Method for detecting abnormal values of a biomarker
The invention proposes a new method for monitoring a health event in a mammal, comprising detecting at least one abnormal value within a series of values related to at least one biomarker, based on appropriate Z-scores.
1. A method for monitoring a health event in a mammal, comprising detecting at least one abnormal value within a series of values related to at least one biomarker, said biomarker corresponding to a physiological parameter or to the level of any biological or chemical entity measured from a biological sample of said mammal, the series of values (x 1 , x 2 , . . . , x n ) related to said at least one biomarker being obtained from independent variables (X 1 , X 2 , . . . , X n ) normally distributed;
said method comprising the following steps of:
E1: determining from each biological sample collected at different periods of time from said mammal, a value related to said at least one biomarker thereby acquiring a series of values (x 1 , x 2 , . . . , x n ) related to said biomarker,
E2: storing the series of values (x 1 , x 2 , . . . , x n ) on a database (DB) stored in a memory ( 12 );
said method comprising the following steps run with a processor ( 14 ) that can retrieve data from the database (DB) in the memory:
E3: calculating, for the whole series of values of step E2 a single value t n of an indicator (T n ), said indicator (T n ) being based on a studentized form (R n,i ) of the variables (X 1 , X 2 , . . . , X n ), said calculation consisting of extracting the maximum observed value (t n ) of the studentized form (R n,i ) calculated for each value of the series of values (x 1 , x 2 , . . . , x n ),
E4: comparing the observed value (t n ) of the indicator (T n ) to the quantile (c a,n ) of the distribution of (T n ) said quantile being stored in the memory,
E5: if the observed value (t n ) of the indicator (T n ) is above the quantile, reporting, on displaying means ( 20 ), a presence of an abnormal value in the series thereby indicating the occurrence of a health event for said mammal;
wherein, when searching for one series of samples which comprises an abnormal value:
a single series x 1 , x 2 , . . . , x n of n values is stored on the database (DB),
n is the number of variables,
X 1 , X 2 , . . . , X n represent the n variables,
the studentized form is a studentized residual expressed as:
R
n
,
i
=
X
i
-
X
¯
n
,
-
i
σ
^
n
,
-
i
1
+
1
n
-
1
the indicator T n is expressed as:
T
n
=
max
i
∈
{
1
,
…
,
n
}
R
n
,
i
where
X
_
n
,
-
i
=
1
n
-
1
∑
k
=
1
,
k
≠
i
n
-
1
X
k
σ
^
n
,
-
i
2
=
1
n
-
2
∑
k
=
1
,
k
≠
i
n
-
1
(
X
k
-
X
_
n
,
-
i
)
2
the relevant table of quantiles of the distribution of T n is table 1;
or, in multivariate case,
a single series x 1 , x 2 , . . . , x n of n values is stored on the database (DB),
n is the number of variables of dimension d,
X 1 , X 2 , . . . , X n are n independent R d valued random vectors, where X i ˜N(μ i , C) and C the covariance matrix is assumed to be invertible
the studentized form is expressed as a normalized length of the residual vector:
R
n
,
i
=
n
-
1
n
d
(
X
i
-
X
¯
n
,
-
i
)
′
C
n
,
-
i
-
1
(
X
i
-
X
¯
n
,
-
i
)
where the notation z′ means the transpose of the vector Z,
the indicator T n is expressed as:
T
n
=
max
i
∈
{
1
,
…
,
n
}
R
n
,
i
where
X
_
n
,
-
i
=
1
n
-
1
∑
k
=
1
,
k
≠
i
n
-
1
X
k
C
n
,
-
i
=
1
n
-
1
-
d
∑
k
=
1
,
k
≠
i
n
-
1
(
X
k
-
X
_
n
,
-
i
)
(
X
k
-
X
_
n
,
-
i
)
′
and the relevant table of quantiles of the distribution of T n is for instance table 1 (for d=2 and d=3),
or wherein, when searching for a series of consecutive observations that are abnormal compared to the rest of the series,
a single series x 1 , x 2 , . . . , x n of n values is stored on the database (DB),
n is the number of variables,
X 1 , X 2 , . . . , X n represent the variables,
φ is the collection of all possible intervals I of consecutive integers included in { 1 , . . . , n} with length 1≤|I|<n, {1, . . . , n}=I∪Ī and I∩Ī=ø,
the studentized form is expressed as:
R
n
,
I
=
X
I
-
X
¯
I
_
σ
^
n
,
I
1
+
1
n
-
1
the indicator T n is expressed as:
T
n
=
max
I
∈
φ
❘
"\[LeftBracketingBar]"
R
n
,
I
❘
"\[RightBracketingBar]"
where
X
¯
I
=
1
❘
"\[LeftBracketingBar]"
I
❘
"\[RightBracketingBar]"
∑
k
∈
I
X
k
X
_
I
_
=
1
n
-
❘
"\[LeftBracketingBar]"
I
❘
"\[RightBracketingBar]"
∑
k
∈
I
_
X
k
σ
^
n
p
2
=
1
n
-
2
(
∑
k
∈
I
(
X
k
-
X
¯
I
_
)
2
+
∑
k
∈
I
_
(
X
k
-
X
¯
I
_
)
2
)
the relevant table of quantiles of the distribution of T n is for instance table 2,
or wherein, when searching for an abnormal series when a sample is split in two subsamples of observations,
two series of n 1 and n 2 values are stored on the database (DB), x 1 , x 2 , . . . , x n 1 and y 1 , y 2 , . . . , y n 2 ,
the studentized forms are studentized residuals expressed as:
R
n
1
,
i
=
X
i
-
X
¯
n
1
,
-
i
σ
^
X
,
-
i
,
Y
1
+
1
n
1
-
1
and
R
n
2
,
j
=
Y
j
-
Y
¯
n
2
,
-
j
σ
ˆ
Y
,
-
j
,
X
1
+
1
n
2
-
1
the indicator T n is expressed as:
T
n
=
max
{
max
i
∈
{
1
,
…
,
n
1
}
❘
"\[LeftBracketingBar]"
R
n
1
,
i
❘
"\[RightBracketingBar]"
,
max
j
∈
{
1
,
…
,
n
2
}
❘
"\[LeftBracketingBar]"
R
n
2
,
j
❘
"\[RightBracketingBar]"
}
where
X
¯
n
1
,
-
i
=
1
n
1
-
1
∑
k
=
1
,
k
≠
i
n
1
X
k
Y
_
n
2
,
-
j
=
1
n
2
-
1
∑
k
=
1
,
k
≠
j
n
2
Y
k
σ
^
X
,
-
i
,
Y
2
=
1
n
-
3
(
∑
k
=
1
,
k
≠
i
n
1
(
X
k
-
X
¯
n
1
,
-
i
)
2
+
∑
k
=
1
n
2
(
Y
k
-
Y
¯
n
2
)
2
)
σ
^
Y
,
-
j
,
X
2
=
1
n
-
3
(
∑
k
=
1
n
1
(
X
k
-
X
¯
n
1
)
2
+
∑
k
=
1
,
k
≠
j
n
2
(
Y
k
-
Y
¯
n
2
,
-
j
)
2
)
and the relevant table of quantiles of the distribution of T n is for instance table 3,
or, in a multivariate case,
two series of n 1 and n 2 values are stored on the database (DB), x 1 , x 2 , . . . , x n 1 and y 1 , y 2 , . . . , y n 2 , -X 1 , X 2 , . . . , X n 1 and Y 1 , Y 2 , . . . , Y n 2 represent the variables as two independent series of independent gaussian R d valued random vectors where X i ˜N(μ x i , C), Y j ˜N(μ Y j , C) and C, the covariance matrix, is assumed to be invertible,
n is the number of variables of dimension d,
the studentized form is expressed as a normalized length of the residual vector:
R
n
1
,
i
=
n
1
-
1
n
1
d
(
X
i
-
X
¯
n
1
,
-
i
)
′
C
X
,
-
i
,
Y
-
1
(
X
i
-
X
¯
n
1
,
-
i
)
R
n
2
,
j
=
n
2
-
1
n
2
d
(
Y
j
-
Y
¯
n
2
,
-
j
)
′
C
Y
,
-
j
,
X
-
1
(
Y
j
-
Y
¯
n
2
,
-
i
)
and the indicator T n is expressed as:
T
n
=
max
{
max
i
∈
{
1
,
…
,
n
1
}
R
n
1
,
i
max
j
∈
{
1
,
…
,
n
2
}
R
n
2
,
j
}
where
X
¯
n
1
,
-
i
=
1
n
1
-
1
∑
k
=
1
,
k
≠
i
n
1
X
k
Y
¯
n
2
,
-
j
=
1
n
2
-
1
∑
k
=
1
,
k
≠
j
n
2
Y
k
C
X
,
-
i
,
Y
=
1
n
-
2
-
d
(
∑
k
=
1
,
k
≠
i
n
1
(
X
k
-
X
¯
n
1
,
-
i
)
(
X
k
-
X
¯
n
1
,
-
i
)
′
+
∑
k
=
1
n
2
(
Y
k
-
Y
¯
n
2
)
(
Y
k
-
Y
¯
n
2
)
′
)
C
Y
,
-
j
,
X
=
1
n
-
2
-
a
(
∑
k
=
1
n
1
(
X
k
-
X
¯
n
1
)
(
X
k
-
X
¯
n
1
)
′
+
∑
k
=
1
,
k
≠
j
n
2
(
Y
k
-
Y
¯
n
2
,
-
j
)
(
Y
k
-
Y
¯
n
2
,
-
j
)
′
)
.
2. The method according to claim 1 , comprising a further step of:
E6: identifying from the series of values reported in step E2 at least one value being considered as abnormal, and
E7: reporting on displaying means ( 20 ) that at least one abnormal value.
3. The method according to claim 1 , further comprising a step ES of running a Shapiro test on the stored values (x 1 , x 2 , . . . , x n 1 ) to check if the variables are normally distributed.
4. The method according to claim 1 , further comprising a step ET of applying a function to the values to turn them into normally distributed variables, such as a log transformation.
5. The method according to claim 1 , wherein the at least one biomarker represented by the series of values is chosen in the following list: ferritin, serum iron, hemoglobin, erythrocyte count, hematocrit levels, complete blood count, platelets, reticulocytes, soluble transferrin receptor, vitamin B9 in red blood cell, blood sugar, cholesterol, triglycerides, serum glutamic oxaloacetic transaminase (SGOT), serum glutamate pyruvate transaminase (SGPT), gamma-glutamyltransferase (γ-GT), lactate dehydrogenase (LDH), bilirubin, electrolytes (e.g. Na + , Cl − , K + , HCO3 − , Ca2 + , Mg2 + ), alkaline phosphatases Magnesium in red blood cells, creatinine, androstenedione, urea, uric acid, haptoglobin, C-reactive protein (CRP), transthyretin, orosomucoid, creatine phosphokinase (CPK), inorganic phosphate (PO4), thyroid-stimulating hormone (TSH), testosterone, cortisol, erythropoietin (EPO), ferritin, luteinizing hormone (LH), Insulin-like growth factor 1 (IGF-1), osteocalcin, calcifediol (25 OHD3).
6. A program for computer comprising code lines loaded on to a non-transitory computer readable medium and to be executed by a processor ( 14 ), said code lines being configured to operate a method according to claim 1 from its step E2 to E4.
7. A system for monitoring a health event in a mammal, comprising detecting at least one abnormal value within a series of values related to at least one biomarker, said biomarker corresponding to a physiological parameter or to the level of any biological or chemical entity measured from a biological sample of said mammal, the system comprising:
a database (DB) stored on a memory ( 12 ), the database comprising at least a series of values (x 1 , x 2 , . . . , x n ) related to said at least one biomarker being obtained from independent variables (X 1 , X 2 , . . . , X n ) normally distributed according to N (μ x , σ 2 );
the values representing the evolution of the biomarker at different period of times, the values (x 1 , x 2 , . . . , x n ) of the biomarker being obtained from independent variables (X 1 , X 2 , . . . , X n ) normally distributed N (μ X , σ 2 ),
a processor ( 14 ) comprising:
calculating means to calculate, for the whole series of values (x 1 , x 2 , . . . , x n ) stored in the database (DB), a single value (t n ) of an indicator (T n ), said indicator (T n ) being based on a studentized form (R n,i ) of the variables (X 1 , X 2 , . . . , X n ), said calculation consisting of extracting the maximum value (t n ) of the studentized residual form (R n,i ) calculated for each value of the series (x 1 , x 2 , . . . , x n ),
comparing means to compare the observed value (t n ) of the indicator (T n ) to the quantile (c a,n ) of the distribution of (T n ),
instruction means to instruct displaying means to report, or reporting means to report on displaying means, a presence of an abnormal value in the series, if the observed value (t n ) of the indicator (T n ) is above the quantile,
wherein, when searching for one series of samples which comprises an abnormal value:
a single series x 1 , x 2 , . . . , x n of n values is stored on the database (DB),
n is the number of variables,
X 1 , X 2 , . . . , X n represent the n variables,
the studentized form is a studentized residual expressed as:
R
n
,
i
=
X
i
-
X
¯
n
,
-
i
σ
^
n
,
-
i
1
+
1
n
-
1
the indicator T n is expressed as:
T
n
=
max
i
∈
{
1
,
…
,
n
}
❘
"\[LeftBracketingBar]"
R
n
,
i
❘
"\[RightBracketingBar]"
where
X
¯
n
,
-
i
=
1
n
-
1
∑
k
=
1
,
k
≠
i
n
-
1
X
k
σ
^
n
,
-
i
2
=
1
n
-
2
∑
k
=
1
,
k
≠
i
n
-
1
(
X
k
-
X
¯
n
,
-
i
)
2
the relevant table of quantiles of the distribution of T n is table 1;
Or, in multivariate case,
a single series x 1 , x 2 , . . . , x n of n values is stored on the database (DB),
n is the number of variables of dimension d,
X 1 , X 2 , . . . , X n are n independent R d valued random vectors, where X i ˜N(μ i , C) and C the covariance matrix is assumed to be invertible
the studentized form is expressed as a normalized length of the residual vector:
R
n
,
i
=
n
-
1
n
d
(
X
i
-
X
¯
n
,
-
i
)
′
C
n
,
-
i
-
1
(
X
i
-
X
¯
n
,
-
i
)
where the notation z′ means the transpose of the vector Z,
the indicator T n is expressed as:
T
n
=
max
i
∈
{
1
,
…
,
n
}
R
n
,
i
where
X
¯
n
,
-
i
=
1
n
-
1
∑
k
=
1
,
k
≠
i
n
-
1
X
k
C
n
,
-
i
=
1
n
-
1
-
d
∑
k
=
1
,
k
≠
i
n
-
1
(
X
k
-
X
¯
n
,
-
i
)
(
X
k
-
X
¯
n
,
-
i
)
′
and the relevant table of quantiles of the distribution of T n is for instance table 1 (for d=2 and d=3),
Or wherein, when searching for a series of consecutive observations that are abnormal compared to the rest of the series,
a single series x 1 , x 2 , . . . , x n of n values is stored on the database (DB),
n is the number of variables,
X 1 , X 2 , . . . , X n represent the variables,
φ is the collection of all possible intervals I of consecutive integers included in {1, . . . , n} with length 1≤|I|<n, {1, . . . , n}=I∪Ī and I∩Ī=ø,
the studentized form is expressed as:
R
n
,
I
=
X
_
I
-
X
_
I
_
σ
^
n
,
I
1
+
1
n
-
1
the indicator T n is expressed as:
T
n
=
max
I
∈
φ
❘
"\[LeftBracketingBar]"
R
n
,
I
❘
"\[RightBracketingBar]"
where
X
¯
I
=
1
❘
"\[LeftBracketingBar]"
I
❘
"\[RightBracketingBar]"
∑
k
∈
I
X
k
X
¯
I
_
=
1
n
-
❘
"\[LeftBracketingBar]"
I
❘
"\[RightBracketingBar]"
∑
k
∈
I
_
X
k
σ
^
n
,
I
2
=
1
n
-
2
(
∑
k
∈
I
(
X
k
-
X
¯
I
)
2
+
∑
k
∈
I
_
(
X
k
-
X
¯
I
_
)
2
)
the relevant table of quantiles of the distribution of Tn is for instance table 2,
or wherein, when searching for an abnormal series when a sample is split in two subsamples of observations,
two series of n 1 and n 2 values are stored on the database (DB), x 1 , x 2 , . . . , x n 1 and y 1 , y 2 , . . . , y n 2 ,
the studentized forms are studentized residuals expressed as:
R
n
1
,
i
=
X
i
-
X
¯
n
1
,
-
i
σ
^
X
,
-
i
,
Y
1
+
1
n
1
-
1
and
R
n
2
,
j
=
Y
j
-
Y
¯
n
2
,
-
j
σ
^
Y
,
-
j
,
X
1
+
1
n
2
-
1
the indicator T n is expressed as:
T
n
=
max
{
max
i
∈
{
1
,
…
,
n
1
}
❘
"\[LeftBracketingBar]"
R
n
1
,
i
❘
"\[RightBracketingBar]"
,
max
j
∈
{
1
,
…
,
n
2
}
|
R
n
2
,
j
|
}
where
X
¯
n
1
,
-
i
=
1
n
1
-
1
∑
k
=
1
,
k
≠
i
n
1
X
k
Y
_
n
2
,
-
j
=
1
n
2
-
1
∑
k
=
1
,
k
≠
j
n
2
Y
k
σ
^
X
,
-
i
,
Y
2
=
1
n
-
3
(
∑
k
=
1
,
k
≠
i
n
1
(
X
k
-
X
¯
n
1
,
-
i
)
2
+
∑
k
=
1
n
2
(
Y
k
-
Y
¯
n
2
)
2
)
σ
^
Y
,
-
j
,
X
2
=
1
n
-
3
(
∑
k
=
1
n
1
(
X
k
-
X
¯
n
1
)
2
+
∑
k
=
1
,
k
≠
j
n
2
(
Y
k
-
Y
¯
n
2
,
-
j
)
2
)
and the relevant table of quantiles of the distribution of T n is for instance table 3,
or, in a multivariate case,
two series of n 1 and n 2 values are stored on the database (DB), x 1 , x 2 , . . . , x n 1 and y 1 , y 2 , . . . , y n 2 , -X 1 , X 2 , . . . , X n 1 and Y 1 , Y 2 , . . . , Y n 2 represent the variables as two independent series of independent gaussian R d valued random vectors where X i ˜N (μ X i , C), Y j ˜N(μ Y j , C) and C, the covariance matrix, is assumed to be invertible,
n is the number of variables of dimension d,
the studentized form is expressed as a normalized length of the residual vector:
R
n
1
,
i
=
n
1
-
1
n
1
d
(
X
i
-
X
¯
n
1
,
-
i
)
′
C
X
,
-
i
,
Y
-
1
(
X
i
-
X
¯
n
1
,
-
i
)
R
n
2
,
j
=
n
2
-
1
n
2
d
(
Y
j
-
Y
¯
n
2
,
-
j
)
′
C
Y
,
-
j
,
X
-
1
(
Y
j
-
Y
¯
n
2
,
-
i
)
and the indicator T n is expressed as:
T
n
=
max
{
max
i
∈
{
1
,
…
,
n
1
}
R
n
1
,
i
max
j
∈
{
1
,
…
,
n
2
}
R
n
2
,
j
}
where
X
¯
n
1
,
-
i
=
1
n
1
-
1
∑
k
=
1
,
k
≠
i
n
1
X
k
Y
¯
n
2
,
-
j
=
1
n
2
-
1
∑
k
=
1
,
k
≠
j
n
2
Y
k
C
X
,
-
i
,
Y
=
1
n
-
2
-
d
(
∑
k
=
1
,
k
≠
i
n
1
(
X
k
-
X
¯
n
1
,
-
i
)
(
X
k
-
X
¯
n
1
,
-
i
)
′
+
∑
k
=
1
n
2
(
Y
k
-
Y
¯
n
2
)
(
Y
k
-
Y
¯
n
2
)
′
)
C
Y
,
-
j
,
X
=
1
n
-
2
-
d
(
∑
k
=
1
n
1
(
X
k
-
X
¯
n
1
)
(
X
k
-
X
¯
n
1
)
′
+
∑
k
=
1
,
k
≠
j
n
2
(
Y
k
-
Y
¯
n
2
,
-
j
)
(
Y
k
-
Y
¯
n
2
,
-
j
)
′
)
.
8. Use of a method according to claim 1 for detecting a potential doping issue.
9. Use of a method according to claim 1 wherein monitoring a health event comprises detecting any potential health issue of the individual, in order to launch further investigations.
10. Use of a program according to claim 6 for detecting a potential doping issue.
11. Use of a system according to claim 7 for detecting a potential doping issue.
12. Use of a program according to claim 6 wherein monitoring a health event comprises detecting any potential health issue of the individual, in order to launch further investigations.
13. Use of a system according to claim 7 wherein monitoring a health event comprises detecting any potential health issue of the individual, in order to launch further investigations.