Estimating the probability of matrix factorization results
View Patent ↗A method for ranking a relationship between drugs and adverse events includes creating a matrix of associations between a plurality of drugs and a plurality of adverse events and factoring the matrix of associates into a pair of matrix factors. The matrix factors, when multiplied, approximate the matrix of associations, and a product of the matrix factors is a matrix of observed scores. The method further includes determining, for each drug and adverse event pair in the matrix of observed scores, a z-score, an expected score for each drug and adverse event pair, and a standard deviation for each drug and adverse event pair, calculating a probability of a relationship between a drug and adverse event using the z-score for the drug and adverse event pair, and determining that the drug and adverse event are related, when the probability of a relationship is greater than a predetermined magnitude.
1. A computer-implemented method for ranking a relationship between drugs and adverse events, the method comprising:
creating, by a computer, a matrix of associations between a plurality of drugs and a plurality of adverse events using a matrix factorization modeling approach, wherein the matrix contains zeros where no connection exists between row/column entities and non-zeros whose magnitude indicate a relative strength of a relationship between row/column entities;
the matrix factorization modeling approach comprising:
factoring, by the computer, the matrix of associates into a pair of matrix factors, wherein the matrix factors, when multiplied, approximate the matrix of associations, wherein a product of the matrix factors is a matrix of observed scores;
determining, by the computer, a z-score for each drug and adverse event pair in the matrix of observed scores from the matrix of observed scores, an expected score for each drug and adverse event pair, and a standard deviation for each drug and adverse event pair;
calculating, by the computer, a probability of a relationship between a drug and adverse event using the z-score for the drug and adverse event pair;
determining, by the computer, that the drug and adverse event are related, when the probability of a relationship is greater than a predetermined non-negative number; and
ranking those drug and adverse event that are related and screening drugs that are related to adverse events using the rankings, wherein the rankings of the drugs and adverse events are used to effect treatments for medical conditions,
wherein the matrix of associations Cis a binary matrix, wherein the expected score M(i, j) for drug i and adverse event j is
M
(
i
,
j
)
=
row
(
i
)
+
column
(
j
)
agents
+
trgts
wherein
row
(
i
)
=
∑
j
=
1
m
C
(
i
,
j
)
wherein m is a number of adverse events,
column
(
j
)
=
∑
i
=
1
n
C
(
i
,
j
)
wherein n is a number of drugs,
|trgts|=number of ‘adverse events’,
|agents|=number of ‘drugs’,
wherein the standard deviations SD(i, j) for drug i and adverse event j is
SD
(
i
,
j
)
=
M
(
i
,
j
)
×
row
(
i
)
+
column
(
j
)
row
(
i
)
×
column
(
j
)
,
and
wherein z-score Zscore(i,j) for drug i and adverse event j is
Z
score
(
i
,
j
)
=
O
(
i
,
j
)
-
M
(
i
,
j
)
SD
(
i
,
j
)
,
wherein O(i,j) is the observed score for drug i and adverse event j.
2. The method of claim 1 , wherein the matrix of associations is derived from unstructured data sources using natural language processing techniques.
3. The method of claim 1 , wherein the matrix of associations is derived from structured data sources.
4. The method of claim 1 , wherein the matrix of associations C is a non-binary matrix, and wherein the expected score M(i, j) for drug i and adverse event j is
M
(
i
,
j
)
=
Coef
(
row
(
i
)
+
column
(
j
)
)
agents
×
trgts
,
wherein
Coef
=
∑
i
=
1
,
j
=
1
n
,
m
C
(
i
,
j
)
2
Count
,
Count=n×m, the number of cells in matrix C,
row
(
i
)
=
∑
j
=
1
m
C
(
i
,
j
)
2
,
and
column
(
j
)
=
c
∑
i
=
1
n
C
(
i
,
j
)
2
.
5. A computer program product for ranking a relationship between drugs and adverse events, comprising a non-transitory program storage device readable by a computer, tangibly embodying a program of instructions executed by the computer to cause the computer to perform a method comprising the steps of:
creating, by a computer, a matrix of associations between a plurality of drugs and a plurality of adverse events using a matrix factorization modeling approach, wherein the matrix contains zeros where no connection exists between row/column entities and non-zeros whose magnitude indicate a relative strength of a relationship between row/column entities;
the matrix factorization modeling approach comprising:
factoring, by the computer, the matrix of associates into a pair of matrix factors, wherein the matrix factors, when multiplied, approximate the matrix of associations, wherein a product of the matrix factors is a matrix of observed scores;
determining, by the computer, a z-score for each drug and adverse event pair in the matrix of observed scores from the matrix of observed scores, an expected score for each drug and adverse event pair, and a standard deviation for each drug and adverse event pair;
calculating, by the computer, a probability of a relationship between a drug and adverse event using the z-score for the drug and adverse event pair;
determining, by the computer, that the drug and adverse event are related, when the probability of a relationship is greater than a predetermined non-negative number; and
ranking those drug and adverse event that are related and screening drugs that are related to adverse events using the rankings, wherein the rankings of the drugs and adverse events are used to effect treatments for medical conditions,
wherein the matrix of associations Cis a Unary matrix, wherein the expected score M(i, j) for drug i and adverse event j is
M
(
i
,
j
)
=
row
(
i
)
+
column
(
j
)
agents
×
trgts
wherein
row
(
i
)
=
∑
j
=
1
m
C
(
i
,
j
)
wherein m is a number of adverse events,
column
(
j
)
=
∑
i
=
1
n
C
(
i
,
j
)
wherein n is a number of drugs,
|trgts|=number of ‘adverse events’,
|agents|=number of ‘drugs’,
wherein the standard deviation SD(i, j) for drug i and adverse event j is
SD
(
i
,
j
)
=
M
(
i
,
j
)
×
row
(
i
)
+
column
(
j
)
row
(
i
)
×
column
(
j
)
,
and
wherein z-score Zscore(i,j) for drug i and adverse event j is
Z
score
(
i
,
j
)
=
O
(
i
,
j
)
-
M
(
i
,
j
)
SD
(
i
,
j
)
,
wherein O(i,j) is the observed score for drug i and adverse event j.
6. The computer program product of claim 5 , wherein the matrix of associations is derived from unstructured data sources using natural language processing techniques.
7. The computer program product of claim 5 , wherein the matrix of associations is derived from structured data sources.
8. The computer program product of claim 5 , wherein the matrix of associations C is a non-binary matrix, and wherein the expected score M(i, j) for drug i and adverse event j is
M
(
i
,
j
)
=
Coef
×
row
(
i
)
+
column
(
j
)
agents
×
trgts
,
wherein
Coef
=
∑
i
=
1
,
j
=
1
n
,
m
C
(
i
,
j
)
2
Count
,
Count=n×m, the number of cells in matrix C,
row
(
i
)
=
∑
j
=
1
m
C
(
i
,
j
)
2
,
and
column
(
j
)
=
c
∑
i
=
1
n
C
(
i
,
j
)
2
.
9. The method of claim 1 , wherein factorizing the matrix further comprises outputting a raw score for every entity type being ranked.
10. The method of claim 1 , wherein calculating an area under a normal distribution curve uses the z-score as an upper limit to determine the relationship between the two or more types of entities.
11. The method of claim 5 , wherein factorizing, the matrix further comprises outputting a raw score for every entity type being ranked.
12. The method of claim 5 , wherein calculating an area under a normal distribution curve uses the z-score as an upper limit to determine the relationship between the two or more types of entities.