An Unsupervised Machine Learning Approach for Clustering Hip

Arthroplasty Patients: Surgery Duration Differs Among

Different Patient Groups

Mohammad Chavosh Nejad

, Rikke Vestergaard Matthiesen

, Iskra Dukovska-Popovska

and John Johansen

Department of Materials and Production, Aalborg University, Aalborg Ø, Denmark

Keywords: Hip Arthroplasty, Patient Clustering, Unsupervised Learning.

Abstract: Operating Rooms (ORs), as the largest source of revenue and costs in hospitals, face the challenge of growing

demand while dealing with limited resources, emphasizing the need for operational efficiency. Duration of

surgery (DOS), a key element in planning surgical resources, fluctuates and depends on many factors

including patients’ characteristics. A better understanding of these factors and the way they affect DOS can

help OR planners in achieving efficient resource allocation. To distinguish between patients from the DOS

perspective, this paper proposes an unsupervised machine learning method that clusters patients into different

groups by considering different clinical and operational features. Seven relevant factors were extracted from

Aalborg University Hospital’s database for 1,847 patients undergoing hip arthroplasty. K-Prototype algorithm

was utilized for developing various clustering models and their performance was assessed by three popular

metrics. Among the different developed models, the one with 7 clusters achieved the highest performance.

One-way ANOVA analysis illustrated that DOS means are significantly different among different clusters (F-

statistic=11.77, P-Value=5.45e-13). Inter-cluster differences were analyzed by Turkey’s Honest Significant

Difference (HSD) test. Besides, evaluating features’ importance showed that Age, BMI, and surgery type are

the most contributing factors in clustering patients.

1 INTRODUCTION

In recent years, healthcare systems deal with several

challenges regarding delivering surgery services. On

one hand, the demand for surgery services is steadily

increasing due to various reasons such as population

aging. On the other hand, operating rooms (ORs),

which are central to hospitals’ costs and revenues,

face strict internal and downstream units’ resource

limitations (Eshghali et al., 2023). Given the high

costs and lack of availability of surgical resources,

increasing the surgical capacity and infrastructure in

hospitals necessitates substantial investment.

Nonetheless, improving resource utilization

efficiency through operational excellence presents a

more cost-effective alternative to meeting growing

demand with the existing resources.

https://orcid.org/0000-0003-3417-4394

https://orcid.org/0000-0003-4184-9476

https://orcid.org/0000-0002-3498-463X

Operating room scheduling at the operational

level refers to assigning surgical resources to patients

in specific time periods (Rahimi & Gandomi, 2021).

A common approach for OR scheduling is to hold

weekly meetings by the scheduling committee to

decide which surgical resources should be assigned to

the patients on the waiting list during the week. The

committee usually consists of a surgeon, an

anesthesiology doctor, a senior nurse, and the

scheduling secretary. Besides the medical

considerations, surgery duration is considered by the

committee because it can affect the operational

performance of the OR and recourse allocation

(Chavosh Nejad et al., 2024). Due to site-specific

operational concerns, different hospitals exhibit

distinct preferences for assigning longer or shorter

surgeries to different timeslots. However, all these

committees should consider distinguishing patients

398

Chavosh Nejad, M., Matthiesen, R. V., Dukovska-Popovska, I. and Johansen, J.

An Unsuper vised Machine Learning Approach for Clustering Hip Arthroplasty Patients: Surgery Duration Differs Among Different Patient Groups.

DOI: 10.5220/0013108700003911

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 18th International Joint Conference on Biomedical Engineer ing Systems and Technologies (BIOSTEC 2025) - Volume 2: HEALTHINF, pages 398-405

ISBN: 978-989-758-731-3; ISSN: 2184-4305

based on their surgery duration. In most of the cases,

they rely on surgeons’ experience for predicting each

individual patient’s DOS which is extremely surgeon-

dependent and prone to personal bias and inaccuracy.

Therefore, a more reliable approach that considers

patients and surgery characteristics for distinguishing

surgery candidates is needed.

As a branch of artificial intelligence, Machine

learning (ML) utilizes computer algorithms to extract

patterns within a given dataset. Unsupervised learning

(UL) algorithms are types of ML methods that group

data based on similar characteristics; a process called

clustering (Melo Riveros et al., 2019). In contrast to

supervised learning, they do not need labeled data,

which is sometimes hardly available, as a target

variable. Unsupervised learning methods have been

frequently used for different purposes in the healthcare

domain. Wang et al. suggested two UL models to

identify latent disease clusters by using patients’

electronic health records (Wang et al., 2020). Similar

research designed by Grant et al. benefited from k-

means clustering for identifying complex patient

profiles (Grant et al., 2020). Furthermore, some studies

assess the relationship of specific factors with the

resulting clusters. Crowson et al. used unsupervised

ML to cluster the comorbidities of patients with

rheumatoid arthritis and analyzed the association of

different patient characteristics with clusters (Crowson

et al., 2023). Two similar research approaches utilized

unsupervised ML for grouping patients and

investigating mortality risk among resulted distinct

clusters (Nouraei et al., 2022; Thongprayoon et al.,

2022). In another research, Ranti et al. grouped total

joint arthroplasty patients by k-mean algorithm and

analyzed the statistical difference in the set of

outcomes (30-day readmission, severe adverse events,

discharge to no-home) among clusters (Ranti et al.,

2020).

As it can be understood from the literature review,

different unsupervised methods have performed well

for clustering patients into different sub-groups.

Nonetheless, to the best of our knowledge, there is no

study in the literature clustering the patients for the

purpose of analyzing the relationship between

different patient groups and their surgery duration. To

fill the research gap, the main aim of this paper is first

to develop an unsupervised clustering model to well-

separate patients into different groups, and second, to

analyze the potential relationship between resulted

groups and their DOS.

2 MATERIALS AND METHODS

The research design encompasses data extraction and

preprocessing, model development, and output

analysis (Figure 1). Hip arthroplasty surgery was

selected as it is a high-demand operation in surgical

settings. The anonymized data was extracted from

Aalborg University Hospital between 2017 and 2020

(n=1847). Various studies suggest different variables,

associated with surgery duration which include

patient demographics (Abbas et al., 2022; Yeung et

al., 2011) and clinical factors (Mannion et al., 2020;

Yuniartha et al., 2021). In this way, the final dataset

included the information related to patients’ age,

Body Mass Index (BMI), sex, number of

comorbidities, number of previous surgeries, and

their surgery type and surgery side. Regarding the

surgery type, KNFB20 refers to uncemented and

KNFB30 refers to hybrid total prosthesis in the hip

joint. The duration of surgery was calculated based on

the data stored in the Patient Administration System

(PAS), where surgeries’ temporal data are registered.

While DOS was not included in clustering model

development, it was used to assess the association of

clusters and surgery duration. The summary of the

extracted data is presented in Table 1.

Figure 1: Research design.

Healthcare data typically comprise mixed data

consisting of both numerical and categorical

variables. This might make it harder for ML

algorithms to extract patterns from the data,

potentially leading to biases toward either categorical

or numerical variables. Therefore, under the data

preprocessing step, categorical variables were

encoded and continuous variables were scaled into

zero to one range for better clustering. Cluster

analysis distinguishes the data based on the distance

function to find out the cluster centers. Different

methods are available for calculating the distance

based on different data types; for instance, Euclidean

distance is used for numerical data, while Hamming

distance is employed for categorical data. Specific

An Unsupervised Machine Learning Approach for Clustering Hip Arthroplasty Patients: Surgery Duration Differs Among Different Patient

Groups

399

algorithms are developed for clustering continuous

data (k-means) or categorical data (k-modes). K-

prototype is a combination of k-means and k-modes

which is suitable for mixed data clustering (Madhuri,

2014) by simultaneously measuring both types of

distances (Kuo & Wang, 2022). The distance d(x,y)

between two points x and y, where x = (x

) and y =

), with x

and y

being numerical features, and

and y

being the categorical features, is given by

equation 1:

Table 1: Patients’ demographics and data summary.

Variable Mean (Std) Frequency (%)

DOS 77.18 (25.67)

Age 67.39 (12.27)

BMI 28.34 (4.74)

Sex Female:947(48%)

Male: 900 (52%)

Side Right: 984 (53%)

Left: 863 (47%)

Number of

Comorbidities

0: 1448 (78%)

1: 314 (17%)

2: 68 (4%)

3: 15 (1%)

4: 2 (0%)

Number of

Surgeries

1: 1708 (92%)

2: 136 (7%)

3: 3 (0%)

Procedure

Type

KNFB20:

942 (51%)

KNFB30:

905 (49%)

𝑑(𝑥,𝑦) = (𝑥

,

−𝑦

,

)



+𝛾𝛿𝑥

,

,𝑦

,











(1)

Where:

• x

n,i

and y

n,i

are the numerical values of the i-

th feature of x and y.

• 𝛿(𝑥

,

,𝑦

,

) is an indicator function for the

categorical features j, defined as equation 2:

𝛿𝑥

,

,𝑦

,

=

1, 𝑖𝑓 𝑥

,

≠𝑦

,

0, 𝑖𝑓 𝑥

,

=𝑦

,

(2)

• 𝛾 is a weighting factor that balances the

contributions of the numerical and

categorical features.

K-prototype has been frequently used in the

healthcare domain and specifically for patient

clustering (Nouraei et al., 2022; Pasin & Gonenc,

2023). Therefore, considering the mixed data in this

research, the K-prototype was utilized to cluster the

patients. To find the best-performing model, we

developed different models with a wide range of

values for a number of clusters (2-15) and gamma

(0.5,0.1,0.01) as two important hyperparameters in K-

prototype. The performance of different models was

compared by using three popular metrics for

clustering models presented in Table 2.

Table 2: Clustering performance metrics.

Metric Range Interpret

Silhouette Score Between -1

and 1

The higher, the

ette

Calinski-

Harabasz Score

Unbounded &

non-negative

The higher, the

ette

Davies-Bouldin

Score

Unbounded &

non-ne

ative

The lower, the

ette

In order to assess the contribution of different

variables in developing clusters, permutation analysis

based on the Silhouette Score was performed. In this

way, each time a specific variable’s values are

randomly shuffled while keeping the other variables’

values fixed. The model is developed again, and the

recent performance is compared with the

performance of the original model. Finally, the

difference and drop in the model’s performance is

considered as the importance of the variable. For

more reliability, the process was repeated 10 times,

and the average importance was reported.

In this study, One-Way Analysis of Variance

(ANOVA) was applied to evaluate the differences in

surgery duration among various patient clusters

(alpha=0.05). One-way ANOVA is a statistical

technique used to test whether there are statistically

significant differences between the means of three or

more independent groups. For further investigation,

we deepened the analysis to pinpoint the clusters with

significantly different DOS by using a pairwise post-

hoc comparison using Tukey’s Honest Significant

Difference (HSD) test. Tukey's HSD test is a

commonly used post-hoc test that compares the

means of each pair of groups to determine which

specific group means are significantly different from

each other, while controlling for Type I errors (false

positives) (Nanda et al., 2021).

3 RESULTS AND DISCUSSION

In total 42 clustering models were developed with

different hyperparameters (14 alternatives for the

number of clusters and 3 options for gamma). As

shown in Figure 2, the model with 7 clusters and

gamma equal to 0.1 reached the best performance

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(silhouette score=0.61, Calinski Harabasz score=

2167.43, and Davies Bouldin Score= 0.63). It should

be noted that in one case (where number_clusters=10

and gamma=0.1) the performance of the cluster was

slightly better than the best model by one metric

(Calinski Harabasz), nonetheless, the best model was

chosen by considering all performance metrics.

Figure 2: Different clustering models’ performance.

The results of multiple permutations for feature

importance analysis (Figure 3) illustrated that the age,

surgery type, and BMI have the highest contribution

in clustering patients, while the sex, number of

surgeries, and surgery side show a lower importance

in distinguishing patients’ groups.

Figure 3: Feature Importance based on Silhouette drop.

The green pie chart in Figure 4 shows the size of

different clusters based on the number of patients

inside them. Cluster 4 was the biggest and Cluster 2

was the smallest group of patients. The rest of the

charts demonstrate the share of patients in different

age quartiles in each cluster. It can be seen that the

youngest patients (Q1) are mostly grouped in clusters

1, 4, and 5 while the oldest patients (Q4) have a bigger

Figure 4: Age quartiles’ share in different clusters.

Figure 5: BMI quartiles’ share in different clusters.

An Unsupervised Machine Learning Approach for Clustering Hip Arthroplasty Patients: Surgery Duration Differs Among Different Patient

Groups

401

share in the rest of clusters. In a similar way, Figure 5

illustrates the share of BMI quartiles in different

patient groups. It’s noticeable that the lightest patients

are grouped in clusters 1,3,7 while the heavier ones

are located in clusters 4 and 5, and clusters 2 and 6

contain the patients with mid-range BMI.

Table 3: ANOVA test results.

One-way ANOVA

F-statistic 11.77

P-value 5.4510

-13

Figure 6 contains four boxplots showing the share

in different categorical variables (surgery type, sex,

surgery side, and the number of comorbidities) along

different clusters. Regarding surgery type and sex, it

is evident that the clusters are well separated in

different categories while regarding the surgery side,

cluster 1 has appeared in both categories. However,

all clusters have appeared in the first two categories

of the number of comorbidities which can be due to

the majority of patients have zero or one

comorbidities in their medical profile. Meanwhile,

the clusters in the rest categories of this variable are

more separated. Moreover, the boxplots illustrate the

differences in different clusters’ DOS in different

categories.

As reported in Table 3, the ANOVA test yielded

an F-statistic of 11.77, indicating a substantial

variance between groups’ means compared to within-

group variance. The associated p-value was

5.45  10

, demonstrating strong statistical

significance. This result leads to the rejection of the

null hypothesis, suggesting that at least one patient

group exhibits a mean surgery duration significantly

different from the others. Investigating the DOS

difference among clusters through post-hoc

comparison using Tukey’s HSD revealed that in

almost half of the pairwise comparisons, there is a

statistically significant difference between clusters

from the surgery duration perspective (Table 4). The

largest difference refers to the clusters 1-2, 1-7, and

5-7 and the smallest difference refers to the clusters

2-7, 3-6, and 4-5.

The analysis of results illustrated that

unsupervised machine learning can distinguish

between different patient groups. It was also shown

that the resulted clusters are statistically different

from the surgery duration perspective. This means

patients in a single group are expected to have similar

DOS, while patients in different groups are supposed

to have different DOS. This patient differentiation is

currently done based on surgeons’ or secretaries’

experience in the scheduling committee prior to the

surgery. Therefore, the derived insight from patient

clustering can be utilized as a supporting tool to

enhance decision-making quality and reliability in

surgical settings. For instance, it can help schedulers

with identifying the patient groups prone to longer

DOS. The results can also be utilized for other

medical to operational purposes. Reviewing the

literature shows that market research, gene sequence

analysis, and object recognition are the most popular

applications of unsupervised ML models in

healthcare (An et al., 2023). Unsupervised ML

clustering can also be used in other research projects

such as surgery scheduling (Thomas Schneider et al.,

2020), operational scenarios analysis (Chavosh

Nejad et al., 2022), or be utilized as an input variable

in developing prediction machine learning models

(Huang et al., 2019).

Figure 6: Categorical variables share in different clusters.

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Table 4: Turkey’s HSD test results.

Group 1 Group 2

Mean

Difference

Adjusted P-

values

Lower

oun

Upper

oun

H-0

Rejection

1 2 13.46 0.00 6.04 20.89 TRUE

1 3 8.98 0.00 2.94 15.02 TRUE

1 4 3.01 0.75 -2.94 8.95 FALSE

1 5 1.89 0.97 -4.26 8.04 FALSE

1 6 8.62 0.01 1.34 15.90 TRUE

1 7 13.38 0.00 6.94 19.82 TRUE

2 3 -4.48 0.53 -11.72 2.76 FALSE

2 4 -10.46 0.00 -17.62 -3.30 TRUE

2 5 -11.57 0.00 -18.90 -4.24 TRUE

2 6 -4.84 0.60 -13.15 3.46 FALSE

2 7 -0.08 1.00 -7.66 7.49 FALSE

3 4 -5.98 0.03 -11.68 -0.27 TRUE

3 5 -7.09 0.01 -13.01 -1.17 TRUE

3 6 -0.36 1.00 -7.46 6.73 FALSE

3 7 4.40 0.36 -1.83 10.62 FALSE

4 5 -1.11 1.00 -6.93 4.71 FALSE

4 6 5.61 0.21 -1.39 12.62 FALSE

4 7 10.37 0.00 4.25 16.50 TRUE

5 6 6.73 0.08 -0.46 13.91 FALSE

5 7 11.49 0.00 5.16 17.82 TRUE

6 7 4.76 0.49 -2.67 12.20 FALSE

4 CONCLUSION

The increasing demand for surgical services by

patients with wide ranges of personal and medical

characteristics makes operational decision-making a

difficult task that necessitates patients grouping. This

paper illustrated that unsupervised machine learning

models are able to cluster patients undergoing hip

arthroplasty surgery based on their personal and

medical characteristics. It was noticed that patients’

age, BMI, and their surgery type are important factors

in clustering them into different groups. Further,

statistical analysis revealed that there is a significant

difference between different patient clusters’ duration

of surgery (DOS) and introduces the inter-cluster

DOS differences. Future studies can include other

clinical, operational, or personal variables for

clustering patients and evaluate their contribution to

grouping patients. They can also expand the idea

through applying patient clustering results in other

research topics such as supervised machine learning

or healthcare operations optimization.

ACKNOWLEDGEMENTS

We would like to thank staff at Aalborg University

Hospital for offering us detailed insights into the

medical and operational conditions surrounding Hip

surgery.

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