Evolutionary Fuzzy Logic-based Model Design in Predicting

Coronary Heart Disease and Its Progression

Christina Brester

1,2 a

, Vladimir Stanovov

, Ari Voutilainen

, Tomi-Pekka Tuomainen

Eugene Semenkin

and Mikko Kolehmainen

Department of Environmental and Biological Sciences, University of Eastern Finland, Kuopio, Finland

Institute of Computer Science and Telecommunications, Reshetnev Siberian State University of Science and Technology,

Krasnoyarsk, Russia

Institute of Public Health and Clinical Nutrition, University of Eastern Finland, Kuopio, Finland

{ari.voutilainen, tomi-pekka.tuomainen, mikko.kolehmainen}@uef.fi

Keywords: Predictive Modeling, Fuzzy Logic, Genetic Algorithm, Kuopio Ischemic Heart Disease Risk Factor Study,

Heterogeneity, Performance Improvement, Knowledge Discovery.

Abstract: Various data-driven models are often involved in epidemiological studies, wherein the availability of data is

constantly increasing. Accurate and, at the same time, interpretable models are preferable from the practical

point of view. Finding simple and compact dependences between predictors and outcome variables makes it

easier to understand necessary interventions and preventive measures. In this study, we applied a Fuzzy Logic-

based model, which meets these requirements, to predict the coronary heart disease (CHD) progression during

a 30-year follow-up. The Fuzzy Logic-based model was automatically designed with an ad hoc Genetic

Algorithm using the data from the Kuopio Ischemic Heart Disease Risk Factor (KIHD) Study, a Finnish

cohort of 2682 men who were middle-aged at baseline in 1980s. Using cross-validation, we found out that the

sample from the KIHD study is heterogeneous and after filtering out 10% of outliers, the predictive accuracy

increased from 65% to 73%. The generated rule bases include 19 fuzzy rules on average with maximum 7

variables in one rule from the initial set of 638 predictor variables. The selected predictors of CHD progression

are informative and diverse representing physical aspects, behavior, and socioeconomics. The Fuzzy Logic-

based model creates a comprehensive set of predictors that enables us to better understand the complexity of

illnesses and their progression. Moreover, the Fuzzy Logic-based model has potential to provide tools to

analyse and deal with heterogeneity in large cohorts.

1 INTRODUCTION

At the present time, epidemiological studies involve

a huge variety of analytical tools, starting from

traditional statistical methods and ending with

intellectual learning algorithms used to train

advanced data-driven models. In many medical

applications, artificial intelligence is a booming trend,

which is supposed to yield fruitful results (Beam and

Kohane, 2016). Indeed, some medical diagnostic

https://orcid.org/0000-0001-8196-2954

https://orcid.org/0000-0002-1695-5798

https://orcid.org/0000-0002-0664-2675

https://orcid.org/0000-0002-1949-3787

https://orcid.org/0000-0002-3776-5707

https://orcid.org/0000-0002-9532-2285

systems show the high accuracy and even surpass

human expertise (Gulshan et al., 2016). To be

effective, these methods require the reliable and

representative data, which allows generalizations

based on the extracted knowledge.

There are many available cohorts describing study

populations, which have recently been used in the

descriptive and predictive modeling (Song and

Chung, 2010). A typical analysis aims either at

investigating influence of a particular risk factor on

360

Brester, C., Stanovov, V., Voutilainen, A., Tuomainen, T., Semenkin, E. and Kolehmainen, M.

Evolutionary Fuzzy Logic-based Model Design in Predicting Coronary Heart Disease and Its Progression.

DOI: 10.5220/0008363303600366

In Proceedings of the 11th International Joint Conference on Computational Intelligence (IJCCI 2019), pages 360-366

ISBN: 978-989-758-384-1

disease development or estimating the probability of

having the disease in the future based on predictors

(Virtanen et al., 2018). Although many studies

present such analyses, their limitations should be

disclosed. Firstly, results depend on the sample size,

its quality, and representativeness (Yan et al., 2017).

The information from questionnaires, which is

included in most of cohorts, is not fully reliable due

to subjectivity and usually contains a lot of missing

values (Lee and Yoon, 2017). Existing trends and

expectations also add some bias to analysis

(Ioannidis, 2005). Secondly, no validation is

normally applied, which puts in doubt the possibility

of extrapolating the results obtained (Riley et al.,

2016). Moreover, in predictive modeling, it is

generally accepted to keep only those subjects who

were healthy when they entered the study (Vartiainen

et al., 2016). This implies that the model cannot be

used to predict disease progression. Therefore, more

sophisticated ways of handling epidemiological data

should be applied to discover genuine potentials of

predictive data-driven models.

In this paper, we focus on one specific cohort, the

Kuopio Ischemic Heart Disease Risk Factor (KIHD)

Study (Kauhanen, 2013). Our goal is to predict the

coronary heart disease (CHD) progression within a

30-year follow-up for healthy subjects as well as

those having CHD at baseline. For people with no

CHD at baseline, “progression” means either

diagnosed CHD or an acute myocardial infarction

(AMI) during the follow-up, for people with CHD or

AMI at baseline, it means a new AMI. As opposed to

traditional epidemiological studies, we test a

statistical approach with no preliminary knowledge-

based variable selection, include subjects and

variables with missing values, and implement cross-

validation to assess the model performance

objectively.

We use a Fuzzy Logic-based model automatically

designed with a modified genetic algorithm.

Generally, Fuzzy Logic systems are easily

interpretable, which makes them preferable for

epidemiological studies. Besides, the presented

approach has some other benefits: 1) to prevent

overfitting, we limit the number of generated rules

and their length; 2) the learning algorithm copes with

missing values so that no imputation is needed; 3) no

initial rule base is required from the domain experts,

as the algorithm is capable of generating a meaningful

rule base and evolving it during the heuristic search.

The main point of the paper is neither the Fuzzy

Logic-based model itself nor its performance, but the

knowledge extracted about the KIHD cohort. Firstly,

we show how heterogeneous the sample is: cross-

validation helps to reveal inconsistency between the

training and test data (Shah et al., 2018). It might be

explained with lots of outliers, mislabeling or absence

of the informative predictors. Nevertheless, filtering

out some subjects leads to the higher model

performance and the improvement of homogeneity in

the sample. Lastly, we analyze the generated fuzzy

rules and the selected predictor variables, which are

meaningful for predicting CHD and its progression.

2 FUZZY LOGIC-BASED

PREDICTIVE MODEL DESIGN

The Hybrid Evolutionary Fuzzy Classification

Algorithm (HEFCA) used in this study was originally

presented by Stanovov et al. (2015) and further

developed by Stanovov et al. (2016). The algorithm

is based on an earlier study (Ishibuchi et al., 2013),

and it implements a specific scheme to generate the

compact and accurate fuzzy rule bases.

The generated fuzzy logic predictive model relies

on the fixed fuzzy terms for input variables,

introducing four granulations into 2, 3, 4, and 5 terms

of a triangular shape and “Don’t Care” condition

(DC) required to simplify the rules. Figure 1 shows

all the fuzzy terms which are used for each input

variable at the same time.

Figure 1: Fuzzy term granulation.

The data preparation step consisted of

transforming each input variable into the interval [0,

1] before applying the fuzzy terms. The normalization

was performed on the training sample and, then,

applied to the test set. The HEFCA algorithm has

previously been modified to handle missing values,

so that these values are considered as “Don’t Care”

condition during the fuzzy inference (Stanovov et al.,

2017).

The main HEFCA steps are as follows:

1) Sample-based initialization

2) Selection (Tournament or Rank-based)

3) Crossover

Evolutionary Fuzzy Logic-based Model Design in Predicting Coronary Heart Disease and Its Progression

361

4) Mutation (3 levels)

5) Michigan part (genetic or heuristic)

6) Operator probability adaptation

7) Stopping criterion check, return to step 2 (the

number of generations left)

The sample-based initialization used randomly

chosen instances from the training sample to generate

realistic rules. In this procedure, for each variable in

the rule, one of 14 fuzzy terms, is chosen with the

probability proportional to the membership function

value for this particular term. After this, every term

was replaced by “Don’t Care” condition with the

probability of 0.9. The quality of each generated rule

was estimated using the confidence value:







→

∑

















∈

∑

















(1)

where A

is the q-th rule left part, k is the class

number, μ

) is the membership value for the input

value x

. The class number corresponding to the

newly generated rule was determined as the class

having the highest confidence. The weight of each

rule was estimated as:





2∙





→1,

(2)

so that the confidence of 1 is transformed to the

weight equal to 1, and the confidence of 0.5 – to zero

weight. If the generated rule had the confidence lower

than 0.5, the rule was generated again until a valid

rule is obtained. This filtering of the rules was shown

to be highly competitive in (Ishibuchi et al., 2005).

The number of rules was limited by NR

max

, and

during the initialization step, the rule base was filled

with NR

max

/2 rules.

The fitness of each rule base was calculated as the

linear combination of three main criteria, i.e., the

error on the training sample with a weight of 100, the

number of rules with a weight of 1, and the average

rule length with a weight of 1.

For selection, there were two different methods

used: the linear rank selection and the tournament

selection with a tournament size of 5. The crossover

step used a specific operator, in which one newly

generated offspring had the random number of rules

from 1 to min(|S

|+|S

|, NR

max

), where |S

| is the size of

the rule base. For the new rule base, the rules either

from the first or the second parent were chosen

randomly.

The mutation operator changed every term in the

rule base to randomly chosen, including “Don’t

Care” conditions with three probability levels:

1/(3|S|), 1/|S|, 3/|S| corresponding to weak, average

and strong mutations.

In the Michigan part, the rule base was considered

as a population of a genetic algorithm. The fitness

value of the rule was estimated as the number of

instances correctly classified with this specific rule.

Three types of the Michigan part were applied:

adding rules, deleting the worst rules, or replacing the

worst rules with the newly generated. The number of

rules to be added, removed or replaced was estimated

as a rounded value of |S|/5, but the total number of

rules was limited by NR

max

. If there were two equal

rules, only one of them received non-zero fitness, and

the second was removed. Generating new rules was

performed in two ways: in the first case, new rules

were generated using the same heuristic as for

initialization, while in the second case they were

generated with genetic operators, namely the

tournament selection, the uniform crossover, and the

average mutation.

To choose among the variants of presented

genetic operators, the self-configuration scheme

originally described by Semenkina and Semenkin

(2014) was applied. The probability value was

assigned to each operator, and initially set to 1/z,

where z is the number of operators of a particular

type, for example, 3 levels of mutation. The

estimation of success of each operator type was using

the averaged fitness values:









∑

















,1,2…,,

(3)

where f

is the fitness the j-th offspring generated with

the i-th operator type, and n

is the number of

offspring generated with the i-th operator. The

operator having the highest fitness was considered as

the winning operator, its probability p

was increased

by10.5/ , while for other operators the

probabilities were decreased by 0.5/, where N is

the total number of generations. The probability of

applying each operator could not be decreased lower

than 0.05. The self-configuration procedure was

applied to two selection types, three mutation types,

and two types of generating new rules in the Michigan

part, i.e., heuristic and genetic.

3 DATA DESCRIPTION

The KIHD population cohort study is an ongoing

project launched in 1984 and carried out in Eastern

Finland where the population has one of the highest

risks of CHD (Salonen, 1988). The baseline

examinations were performed in 1984–1989 for 2 682

randomly chosen middle-aged men (42, 48, 54, and

60 years) living in the city of Kuopio and the

FCTA 2019 - 11th International Conference on Fuzzy Computation Theory and Applications

362

surrounding area. The examinations included

hundreds of physiological, clinical, and biochemical

measurements as well as the information from

questionnaires focused on physical, psychological,

and socioeconomic aspects of health behavior.

Although the KIHD project was mainly initiated

to investigate risk factors of cardiovascular diseases

(CVDs), other disorders such as cancer, diabetes, and

dementia, have been constantly recorded too. The

health of subjects is followed based on linkages to

several national registers which provide the updated

information on newly diagnosed cases of CVDs and

other disorders yearly.

In this paper, we focus on predicting CHD and its

progression among the KIHD participants from

1984–1989 up to 2016 based on the baseline

measurements. The initial amount of predictor

variables involved in the current study is 947. An

outcome variable takes one of two possible values,

which is defined according to the rules introduced in

Table 1. Generally, there are three categories of

subjects based on the CHD diagnosis at the baseline

examination: “no CHD”, “CHD”, and “unknown”,

which means that this information is missing. For the

first “no CHD” group, progression corresponds to

two possible situations: progression up to CHD and

progression up to AMI (including death). For the

second “CHD” group, progression means a new AMI

(also including death). The third “unknown” group

includes only subjects with incidents of AMI during

the follow-up, which also means progression. The

rest of this group has been excluded from modelling

since we cannot be sure about the development of

CHD for these subjects (the last line in Table 1). All

other cases have “no progression” labels.

Table 1: CHD development and corresponding labels.

Baseline status

(CHD diagnosed by

a doctor)

Diagnosis or event

during the follow-up

Label (outcome

variable)

no CHD CHD and/or AMI progression

no CHD

neither CHD nor

AMI

no progression

CHD AMI progression

CHD CHD no progression

unknown

(information is

missing)

AMI progression

unknown

(information is

missing)

CHD ?

Due to inconsistency we excluded 1) subjects who

had neither CHD nor AMI during the follow-up but

died from other CVDs or as a result of any non-CVD

reason as well as 2) subjects who self-reported a

previous myocardial infarct at the baseline

examination but had no diagnosed CHD. After these

manipulations, we had 1402 subjects in the sample.

Moreover, we excluded subjects with more than

25% of missing values in the vector of predictors and

variables with more than 10% of missing values.

Eventually, we ended up with 1369 subjects (551 “no

progression” and 818 “progression”) and 683

variables in the sample.

4 EXPERIMENTAL RESULTS

In all the modeling experiments executed, the

following parameters of HEFCA were used: the

population size was 100, the number of generations

was 500, and the maximum number of rules was 40.

The first set of experiments using 5-fold cross-

validation led to the results presented in Table 2.

Table 2: Fuzzy Logic model performance and the number

of rules generated for every fold.

Fold

Accuracy on the

training data

Accuracy on

the

est data

The number

of rules

1 0.742 0.672 16

2 0.736 0.664 17

3 0.726 0.667 20

4 0.720 0.611 19

5 0.721 0.641 22

Average 0.729 0.651 18.8

Compared to other statistical approaches utilizing

the KIHD cohort (Brester et al., 2018a), the training

accuracy was relatively high, whereas the test

accuracy was much lower, which may also be

observed in the convergence graphs presented in

Figure 2.

During the first 100 generations a clear decreasing

trend was observed for both training and test sets,

however, after this the decrease of the training error

did not lead to any improvements on the test set,

which may have several reasons, including overfitting

and sample heterogeneity. The latter has been

previously tested using other methods, and it was

established that the sample has numerous outliers,

i.e., instances which are significantly different from

those presented in the sample (Brester et al., 2018b).

Evolutionary Fuzzy Logic-based Model Design in Predicting Coronary Heart Disease and Its Progression

363

Figure 2: The number of wrong predictions on training and

test samples during each run (fold) of cross-validation.

For sample filtering, the entire available dataset

(training and test examples together) was used to

perform training within 25 independent runs of

HEFCA, and for each subject we recorded if it was

classified correctly (getting the score of 1),

incorrectly (score = 0) or not classified, i.e., not

described by any rule (score = -1). After these

independent runs, subjects were sorted by the total

scores, which are presented in a graphical form in

Figure 3.

Figure 3: Scores of outlier candidates.

From Figure 3 it can be observed that most of the

sample, around 800 subjects, is relatively easy to

classify, i.e. they are having scores of 20 and more.

However, other 600 subjects have much lower scores,

which means that these subjects are either never

classified

using the generated rule base

or have very

small chance to be classified. Moreover, some

subjects had negative scores, which mean that they

were not even covered with fuzzy rules in many

cases.

Based on these observations and the knowledge

about the sample structure, the next set of

experiments was performed using three variants of

sample filtering: deleting 5%, 10% or 15% of

instances with the lowest scores (Figure 3).

Table 3: Training and test accuracies for three filtered

samples averaged over 5 folds.

Percentage

of removed

cases

Accuracy on

the training

data

Accuracy on

the test data

The

number

of rules

5% 0.763 0.686 20.2

10% 0.796 0.731 17.2

15% 0.852 0.766 19

Removing outliers significantly improved the

classification quality of rule bases designed by

HEFCA, for both training and test samples (Table 3).

Also, the training and test errors now had similar

decreasing trends (Figure 4).

Figure 4: The number of wrong predictions on training and

test samples during each run (fold) of cross-validation, 10%

outliers removed.

FCTA 2019 - 11th International Conference on Fuzzy Computation Theory and Applications

364

Figure 5: Examples of the rules generated by HEFCA. Each rule is separated with dashed borders. Rules of blue color

corresponds to “no progression” predictions; rules of red color represent “progression” predictions.

Additionally, we analyzed the most frequently

used rules, which were generated in the experiment

after filtering out 10% of the sample (Figure 5). Ten

rules were randomly selected from different folds of

cross-validation. There are some rules including only

one variable, which usually has clear relevance to the

output variable, e.g., cardiovascular disease before

baseline or maximal oxygen uptake. So, the binary

variable “cardiovascular disease before baseline”

took 1 if a subject had CVD before the baseline

examination and 0 otherwise. Looking at its term

shape, we see that the value of 0 has the lowest

membership, consequently, the rule is not applied in

such cases, whereas the value of 1 has the highest

membership and leads to the “CHD progression”

prediction. On the contrary, only low values of the

“maximal oxygen uptake” variable have the high

membership and correspond to the “CHD

progression” prediction. A similar analysis could be

done for other variables to understand their

relationship with the outcome.

Longer rules combine predictors from different

categories: behavioral characteristics, medication,

diet, results of some exercises and tests, even

socioeconomic variables. The most frequently used

predictor variables are age; blood pressure, oxygen

uptake, electrocardiogram in exercises; smoking and

drinking; diseases in the past.

Interestingly, having a similar term shape, the

same predictors might be included in several rules,

which correspond to different outcome values. This

implies that in combination with different risk factors

their influence on the outcome may vary.

5 CONCLUSIONS

This article introduced the results of the data-driven

predictive modeling, where the Fuzzy Logic-based

model was used to predict CHD and its progression

for the subjects from the KIHD study. The specially

modified genetic algorithm was applied to generate

the fuzzy rule base from 683 predictors, which were

available after data preprocessing. As opposed to

traditional epidemiological studies, we did not

exclude subjects with CHD diagnosed at the baseline

examination but predicted its progression, which in

fact is more reasonable from the practical point of

view.

The experimental results showed heterogeneity of

the KIHD sample: filtering out 10% of the data led to

the higher consistency between training and test sets

in the cross-validation procedure and the accuracy

improvement from 65% to 73%. The other important

result was that the variables, which were selected for

predicting CHD and its progression, were diverse but

still informative, and them created a comprehensive

and predictable set.

As a next step, we are planning to expand the

KIHD sample using genetical variables and perform

similar modeling experiments as presented in this

paper. Also, other cohorts should be involved to

Evolutionary Fuzzy Logic-based Model Design in Predicting Coronary Heart Disease and Its Progression

365

investigate advantages of Fuzzy Logic-based models

for epidemiological studies more thoroughly.

ACKNOWLEDGEMENTS

The reported study was funded by Russian

Foundation for Basic Research, Government of

Krasnoyarsk Territory, Krasnoyarsk Regional Fund

of Science, to the research project: 18-41-242011

«Multi-objective design of predictive models with

compact interpretable strictures in epidemiology».

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