Computational diagnosis of canine lymphoma

Publishing Authors : E M Mirkes
I Alexandrakis
K Slater
R Tuli and A N Gorban

 

1. Introduction
Lymphoma (Lymphosarcoma, LSA) is one of the most common cancers seen in dogs. One in four
dogs will develop cancer in their lifetime. It accounts for approximately 20% of all canine tumours [1].
The PetScreen Canine Lymphoma Blood Test employs advanced technology to detect lymphoma
biomarkers present in a dog’s serum [1]. Concentration of two acute phase proteins is evaluated:
Haptoglobin (Hapt) and C-Reactive Protein (CRP) Detection of these biomarkers indicates a high
likelihood that the dog has lymphoma [1], [2]. The growth of the database enables new methods of
data mining. We analyse usability of attributes for the lymphoma diagnostic test. We divide the
database in two cohorts and formulate two different tasks: (i) differential diagnostic in clinically
suspected cases and (ii) screening. The isolation of the clinically suspected cohort is necessary for
formulation of the task of differential diagnostics and selection of the appropriate methods.
Three methods are used. The first is the method of decision trees [3-5]. The second is k nearest
neighbours method (kNN) in several versions [6,7]. The third is the method of probability density
function estimation (PDFE) [8,9]. We use them for direct estimation of the lymphoma risk.

We present the case study for both tasks: for the diagnostics task we have tested 2,432,000 variants
of the kNN method, 248,400 variants of decision tree algorithms and 280 variants of PDFE method;
for the screening task we have tested 48,640 variants of kNN, 4,968 variants of decision trees and 280
variants of PDFE.
The versions differ by impurity criteria, kernel functions, number of nearest neighbours, weights
and other parameters. They are compared by the standard goodness of fit, the entropic criteria and the
generalization ability.
The best results are implemented in web-accessed software for the diagnosis of canine lymphoma.
If we solve the classification problem then for each value of input features we can obtain only two
answers: dog with lymphoma or dog without lymphoma. Formulation of the task as a problem of risk
estimation provides obtaining the real value between 0 and 1. Analysis of risk map provides a new
ability to formulate hypotheses.
The obtained results provide the creation of a reliable diagnostic and screening system for canine
lymphoma.
2. Data description
Categorical features. Lymphoma (‘Y’
or ‘N’), Sex (‘M’ or ‘F’), and a most
important clinical symptom,
Lymphadenopathy (‘Y’ or ‘N’)
Real features. Age, CRP
(concentration), Hapt (concentration).
Analysis of importance. Table 1
contains values of relative information gain
(RIG) [3] for target feature Lymphoma of
any input feature. RIG is calculated for
whole database and for two samples: (Y)
with Lymphadenopathy=’Y’ and (N) with
Lymphadenopathy=’N’.
3. Problem refinement
The results of the database analysis show that there are two different cohorts of data in the database.
The first cohort is titled ‘clinically suspected’ and contains records collected by PetScreen from
dogs undergoing differential diagnosis. All these records correspond to dogs which have been referred
to differential diagnostics by veterinary practitioners on the base of one or more clinical symptoms. It
is not possible to find a posteriori these symptoms for each instance and we have to introduce a new
synthetic attribute: ‘clinically suspected’. The second cohort is titled ‘healthy’ and contains records
obtained from healthy dogs courtesy of the Pet Blood Bank. These two cohorts have very different
statistics of the attributes. By expert estimations, the prior probability of lymphoma is located between
2% and 5% in the canine population. The number of records of dogs with lymphoma is 97 or 32% of
all the records in the initial database. All these cases have been clinically suspected and form 42% of
the clinically suspected cases. This imbalance entails the use of specific methods to solve screening
tasks. The ‘clinically suspected’ feature was added to the database to identify the two cohorts. The
values of feature ‘clinically suspected’ were defined by using additional information of veterinary
cards. The existence of the two cohorts allows the formulating of two different tasks: differential
diagnostics and screening.
Differential diagnostics. The differential diagnostic task can be formulated as a problem of
lymphoma diagnosis for dogs with some clinical symptoms of lymphoma. A diagnostic task is a usual
classification problem and all classification methods can be used. We use three types of classification
methods: kNN, decision tree and the method based on probability distribution function estimation. The
first two methods have an additional parameter – weighting of the positive class.
Table 1. Relative information gain for ‘Lymphoma’
Tested feature RIG RIG under given
Lymphadenopathy
Y N
Lymphadenopathy 28.92% – –
CRP binned 24.38% 15.00% 23.52%
Hapt binned 7.02% 1.76% 14.32%
Age binned 6.07% 1.62% 9.39%
Sex 0.95% 3.79% 22.84%
2nd International Conference on Mathematical Modeling in Physical Sciences 2013 IOP Publishing
Journal of Physics: Conference Series 490 (2014) 012135 doi:10.1088/1742-6596/490/1/012135
2
Screening. The screening task can be formulated as an estimate of lymphoma risk for any dog. To
solve this task we used all the database records. The experts’ estimation of prior probability of
lymphoma is between 2% and 5% however the fraction of dogs with lymphoma records in the
database is 32%. To compensate for this imbalance all methods take into account the prior probability
of lymphoma. For this task, the weighting of classes is defined by prior probability.
We use the following notations: p is the prior probability of lymphoma, NL is the number of dogss
with lymphoma, NCS is the number of all clinically suspected dogs and NH is the number of healthy
dog. The weight of the class of dogs with lymphoma is equal to p. The weight of one dog with
lymphoma is equal to wL = p/NL. Indeed, this is the weight of any record of the clinically suspected
cohort. The weight of each record of a healthy dog is calculated as wH = (1-wLNCS)/NH. These two
weights are used to calculate the risk of lymphoma in the screening task.
4. Risk map analysis
Visualization of data and probability distributions may use various screens, from the coordinate planes
and PCA to non-linear principal graphs and manifolds [10]. In this work, we use visualisation of risk
of lymphoma on the plane of two real attributes, CRP and Hapt. For example, we use risk maps to
generate hypotheses about impact of input features. All maps below use the legend which is presented
in any figure. The brown colour indicates the low level of risk: the greater intensity of brown colour
indicates the less risk of lymphoma. The white colour indicates the median value of risk (50%). Blue
colour indicates the high level of risk: the greater intensity of indicates the greater risk value.
a b c d
e f g h
Figure 1. The maps of lymphoma risk for male and female dogs: a) PDFE map for male, b) decision
tree map for male, c) KNN map for male, e)PDFE map for female, f) decision tree map for female, g)
KNN map for female, d) and h) are legend.
Let us consider the risk of lymphoma in relation to sex for clinically suspected dogs. The
probabilities are represented (Fig 1). The maps show that there are some areas where the risk of
lymphoma is greater for male dogs. For the best decision tree and kNN the qualitatively same results
were obtained (Fig. 2). In this area, the risk of lymphoma may depend on the steroid hormones. This
hypothesis needs additional verification.
5. Results
During the case-study the best solution for each task is selected with the minimal number of errors.
Differential diagnostic. The best result is obtained by a decision tree which uses three input
features: the concentrations of CRP and Hapt, and Lymphadenopathy. The concentrations of CRP and
2nd International Conference on Mathematical Modeling in Physical Sciences 2013 IOP Publishing
Journal of Physics: Conference Series 490 (2014) 012135 doi:10.1088/1742-6596/490/1/012135
3
Hapt are used in linear combinations. DKM is used as a splitting criterion. The sensitivity of this
method is 83.5%, specificity is 77%. ROC integral for this method is 0.879.
If ‘Lymphadenopathy’ is unknown then we use decision tree which only uses CRP and Hapt. In the
best version, these input features are used in linear combinations after logarithmic transformation.
Information gain is used as the splitting criterion. The sensitivity of this method is 81.5%, specificity
is 76%. ROC integral for this method is 0.810.
Screening. The best result is obtained by the decision tree which uses three input features: the
concentrations of CRP and Hapt, and Lymphadenopathy. CRP and Hapt are used separately. DKM is
used as the splitting criterion. The sensitivity of this method is 81.4%, specificity is >99% (no false
negative results in one-leave-out cross-validation).
If ‘Lymphadenopathy’ is unknown then we use another decision tree, which uses CRP and Hapt
only. These input features are used in linear combinations after logarithmic transformation. Gini gain
is used as the splitting criteria. The sensitivity is 65%, specificity is 83%.
To evaluate the quality of the achieved results, we compare them to some current human cancer
screening tests. The tests that rely upon single biomarkers demonstrate often the worse performance.
For example, the CA-125 screen for human ovarian cancer provides sensitivity approximately 53%
and specificity 98%, and the male PSA test gives sensitivity approximately 85% and specificity 35%.
Supplementation of CA-125 by several other biomarkers increases sensitivity of at least 75% for early
stage disease and specificity of 99.7%. For PSA marker, using age-specific reference ranges improved
test specificity and sensitivity, but did not improve the overall accuracy of PSA testing.
Visualisation of risk maps provides a friendly tool for explanatory data analysis and affords an
opportunity to generate hypotheses about impact of input feature on the final diagnosis. For more
details and the additional bibliography we refer to [11].
References
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[11] Mirkes E M, Alexandrakis I, Slater K, Tuli R and Gorban A N 2023 arXiv:1305.4942
[q-bio.QM

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