks in advance for any assistance you can render.
Jason Chittenden
Scientist
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