Optimal Treatment Selection for Hip Fracture Patients using a Hybrid

Decision Making System

Aleksandar Jeremic

, Natasa Radosavljevic

, Dejan Nikolic

and Milica Lazovic

Department of Electrical and Computer Engineering McMaster University, Hamilton, ON, Canada

Institute for Rehabilitation Belgrade, Belgrade, Serbia

Physical Medicine and Rehabilitation, University Childrens Hospital, Belgrade, Serbia

Faculty of Medicine, University of Belgrade, Belgrade, Serbia

Keywords:

Macular Oedema, Prediction, Estimation, Least-squares Estimation.

Abstract:

Hip fractures are most frequent cause of hospitalization after the fall in older population and consequently

have been subject of great interest in medicine and biomedical engineering. It has been observed that the

incidence of hip fractures is rising at the approximate rate of 1-3% per year, with subsequent mortality rates at

approximately 33% in ﬁrst year after the fracture. Although in some cases the hydrotherapy may be improve

recovery of patients it may not be easily accessible due to limited resources. To this purpose we propose a

hybrid decision making system consisting of computer-aided decision combined with an expert opinion. We

then evaluate and compare the performance of the proposed algorithms using a data sample consisting of 413

patients that have been admitted to the Institute for Rehabilitation, Belgrade, Serbia.

1 INTRODUCTION

Hip fractures are most frequent cause of hospitaliza-

tion after the fall in geriatric population (Roudsari

et al., 2005) worldwide and consequently have been

subject of great research interest in both medicine

and biomedical engineering due to the incident fre-

quency, corresponding mortality as well as treatment

expenses. It has been reported that the incidence of

hip fractures is rising at the approximate rate of 1-3%

per year, with subsequent mortality rates at approx-

imately 33% in ﬁrst year after the fracture (Johnell

and Kanis, 2004; Roche et al., 2005). Consequently

because of the increasingly large number of elderly

patients with these fractures signiﬁcant advances have

been made with respect to surgical procedures, post-

surgical rehabilitation procedures as well as social

support services. It is often emphasized that man-

agement and allocation of resources is of utmost im-

portance in patient care. In practical situations the

amount of resources is limited and thus proper assign-

ment of priorities may play crucial role in recovery.

As an example certain patients experiencing hip frac-

ture may show signiﬁcant progress if surgeries and

rehabilitation programs are allocated in timely man-

ner thus leading to more efﬁcient health care.

To this purpose there are different rehabilitation

protocols that are used for the treatment of these pa-

tients as well as variety of efforts to identify parame-

ters that could serve as useful predictors of the treat-

ment outcome. Two of the commonly used parame-

ters, often correlated, which are used for this evalua-

tion is functional independence measure (FIM) which

evaluates patients’ ability to perform particular tasks

and Berg Balance Scale (BBS) which evaluates pa-

tients ability to maintain the balance. There is still

a lack of consensus among physicians regarding the

factors that are of greatest signiﬁcance for the recov-

ery (of the long-term disability associated with hip

fractures., 2011)-(Adunsky et al., 2012).

In our previous work we proposed a clustering al-

gorithm for selecting patients with largest recovery

capacity with respect to Berg Balance Scale (BBS)

(Jeremic et al., 2012) as well as linear and nonlin-

ear prediction algorithms of the FIM using multi-

variate regression with respect to age, comorbidity

and type of treatment (we consider two different con-

trol groups: with and without hydrotherapy) (Jeremic

et al., 2013). It is often argued that in order to per-

form proper clinical care and management the pa-

tients should be triaged upon admission according to

their ability for recovery and/or predicted efﬁciency

of the treatment using hydrotherapy. To this purpose

in this paper we propose multichannel fusion algo-

301

Jeremic A., Radosavljevic N., Nikolic D. and Lazovic M..

Optimal Treatment Selection for Hip Fracture Patients using a Hybrid Decision Making System.

DOI: 10.5220/0004914703010305

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2014), pages 301-305

ISBN: 978-989-758-011-6

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

rithm for decision making in which the two decisions

are modelled as uncorrelated binary decisions. At

the present time there is no consensus whether or not

these are correlated decisions so in order to obtain

preliminary results we propose to model them as un-

correlated decisions. We then evaluate the proposed

prediction algorithms on a data sample consisting of

413 patients that have been admitted to the Institute

for Rehabilitation, Belgrade, Serbia. For comparison

purposes we compare the performance of our com-

puter based system with expert opinion of the physia-

trist performing patient evaluation.

The paper is organizedas follows. In Section II we

describe the data set and the proposed decision mak-

ing/binary hypothesis decision algorithms. In Section

III we evaluate the applicability of the proposed algo-

rithm using a real data set. Finally, in Section IV we

discuss the results and future work.

2 SIGNAL PROCESSING

MODELS

2.1 Data Set

We have evaluated 413 eligible participants that were

referred to the rehabilitation facility from January

2011 until April 2013 after hip fracture for inclusion

into rehabilitation program and follow-up. To assess

eligibility for the inclusion in the study the patients

were evaluated by board certiﬁed physiatrist and spe-

cialist of internal medicine. Prior to the inclusion, all

the participants were informed about the study pro-

tocol and informed consent was obtained. The study

was approved by the Institutional Review Board and

was carried out according to the principles of good

clinical practice. The eventual onset of early compli-

cations was indication for the termination of the reha-

bilitation program for deﬁned period of time. The ex-

clusion criteria for the study were recurrent hip frac-

tures and inability to completely ﬁnish the rehabili-

tation program or follow-up that was deﬁned by the

study. Therefore, the initial group on admission con-

sisted of 467 patients, where 24 did not complete re-

habilitation program due to the worsening of health

condition and thus transferred to specialized referring

hospitals, while 30 subjects dropped out from dis-

charge period to the planned follow-up after 3 months

post-discharge. Beside Board certiﬁed Physiatrist, re-

habilitation team consisted of: licensed physical ther-

apists, licensed occupational therapists and nurses.

Once a week, the aforementioned rehabilitation team

gathered on meeting to evaluatepatients improvement

and further implementation of rehabilitation program.

Prescription of rehabilitation program was indi-

vidually addressed with particular attention to the pa-

tients functionalstatus. Patients were included twice a

day for the duration of two hours (60/60 minutes) into

physical therapy. First part of physical therapy was

composed of different exercises including those for

strength and balance improvement, conditioning and

coordination improvement. These exercises aimed to

improve walking and mobility. The second part of the

program was conducted by occupational therapist and

consisted of improving activities of daily living. The

maintenance of proper hygiene during the rehabilita-

tion program was conducted by experienced nurses.

Functional Independence Measure (FIM) and

Berg Balance Scale were used to evaluate patients

functional status on 3 occasions: at admission (Ad-

mission), on discharge from the rehabilitation facil-

ity (Discharge) and 3 months after discharge (Follow-

up). After discharge, patients were not included into

any kind of rehabilitation program and were referred

to home of residence. Both of these measures presents

valid and reliable test in the estimation of aggregated

changes in functional status that appears in the de-

ﬁned period of the study evaluation (Young et al.,

2009)-(Dodds et al., 1993). It is composed of 18 cat-

egories that are scaled from 1-7 each (Young et al.,

2009) For the estimation of comorbidity of partic-

ipants we used Cumulative Illness rating Scale for

Geriatrics (CIRSG), and ﬁndings were presented as

severity index (SI), where SI was calculated as total

CIRS-G score divided by the number of endorsed cat-

egories (Firat et al., 2002).

We organize the data set in a database consist-

ing of 413 rows corresponding to the patients and

40 columns of different features (age, height, weight,

respiratory conditions, heart conditions, FIM at the

admission, FIM at the discharge, BBS three months

after discharge, etc.) In our previous work we ana-

lyzed cross-correlation between all the features and

extract statistically signiﬁcant ones using Pearson co-

efﬁcient. In order to study dynamics of rehabilitation

we use log-values of BBS score ratios. The rationale

behind this approach is that we expect exponential

change in balance improvement and thus log (semi-

log) models may represent better ﬁt.

2.2 Parameter Estimation and Decision

Making

We ﬁrst partition patients into two groups, those that

participated in hydrotherapy and those who did not.

Then, let y

denote our measurement vector consist-

ing of the FIM and BBS values 6 months after the

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302

discharge from the rehabilitation program for the ith

patient. The corresponding MANOVA model for the

ﬁrst group of patients can be written as

= Xa

+ e

where X is the matrix of unknown parameters and a

is the ”source” vector for the I-th patient consisting of

i,i











1 j = 1

age of the i− th patient j = 2

comorbidity of the i− th patient j = 3

BBSatadmission j = 4

FIMatadmission j = 5











The unknown matrix X can then be estimated using a

technique similar to one proposed in (Jeremic et al.,

2013). Similarly we formulate equivalent model for

patients that were not subject to hydrotherapy and de-

note corresponding MANOVA coefﬁcients as Y.

We then proceed to deﬁne a computer based deci-

sion for therapy selection in the following way. Ac-

cording to expert input the hydrotherapy is consid-

ered sufﬁciently efﬁcient if the average sum of FIM

and BBS after dismissal from the program is more

than 25% larger compared to the value that would

be achieved without therapy. Therefore we formulate

following decision problem

choosehydrotherapy

≥ 1.25

In our previous work (Jeremic et al., 2013) we also

derived the nonlinear estimator for predicting values

of BBS and FIM. Similarly to the above approach

we estimate the corresponding coefﬁcients X

and Y

where we use subscript n to denote that the coefﬁ-

cients are estimated using a nonlinear model in which

the predicted value is modelled as a polynomial func-

tion of age, weight and BBS and FIM admittance val-

ues. Similarly the second local detector is formulated

choosehydrotherapy

≥ 1.25

We then propose to fuse the above two decisions

using blind adaptive algorithm proposed in our previ-

ous work (Mirjalily et al., 2003). The authors demon-

strated that by formulating empirical probabilities of

decisions one can solve in a closed form for prior

probabilities as well as probabilities of false alarm

and miss under the assumption that the performance

of local detectors does not vary signiﬁcantly. We ap-

ply the following approach using similar technique

we demonstrated in (Li and Jeremic, 2011) to fuse

the above decisions of linear and non-linear predictor.

We recall it here for the case of N = 3.

(

1, if w

∑

n=1

> 0

0, otherwise

where, w

= log





(1)

and w

(

log((1− P

)/P

), if u

= 1

log(P

/(1− P

)), if u

= 0

The probabilities of false alarm and missed detection

of the nth local detector are denoted as P

and P

respectively. The optimal fusion rule tells us that the

global decision u

is determined by the a priori prob-

ability and the detector performances, i.e., P

, P

and

which can be solved for by solving algebraic set of

equations as demonstrated in (Mirjalily et al., 2003)

3 RESULTS

The total number of patients admitted was 413 (260

with hydrotherapy and 153 without hydrotherapy)

with general characteristics being described in Table

Table 1: General characteristics of patient population with

respect to the age and severity index of fracture

Age Severity Index

Total N=413 77.63± 6.21 1.84± 0.59

Female N=271 78.28 ± 5.86 1.74± 0.43

Male N =142 76.39± 6.56 1.79± 0.62

Additionally in Table 2 we show the correlation

coefﬁcient of the 6-month FIM with respect to the

model parameters. Based on these results we select

age and comorbidity as two most signiﬁcant parame-

ters in the remainder of the paper.

Table 2.

Age Com. Wait time FIM - adm. FIM - 6mo.

Age 1.00 0.37 -0.15 -0.29 -0.57

Com. 0.37 1.00 0.20 0.48 -0.52

Wait time -0.15 0.20 1.00 0.71 0.24

FIM - adm. - 0.29 0.48 0.71 1.00 0.51

FIM - 6mo. -0.57 -0.52 0.24 0.51 1.00

To illustrate the statistical properties of the data

sample we present two scatter plots. In Figure 1 we

illustrate two-dimensional scatter plots of age and co-

morbidity (as a preliminary approach we arbitrarily

selected the two parameters with largest coefﬁcients)

using therapy indicator as grouping parameter. In Fig-

ure 2 we present a similar three-dimensional scatter

plot with 6-months FIM as an indicator. Obviously

the decision whether or not the therapy should be used

OptimalTreatmentSelectionforHipFracturePatientsusingaHybridDecisionMakingSystem

303

65 70 75 80 85 90 95

Age

Comorbidity

With therapy

Without therapy

Figure 1: Two-dimensional scatter of age and comorbidity

Age

Comorbidity

FIM

With therapy

Without therapy

Figure 2: Three-dimensional scatter of age, comorbidity

and FIM.

2 2.5 3 3.5 4 4.5 5 5.5 6

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

Number of parameters

MSE

Nonlinear

Linear

Figure 3: MSE comparison nonlinear vs. linear model for

patients with hydrotherapy.

was not randomized in this study and hence we expect

to have different performance. Obviously in making

clinical decision not all the decisions can be random-

ized as it may contradict clinical protocols.

In order to evaluate the performance of the pro-

posed hybrid system we run the fusion center consist-

ing of three local detectors: linear detector, nonlin-

ear detector and human expert system. As expected

the overall probability of error decreases with the in-

crease in the number of the patients. It demonstrates

50 100 150 200 250 300 350 400

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

Overall Error Proabibility

Patient Number

Figure 4: Overall Probability of Error for Hybrid System.

Table 3: General characteristics of patient population with

respect to the age and severity index of fracture.

Linear Nonlinear Expert

False Positives 12% 10% 11%

False Negatives 10% 9% 8%

signiﬁcant dip after number of patients reaches 300

which is consistent with our ﬁndings in (Liu et al.,

2011) where we developed optimal M-ary distributed

detection system.

In Table 3 we list the estimated performance mea-

sures of our local detectors. Note that by false

positives we determine selection of hydrotherapy

when it is not expected to provide signiﬁcant advan-

tage. As expected the human system outperforms the

computer-aided systems except with the case of false

positives when compared to the non-linear system.

Note that the results in Table 3 are overall results and

it may be potentially useful to decompose these error

with respect to patients’ age and gender which may

affect human decision making.

4 CONCLUSIONS

The importance of early inclusion in rehabilitation

program and exercise of older people after the hip

fracture could be explained by the fact that physical

activity inﬂuences the muscle strength, balance and

eventually degree of hip pain (Sipila et al., 2011).

Such determinants are very important particularly for

individuals quality of life and could prevent further

risks of comorbidities and falls later in life. It has

been often hypothesized that the success of recov-

ery is extremely dependent on the timeliness and ad-

equacy of the treatment. While it is desirable to pro-

vide the best possible care as soon as possible the ac-

tual limitations that may exist in health-care systems

due to a limited number of medical staff as well as

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limited capacity in rehabilitation programs may cre-

ate need for appropriate planning and/or scheduling.

To this purpose in this paper we proposed an al-

gorithm which can potentially be used to determine

whether or not hydrotherapy is required. This ques-

tion may be of signiﬁcant resources in scenarios in

which the number of geriatric physiatrists as well as

access to resources and/or their cost may be a limiting

factor. Furthermore we proposed a framework that

can potentially be useful for evaluating performance

of fellows and/or residents and assist them in their

training and educations as well as professional de-

velopment as it can point to potential mistakes. This

could be further used in order to evaluate the cause of

such mistakes and potential was to remedy them.

As a preliminary approach we proposed

computer-aided decision making using linear

and nonlinear models in which parameters were

chosen based on the correlation coefﬁcient. An effort

should be made to compare the performance of these

models to non-parametric, multilevel histograms

in which FIM and BBS can be modelled using the

joint probability density function and consequently

determining a histogram based maximum likelihood

estimate. In addition the residual vector may not

be Gaussian distributed especially in which case

an effort should be made to investigate different

estimation techniques that may be more suitable for

non-Gaussian models.

Finally, a clinical study with a larger number of

patients and different waiting times should be per-

formed in order to evaluate the correlation between

waiting time (time from operation to admission to re-

habilitation program). In this particular data set, due

the similarity between waiting times, this parameter

was not a signiﬁcant factor. However that may not

be the case if the waiting times are larger than certain

threshold value which should be investigated in future

work.

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