System and method for online domain adaptation of models for hypoglycemia prediction in type 1 diabetes
Embodiments relate to an adaptive glycemia monitoring and forecasting system that includes an event monitor configured to receive blood glucose levels of an individual or information about an activity performed by the individual, and generate an event output. The system includes a control module configured to pull observation data, predictor variables, and population estimated vector of covariate weightings coefficients from a database, and generate updated estimated vector of covariate weightings coefficients for the individual user based on the event output. The updated estimated vector of covariate weightings coefficients are determined by a cross-entropy loss objective function. The updated estimated vector of covariate weightings coefficients are used to predict at least one or more of a predicted hypoglycemia state, a predicted normal glycemia state, or a predicted hyperglycemia state for the individual user.
1 . An adaptive glycemia monitoring and forecasting system, comprising:
an event monitor configured to receive blood glucose levels of an individual or information about an activity performed by the individual, and generate an event output;
a control module having a processor and a memory, wherein:
the memory includes a database having:
observation data representative of historical events correlated to changes in blood glucose levels for a population of subjects;
predictor variable(s) that predict the historical events for the population of subjects using a generalized linear model; and
population estimated vector of covariate weightings coefficients (β{circumflex over ( )}_pop) representative of the influence of the predictor variable(s) on the outcome of an observation, the observation being event data and predictor variable data representative of at least one or more of a hypoglycemia state, a normal glycemia state, or a hyperglycemia state;
the control module is configured for:
receiving the event output and generating target-based estimated vector of covariate weightings coefficients (β) representative of the influence of the predictor variable(s) on the outcome of an observation for an individual subject based on the event output, wherein β is determined using a cross-entropy loss objective function;
updating the generalized linear model with the target-based estimated vector of covariate weightings coefficients β and generating a prediction output, the prediction output being at least one or more of a predicted hypoglycemia state, a predicted normal glycemia state, or a predicted hyperglycemia state based on the event output and the target-based estimated vector of covariate weightings coefficients β; and
transmitting the prediction output in a format for receipt by a prediction output receiving device.
2 . The system of claim 1 , in combination with the prediction output receiving device comprising at least one or more of:
an insulin pump;
a decision support system; or
a computer device.
3 . The system of claim 2 , wherein:
the prediction output receiving device is configured for adjusting delivery of insulin based on the prediction output.
4 . The system of claim 2 , wherein:
the computer device is configured to generate a user interface displaying any one or combination of textual or graphical information representative of the prediction output.
5 . The system of claim 1 , wherein:
the generalized linear model includes a design matrix (X) and an observation vector (Y):
X
=
[
x
1
,
1
…
x
1
,
K
⋮
⋱
⋮
x
N
,
1
…
x
N
,
K
]
;
Y
=
[
y
1
⋮
y
N
]
;
for N observations on a predictor variable K, K, {x i,j }∈z, 130 K ;
predictor variable j being associated with an observation i; and
a class label transform y i is defined by {y i }∈{0,1};
the generalized linear module being configured with
E
[
Y
]
=
π
and
log
π
1
-
π
=
X
β
+
ϵ
,
wherein:
π is a vector of estimated probabilities, wherein an estimated probability that y=1, {circumflex over (π)}, given an associated x vector of features, is given by
π
^
=
1
1
+
e
-
x
β
;
and
ϵ is a vector of independent Gaussian noise with distribution N(0, σI n×n ).
6 . The system of claim 5 , wherein:
the cross-entropy loss objective function is
L
(
β
)
=
-
∑
i
=
1
N
y
i
log
(
1
1
+
e
-
x
i
β
)
+
(
1
-
y
i
)
log
(
1
-
1
1
+
e
-
x
i
β
)
.
7 . The system of claim 6 , wherein:
the control module is configured for minimizing the cross-entropy loss objective function to determine a maximum β.
8 . The system of claim 7 , wherein:
the maximum β is used to update the generalized linear model.
9 . The system of claim 8 , wherein:
the control module is configured to update the generalized linear model with the maximum β based on a learning rate (η) and a loss function gradient defined by:
β
β
-
η
∇
L
(
β
)
==
β
β
-
η
(
π
^
-
y
)
x
T
.
10 . The system of claim 9 , wherein:
the control module is configured to query event output data from the event monitor via a plurality of queries set by a query period.
11 . The system of claim 10 , wherein:
the control module is configured to generate a maximum β for each query and to update the generalized linear model for each query period.
12 . A method of adaptively forecasting glycemia, the method comprising:
receiving, by an event monitor, blood glucose levels or user activity, and generating an event output;
retrieving by a control module having a memory: p 2 observation data representative of historical events correlated to changes in blood glucose levels for a population of subjects;
predictor variable(s) that predict the historical events for the population of subjects using a generalized linear model; and
population estimated vector of covariate weightings coefficients (β{circumflex over ( )}_pop) representative of the influence of the predictor variable(s) on the outcome of an observation, the observation being event data and predictor variable data representative of at least one or more of a hypoglycemia state, a normal glycemia state, or a hyperglycemia state;
wherein the control module is configured for:
receiving the event output and generating target-based estimated vector of covariate weightings coefficients (β) representative of the influence of the predictor variable(s) on the outcome of an observation for an individual subject based on the event output, wherein β is determined using a cross-entropy loss objective function;
updating the generalized linear model with the target-based estimated vector of covariate weightings coefficients β and generating a prediction output, the prediction output being at least one or more of a predicted hypoglycemia state, a predicted normal glycemia state, or a predicted hyperglycemia state based on the event output and the target-based estimated vector of covariate weightings coefficients β; and
transmitting the prediction output to a device prediction output receiving device.
13 . The method of claim 12 , comprising:
adjusting delivery of insulin based on the prediction output.
14 . The method of claim 12 , comprising:
generating a user interface displaying any one or combination of textual or graphical information representative of the prediction output.
15 . The method of claim 12 , wherein:
generating a design matrix (X) and an observation vector (Y) for the generalized linear model, X and Y defined by:
X
=
[
x
1
,
1
…
x
1
,
K
⋮
⋱
⋮
x
N
,
1
…
x
N
,
K
]
;
Y
=
[
y
1
⋮
y
N
]
;
for N observations on a predictor variable K, K, {x i,j }∈ K ;
predictor variable j being associated with an observation i;
a class label transform y i is defined by {y i }∈{0,1};
utilizing
E
[
Y
]
=
π
and
log
π
1
-
π
=
X
β
+
ϵ
in the generalized linear module, wherein:
π is a vector of estimated probabilities, wherein an estimated probability that y=1, {circumflex over (π)}, given an associated x vector of features, is given by
π
^
=
1
1
+
e
-
x
β
;
and
ϵ is a vector of independent Gaussian noise with distribution N(0, σI n×n ).
16 . The method of claim 15 , wherein:
the cross-entropy loss objective function is
L
(
β
)
=
-
∑
i
=
1
N
y
i
log
(
1
1
+
e
-
x
i
β
)
+
(
1
-
y
i
)
log
(
1
-
1
1
+
e
-
x
i
β
)
.
17 . The method of claim 16 , comprising:
minimizing the cross-entropy loss objective function to determine a maximum β.
18 . The method of claim 17 , comprising:
updating the generalized linear model with the maximum β.
19 . The method of claim 18 , comprising:
updating the generalized linear model with the maximum β based on a learning rate (η) and a loss function gradient defined by:
β
β
-
η
∇
L
(
β
)
==
β
β
-
η
(
π
^
-
y
)
x
T
.
20 . The method of claim 19 , comprising:
querying event output data via a plurality of queries set by a query period.