Methods and systems for predicting occurrence of an event
View Patent ↗Embodiments of the present invention are directed to methods and systems for training a neural network having weighted connections for classification of data, as well as embodiments corresponding to the use of such a neural network for the classification of data, including, for example, prediction of an event (e.g., disease). The method may include inputting input training data into the neural network, processing, by the neural network, the input training data to produce an output, determining an error between the output and a desired output corresponding to the input training data, rating the performance neural network using an objective function, wherein the objective function comprises a function C substantially in accordance with an approximation of the concordance index and adapting the weighted connections of the neural network based upon results of the objective function.
1. Apparatus for predicting occurrence of a medical condition in a patient under consideration comprising:
a neural network having weighted connections, an input and an output, said weighted connections resulting from training said neural network;
wherein said input is configured to receive data for said patient under consideration and, based on said weighted connections, said neural network is configured to provide at said output a prognostic indicator of the risk of occurrence of the medical condition in said patient; and
wherein said neural network is trained with an objective function C for providing a rating of the performance of the neural network, wherein the objective function C is a differentiable approximation of the concordance index, said training of said neural network with the objective function C comprising conducting pair-wise comparisons between prognostic indicators from said neural network of pairs of patients i and j from a training dataset comprising both censored and non-censored data and adapting said weighted connections of said neural network as a result of said comparisons, said pairs of patients from said training dataset comprising:
patients i and j who have both experienced the medical condition, and the time t i to occurrence of the medical condition of patient i is shorter than the time t j to occurrence of the medical condition of patient j; and
patients i and j where only patient i has experienced the medical condition, and the time t i to occurrence of the medical condition in patient i is shorter than a follow-up visit time t j for patient j.
2. The apparatus according to claim 1 , wherein said neural network is configured to receive at said input data for said patient under consideration comprising clinical data, molecular biomarker data, and histopathological data resulting from machine vision analysis of tissue, and based on said weighted connections, to provide at said output said prognostic indicator for said patient.
3. The apparatus according to claim 1 , wherein said medical condition comprises recurrence of prostate cancer and said prognostic indicator indicates a likelihood of recurrence of prostate cancer in said patient under consideration within a certain amount of time.
4. The apparatus according to claim 1 , wherein the function C is defined according to
C
=
∑
(
i
,
j
)
∈
Ω
R
(
t
^
i
,
t
^
j
)
|
Ω
|
,
wherein Ω comprises said pairs of patients (i, j), wherein R is defined according to
R
(
t
^
i
,
t
^
j
)
=
{
(
-
(
t
^
i
-
t
^
j
-
γ
)
)
n
:
t
^
i
-
t
^
j
<
γ
0
:
otherwise
}
,
wherein {circumflex over (t)} i and {circumflex over (t)} j include prognostic estimates for patients i and j, respectively, and wherein 0<γ<1 and n>1.
5. The apparatus according to claim 1 , wherein the function C is defined according to
C
ω
=
∑
(
i
,
j
)
∈
Ω
-
(
t
^
i
-
t
^
j
)
·
R
(
t
^
i
,
t
^
j
)
D
,
wherein
D
=
∑
(
i
,
j
)
∈
Ω
-
(
t
^
i
-
t
^
j
)
is a normalization factor, and Ω comprises said pairs of patients (i, j), wherein R is defined according to
R
(
t
^
i
,
t
^
j
)
=
{
(
-
t
^
i
-
t
^
j
-
γ
)
)
n
:
t
^
i
-
t
^
j
<
γ
0
:
otherwise
}
,
wherein {circumflex over (t)} i and {circumflex over (t)} j include prognostic estimates for patients i and j, respectively, and wherein 0<γ<1 and n>1.
6. The apparatus according to claim 1 , wherein said medical condition comprises recurrence of prostate cancer and said prognostic indicator indicates an amount of time in which recurrence of prostate cancer in said patient under consideration is likely to occur.
7. A method for predicting occurrence of a medical condition in a patient under consideration:
inputting data into a neural network having weighted connections in order to produce an output, said weighted connections resulting from training said neural network;
wherein said inputting data comprises inputting data for said patient under consideration and said output comprises a prognostic indicator indicative of the risk of occurrence of the medical condition in said patient; and
wherein said training said neural network comprises training said neural network with an objective function C that provides a rating of the performance of the neural network, wherein the objective function C is a differentiable approximation of the concordance index, said training of said neural network with the objective function C comprising conducting pair-wise comparisons between prognostic indicators from said neural network of pairs of patients i and j from a training dataset comprising both censored and non-censored data and adapting said weighted connections of said neural network as a result of said comparisons, said pairs of patients from said training dataset comprising:
patients i and j who have both experienced the medical condition and the time t i to occurrence of the medical condition of patient i is shorter than the time t j to occurrence of the medical condition of patient j; and
patients i and j where only patient i has experienced the medical condition and the time t j to occurrence of the medical condition in patient i is shorter than a follow-up visit time t j for patient j.
8. The method according to claim 7 , wherein said inputting data for said patient under consideration comprises inputting data for said patient comprising clinical data, molecular biomarker data, and histopathological data resulting from machine vision analysis of tissue, and based on said weighted connections, outputting said prognostic indicator for said patient.
9. The method according to claim 7 , wherein said medical condition comprises recurrence of prostate cancer and the prognostic indicator is indicative of a likelihood of recurrence of prostate cancer in said patient under consideration within a certain amount of time.
10. The method according to claim 7 , wherein the function C is defined according to
C
=
∑
(
i
,
j
)
∈
Ω
R
(
t
^
i
,
t
^
j
)
|
Ω
|
,
and wherein Ω comprises said pairs of patients (i, j) wherein R is defined according to
R
(
t
^
i
,
t
^
j
)
=
{
(
-
(
t
^
i
-
t
^
j
-
γ
)
)
n
:
t
^
i
-
t
^
j
<
γ
0
:
otherwise
}
,
wherein {circumflex over (t)} i and {circumflex over (t)} j include prognostic estimates for patients i and j, respectively, and wherein 0<γ<1 and n>1.
11. The method according to claim 7 , wherein the function C is defined according to:
C
ω
=
∑
(
i
,
j
)
∈
Ω
-
(
t
^
i
-
t
^
j
)
·
R
(
t
i
^
,
t
^
j
)
D
,
wherein
D
=
∑
(
i
,
j
)
∈
Ω
-
(
t
^
i
-
t
^
j
)
is a normalization factor, and wherein Ω comprises said pairs of patients (i, j), wherein R is defined according to
R
(
t
^
i
,
t
^
j
)
=
{
(
-
(
t
^
i
-
t
^
j
-
γ
)
)
n
:
t
^
i
-
t
^
j
<
γ
0
:
otherwise
}
,
wherein {circumflex over (t)} i and {circumflex over (t)} j include prognostic estimates for patients i and j, respectively, and wherein 0<γ<1 and n>1.
12. The method according to claim 7 , wherein said medical condition comprises recurrence of prostate cancer and outputting said prognostic indicator comprises outputting a prognostic indicator indicative of an amount of time in which recurrence of prostate cancer in said patient under consideration is likely to occur.
13. Computer readable media comprising computer instructions for causing a computer to perform the method comprising:
inputting data into a neural network having weighted connections in order to produce an output, said weighted connections resulting from training said neural network;
wherein said inputting data comprises inputting data for said patient under consideration and said output comprises a prognostic indicator indicative of the risk of occurrence of the medical condition in said patient; and
wherein said training said neural network comprises training said neural network with an objective function C that provides a rating of the performance of the neural network, wherein the objective function C is an differentiable approximation of the concordance index, said training of said neural network with the objective function C comprising conducting pair-wise comparisons between prognostic indicators from said neural network of pairs of patients i and j from a training dataset comprising both censored and non-censored data and adapting said weighted connections of said neural network as a result of said comparisons, said pairs of patients from said training dataset comprising:
patients i and j who have both experienced the medical condition and the time t i to occurrence of the medical condition of patient i is shorter than the time t j to occurrence of the medical condition of patient j; and
patients i and j where only patient i has experienced the medical condition and the time t i to occurrence of the medical condition in patient i is shorter than a follow-up visit time t j for patient j.
14. The computer readable media according to claim 13 , wherein said inputting data for said patient under consideration comprises inputting data for said patient comprising clinical data, molecular biomarker data, and histopathological data resulting from machine vision analysis of tissue, and based on said weighted connections, outputting said prognostic indicator for said patient.
15. The computer readable media according to claim 13 , wherein said medical condition comprises recurrence of prostate cancer and outputting said prognostic indicator comprises outputting a prognostic indicator indicative of a likelihood of recurrence of prostate cancer in said patient under consideration within a certain amount of time.
16. The computer readable media according to claim 13 , wherein the function C is defined according to
C
=
∑
(
i
,
j
)
∈
Ω
R
(
t
^
i
,
t
^
j
)
|
Ω
|
,
and wherein Ω comprises said pairs of patients (i, j), wherein R is defined according to
R
(
t
^
i
,
t
^
j
)
=
{
(
-
(
t
^
i
-
t
^
j
-
γ
)
)
n
:
t
^
i
-
t
^
j
<
γ
0
:
otherwise
}
,
wherein {circumflex over (t)} i and {circumflex over (t)} j include prognostic estimates for the patients i and j, respectively, and wherein 0<γ<1 and n>1.
17. The computer readable media according to claim 13 , wherein the function C is defined according to:
C
ω
=
∑
(
i
,
j
)
∈
Ω
-
(
t
^
i
-
t
^
j
)
·
R
(
t
i
^
,
t
^
j
)
D
,
wherein
D
=
∑
(
i
,
j
)
∈
Ω
-
(
t
^
i
-
t
^
j
)
is a normalization factor, and wherein Ω comprises said pairs of patients (i, j), wherein R is defined according to
R
(
t
^
i
,
t
^
j
)
=
{
(
-
(
t
^
i
-
t
^
j
-
γ
)
)
n
:
t
^
i
-
t
^
j
<
γ
0
:
otherwise
}
,
wherein {circumflex over (t)} i and {circumflex over (t)} j include prognostic estimates for the patients i and j, respectively, and wherein 0<γ<1 and n>1.
18. The computer readable media according to claim 13 , wherein said medical condition comprises recurrence of prostate cancer and outputting said prognostic indicator comprises outputting a prognostic indicator indicative of an amount of time in which recurrence of prostate cancer in said patient under consideration is likely to occur.