System and method for personalized dosing of pharmacologic agents
A system and method for personalized dosing of a pharmacologic agent include: executing, using a processing device, a plurality of dosing regimen program modules to determine a respective plurality of dose sets in response to receiving, from an input device, a target response value for a patient; and executing, using the processing device, a dosing selection algorithm module, following executing the plurality of dosing regimen program modules and in response to receiving from the input device a response profile and a monitoring frequency of the patient, to determine a recommended dose set computed as a combination of the plurality of dose sets weighted by degrees of matching computed using fuzzy sets and the response profile.
1. A method for treating anemia in a subject using erythropoietic stimulating agents (Epo), comprising:
obtaining a target hemoglobin value (Hb target ), a current hemoglobin value (Hb k ), a rate of change of hemoglobin value (ΔHb k ), and an Epo dose received value (Epo k ) related to an amount of Epo being received by the subject;
determining an initial recommended Epo dose (Epo k+1,i *) for each of i dosing regimens based on the target hemoglobin value (Hb target ), the current hemoglobin value (Hb k ), the rate of change of hemoglobin value (ΔHb k ), and the previous Epo dose prescribed value (Epo k );
determining a next recommended Epo dose (Epo k+1 ) based on the initial recommended Epo doses for the i dosing regimens weighted by degrees of matching computed using fuzzy membership functions;
determining, using a dose-response model, a Hb k+1 value and a predicted hemoglobin response value (ΔHb k+1 ) for a subject with a respective Epo sensitivity profile based on the Hb k value, the ΔHb k value, and a proposed Epo k+1 value;
determining, using an optimization algorithm, the Epo k+1,i * value by determining the proposed Epo k+1 value using the Hb target value, the Epo k value, the Hb k+1 value and the ΔHb k+1 value, and then iteratively re-determining the proposed Epo k+1 value until the proposed Epo k+1 values converge to the Epo k+1,i * value; and
administering the next recommended Epo dose to the subject;
wherein the dose-response model is substantially according to the function:
[
dHb
dt
d
Δ
Hb
dt
]
=
[
-
2
T
i
1
T
i
2
1
0
]
[
Hb
Δ
Hb
]
+
[
K
i
T
i
2
0
]
Epo
where:
K i —erythropoietic response (1,000 Units Epo per 1 g/dL Hb change)
T i —time constant
Epo—dose (1,000 Units)
Hb—hemoglobin level (g/dL)
ΔHb—hemoglobin rate of change (g/dL per day); and
wherein the optimization algorithm is substantially according to the function:
OFV
=
∑
k
p
=
1
H
p
(
Hb
target
-
Hb
k
p
)
2
+
λ
i
∑
k
c
=
1
H
c
Δ
Epo
k
c
2
where:
k p , k c —time steps (weeks)
H p —prediction horizon (weeks)
H c —control horizon (weeks)
λ i —dose change suppression (non-dimensional)
Hb kp —hemoglobin at step k p
ΔEpo kc —change in dose from step k c-1 to k c ;
Subject to constraints:
0≦Epo≦90,000 units per week
0≦Hb≦20 g/dL
−0.5<ΔHb<0.5 g/dL per week
where: ΔHb=Hb kp −Hb kp-1 .
2. A method for treating anemia in a subject using erythropoietic stimulating agents (Epo), comprising:
obtaining a target hemoglobin value (Hb target ), a current hemoglobin value (Hb k ), a rate of change of hemoglobin value (ΔHb k ), and an Epo dose received value (Epo k ) related to an amount of Epo being received by the subject;
determining an initial recommended Epo dose (Epo k+1,i *) for each of i dosing regimens based on the target hemoglobin value (Hb target ), the current hemoglobin value (Hb k ), the rate of change of hemoglobin value (ΔHb k ), and the previous Epo dose prescribed value (Epo k );
determining a next recommended Epo dose (Epo k+1 ) based on the initial recommended Epo doses for the i dosing regimens weighted by degrees of matching computed using fuzzy membership functions;
determining, using a dose-response model, a Hb k+1 value and a predicted hemoglobin response value (ΔHb k+1 ) for a subject with a respective Epo sensitivity profile based on the Hb k value, the ΔHb k value, and a proposed Epo k+1 value; and
determining, using an optimization algorithm, the Epo k+1,i * value by determining the proposed Epo k+1 value using the Hb target value, the Epo k value, the Hb k+1 value and the ΔHb k+1 value, and then iteratively re-determining the proposed Epo k+1 value until the proposed Epo k+1 values converge to the Epo k+1,i * value; and
administering the next recommended Epo dose to the subject;
wherein “i” equals 5 such that there are 5 dosing regimens; and
wherein Epo k+1 is determined substantially according to the equation:
Epo
k
+
1
=
w
R
1
Epo
k
+
1
,
1
*
+
w
R
2
Epo
k
+
1
,
2
*
+
w
R
3
Epo
k
+
1
,
3
*
+
w
R
4
Epo
k
+
1
,
4
*
+
w
R
5
Epo
k
+
1
,
5
*
w
R
1
+
w
R
2
+
w
R
3
+
w
R
4
+
w
R
5
where:
w R1 =f MF (Epo k , μ 1 , s 1l , s 1r ) μ 1 =0 s 1l =1.0 s 1r =0.9*(Hb target −Hb 0 )
w R2 =f MF (Epo k , μ 2 , s 2l , s 2r ) μ 2 =3*(Hb target −Hb 0 ) s 2l =s 1r s 2r =1.35*(Hb target −Hb 0 )
w R3 =f MF (Epo k , μ 3 , s 3l , s 3r ) μ 3 =7.5*(Hb target −Hb 0 ) s 3l =s 2r s 3r =2.25*(Hb target −Hb 0 )
w R4 =f MF (Epo k , μ 4 , s 4l , s 4r ) μ 4 =15*(Hb target −Hb 0 ) s 4l =s 3r s 4r =s 4l
w R5 =f MF (Epo k , μ 5 , s 5l , s 5r ) μ 5 =22.5*(Hb target −Hb 0 ) s 5l =s 4r s 5r =100.0 and
where f MF is a fuzzy membership function substantially according to the equation:
f
MF
(
x
,
μ
,
s
l
,
s
r
)
=
{
exp
(
-
(
x
-
μ
)
2
s
l
2
)
x
<
μ
1
x
=
μ
exp
(
-
(
x
-
μ
)
2
s
r
2
)
x
>
μ
.