WEB-BASED SYSTEM FOR ASSESSING RISK FACTORS FOR FALLS IN COMMUNITY-DWELLING ELDERLY PEOPLE USING THE ANALYTIC HIERARCHY PROCESS

IJAHP ARTICLE: Pecchia, Bath, Pendleton, Bracale/Web-based System for Assessing Risk
Factors for Falls in Elderly People

International Journal of the 135 Vol. 2, Issue 2, 2010
Analytic Hierarchy Process ISSN 1936-6744

WEB-BASED SYSTEM FOR ASSESSING RISK FACTORS FOR
FALLS IN COMMUNITY-DWELLING ELDERLY PEOPLE USING

THE ANALYTIC HIERARCHY PROCESS

Leandro Pecchia∗
Department of Biomedical, Electronic and Telecommunication Engineering,

University Federico II of Naples
Naples, Italy

E-mail: leandro.pecchia@unina.it

Peter A. Bath
Health Informatics Research Group and Centre for Health Information Management

Research (CHIMR), Department of Information Studies
University of Sheffield

Sheffield, UK
E-mail: p.a.bath@sheffield.ac.uk

Neil Pendleton

School of Translational Medicine
University of Manchester

Manchester, UK
E-mail: neil.pendleton@manchester.ac.uk

Marcello Bracale

Department of Biomedical, Electronic and Telecommunication Engineering,
University Federico II of Naples

Napoli, Italy
E-mail: bracale@unina.it

ABSTRACT

Falls occur frequently among older people and represent the most common cause of
injury-related morbidity and mortality in later life. Preventing falls is an important way to
reduce injuries, hospitalizations, and injury-related morbidity and mortality among older

∗ Corresponding author
This project of research, and so far the collaboration between the University of Sheffield
and Napoli, was in part supported by academic award for mobility of Ph.D. students from
University Federico II. An earlier version of this paper was given at the ISAHP 2009
conference (Pecchia et al., 2009).

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people. The research literature has identified hundreds of risk factors for falls among
elderly people. Prioritizing risk factors for falls is useful for designing effective and
efficacious prevention programs. The aim of this study was to use the Analytic Hierarchy
Process to develop a hierarchy of risk factors for falls based on the knowledge and
experience of experts working in this field. We designed and developed a web portal for
participants to submit responses to electronic questionnaires in order to reach the highest
number of respondents quickly and to reduce errors in responding. We contacted the
person responsible for the Falls sections of four scientific societies. Finally, we propose a
correction method to modify respondents’ relative importance on based on the coherence
of their responses, in order not to exclude experts who had submitted the questionnaire
twice.

Keywords: AHP falls in elderly people, web service

1. Introduction
Evidence-based medicine and health care is becoming increasingly important for
assessing the effectiveness of a new health care program. Nonetheless, in order to
maximize the effectiveness, health care professionals (HCPs) need to incorporate
empirical and experiential evidence with physiological and biomedical principles,
considering also the individual patient’s condition — whom they may know personally
— their professional values, and features of the system (Tonelli, 2001). The relative
weight given to each of these areas is not predetermined, but varies according to specific
patient’s condition and the HCPs’ experience. Therefore, it is important to understand the
perspectives of HCPs on how they balance factors affecting decision-making and care,
and whether there is any consistency among them. Everyday practice, in fact, often
differs from evidence-based procedures reported through guidelines.

Our study aims to investigate the opinion of a wide number of professional caregivers,
with different specializations and experiences, in facing the complex and multi-factorial
problem of preventing falls in home-dwelling elderly people. We used the Analytic
Hierarchy Process (AHP) (Saaty, 1980), to develop a hierarchy of risk factors for falls
based on the knowledge and experience of experts working in this field. Another reason
leading us to investigate experts’ opinion was that not all falls cause injuries, and for this
reason, since we were interested in prioritizing risk factors for any kind of falls, we chose
not to base our hierarchy on hospital reports.

Falls occur frequently among older people and represent the most common cause of
injury-related morbidity and mortality in later life (King and Tinetti, 1995; Nevitt and
Cummings, 1989). The annual incidence of falls among older people is estimated to be
between 15% and 40% in community-dwelling people aged 65 and over. The
consequences of falls range from psychological harm (Parry and Steen, 1982), physical

Rob
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http://dx.doi.org/10.13033/ijahp.v2i2.61

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Factors for Falls in Elderly People

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injuries (Lord and Sherrington, 2007), and hospitalization, to death. Falls can also
negatively affect well-being, mobility, autonomy, and overall quality of life. Preventing
falls is therefore an important way to reduce injuries, hospitalizations, and injury-related
morbidity and mortality among older people (Oakley, 1996). Identifying and prioritizing
risk factors for falls is useful for designing effective and efficacious prevention programs.

The research literature has identified hundreds of risk factors for falls among elderly
people (Gillespie 2000), and it is well established that falls risk in old age is complex and
multi-factorial. Moreover, it has been shown that reducing risk factors (Tinetti, 1996) and
developing multi-factorial interventions (Tinetti, 1994) are important strategies for
reducing the frequency of falls in home-dwelling elderly people. However, we did not
find any reports in the research literature of the views of health care professionals on the
relative importance of these risk factors. The aim of our study was to examine the views
of health care professionals on the relative importance of risk factors for falls in
community-dwelling older people.

In order to reach a wider number of experts, we designed and developed a web-based
system for respondents to submit questionnaires and to analyze the results. The
respondents could not discuss their opinion among themselves to reach a consensus, as
we were interested in investigating differences in the opinions of professionals.
Moreover, we chose not to submit the same questionnaire to the same respondents twice,
since this was time consuming for them, as clinicians, and would have reduced the
responses we received. This led us to adapt the AHP methods to our specific needs, as is
discussed further in this paper. Although this represents a limitation of the study, this is
nonetheless only the first step in our research and further research could utilize a focus
group approach with fewer numbers of experts to reach consensus using a more iterative
approach.

The aim of this paper is to describe the system we developed and, because we modified
the AHP method slightly to adapt it to our specific needs, we present and discuss the
effects of these adaptations. In order to demonstrate the effectiveness of the web
application and the effect of the proposed adaptations, preliminary results from this
research are presented.

2. Method
The method used to prioritize the risk factors is an application of the Analytic Hierarchy
Process (AHP), implemented via the World Wide Web. We adopted AHP as an analytic
decision-making method to understand the risk of falls in older people, a problem that is
complex, multi-factorial, and multi-dimensional, and therefore suited to this approach
(Saaty, 2005).

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Analytic Hierarchy Process ISSN 1936-6744

2.1 Hierarchy of risk factors
Using the research literature, we identified a range of risk factors for falls, and designed a
tree by grouping them into categories (that is, general and clinical) and sub categories
(that is, physical, mental, socio-environmental, physical health, drugs and medical
conditions). We then developed and piloted a questionnaire asking experts to compare
pairs of categories, sub-categories, and factors. The tree of factors with their relative
priority weights lead us to the hierarchy. This hierarchic approach allows the construction
of a consistent step-by-step framework for decision-making.

2.2 Questionnaires
In order to reach the highest number of respondents, we designed an electronic
questionnaire, located at: http://hosting.vaisuinternet.it/, and a web-based service
(Pecchia, 2008), to analyze the answers remotely. For each pair of category of risk factors
(Ri, Rj) the respondent was asked the following question: “in your opinion is Ri,
compared to Rj: much more important, moderately more important, equally important,
moderately less important, much less important.” We posed similar questions to compare
the categories of risk factors. Several numerical scales have been proposed, apart from
the Saaty fundamental scale, such as the geometrical scale (Finan, 1999, Ji, 2003,
Lootsma, 1993) and the Salo-Hamalainen scale (Salo, 1997). The Saaty scale and the
geometrical scale are the most commonly used ones. The Saaty scale has been supported
by Saaty’s empirical evidence, but, as described above, it is not a transitive scale. As
demonstrated by Dong (2008) et al., the geometrical scale is thought to be transitive;
however, as Saaty (1994) points out, it is difficult to determine the parameters of the
geometrical scale. Therefore, in accordance with the natural scale of Saaty (Table 1), we
gave a numerical value to each judgment:

Table 1
Saaty Fundamental Scale

Judgments Score
much more important 5
moderately more important 3
equally important 1
moderately less important -3
much less important -5

Piloting the questionnaire, as described below, we decided to use 5 (“much more
important”) as the maximum magnitude, since the first group of respondents in the pilot
appeared to be unclear about using the larger scale, because respondents reported that, in
their opinion, there were not factors dominating the others greater than “much more”.
The negative signs were used in order to incorporate the responses into a single question,
which factor was dominant and by how much. The negative numbers ( ija ) were then

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transformed, via a web service, in its positive reciprocal ( *ija ), using the transformation in
equation 1:

ij
ij a

a
1* −=

(1)

This relation means that, mathematically, if Ri is “moderately less important” than Rj (
5−=ija ), then Rj should be much more important than Ri ( 5=jia ), therefore the

reciprocity of the judgments matrix implies 51=ija . Moreover, respondents were
permitted to use intermediate judgments (as shown in
Figure 4), scored with even numbers (positive and negative), to express further insights,
or if they could not decide between adjacent categories.

2.3 Judgments matrixes
With the scores provided by each respondent, the web service automatically evaluated the
judgment matrix A. It has been shown that, if the judgments are consistent (see next
section for details), the normalized eigenvector of this matrix expresses the relative
importance of each risk factor. We iterated this step for each category of risk factor.
Finally, the same algorithm allows the relative importance of each category of risk factors
to be assessed.

As explained in the following paragraphs, we chose not to compute the average judgment
matrix by calculating the geometrical mean between each element. Instead, we evaluated
a matrix, and so far a vector of global priorities, for each respondent. This allowed us to
present the spread of the opinions of the respondents, reporting a range of global priority
weights for each factor. Then we computed the algebraic mean of these weightings with
the relative importance of each respondent, as stated below.

2.4 Consistency
From each matrix it is possible to estimate the consistency of the responses from each
respondent, in order to test the transitivity of judgments, which is a fundamental
hypothesis in each decision making method. Obviously, a perfect coherence is difficult to
achieve for complex judgments. Nevertheless, it is always important to assess the degree
of coherence of respondents because a high level of inconsistency by individuals can lead
to a low level of consistency in the decision framework.

The AHP allows the consistency of any questionnaire responses to be measured by
posing some redundant questions (Saaty, 2005b, Saaty 1996). For instance, to compare
the three elements, A, B, and C, the respondent is asked to perform the comparison of B
with C ( BCa ), which could be deduced by the pair comparisons A-B ( ABa ) and A-C (

ACa ).The answer is then compared with the deduced judgment and the difference

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represents the degree of inconsistency. If the two judgments are not perfectly consistent,
there will be an error, which can be quantified as:

AC
BCBC a

a
aerror −=

(2)

This error is zero if the judgments are perfectly consistent. Mathematically, the
consistency of each response is measured with the error generalized defined as:

11 * ijijij aaaerror −=
(3)

Nevertheless, inconsistency is often due to distractions or loss of interest by the
respondent and not to a global inconsistency in the respondent’s opinion. This is
particularly true in a web based response system. For this reason, when responses are
inconsistent, the questionnaire should be re-submitted to the respondent. This strategy is
possible when the respondent can meet with the researchers to discuss and settle
inconsistencies in responses; however, this was not possible in this study, the exception
to this being the piloting.

At this point, we chose a threshold error and excluded respondents with a higher level of
inconsistency. Then we used the inverse of the consistency index to correct the relative
importance of each respondent before pooling the data. This method of pooling
techniques is that used in meta-analysis (Sutton et al., 2000)

Finally, we modeled the error as an accuracy-error, which is zero when the framework is
completely consistent. An increasing error means a progressive loss of consistency
individually and overall. This error is then propagated until the final index of relative
importance affecting its precision is estimated. For instance, if a respondent judges A>B
and B>C, she/he should judge A>>C. A direct answer of A>C or A>>>C, is not perfectly
consistent, but it is certainly more consistent than A<C or A=C. The AHP defines a
method to assess the degree of inconsistency. We adopted this technique to correct the
relative importance of respondents in order to pool the final data as described above.
Moreover, we used this error to define the interval of precision of each relative weight.

2.5 Assessment of relative importance
As stated above, after excluding inconsistent respondents and comparing the risk factors,
we calculated the Relative Importance index (RI) within each sub-category (termed
“intra-categorical weights” or “Local Weights”, LW). From the pair-wise comparisons of
categories and sub-categories, we estimated the relative importance of each of them
(“inter-categorical weights”, ICW). Finally, by using both weights, we estimated the
global relative importance of each risk factor (“global weights”, GW). All those weights

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are affected by the error described above, and have to be reported with an imprecision of
less than, or equal to, the threshold-error.

2.6 The web system
To reach a wider range of respondents, we designed and developed a web portal for
completion of the questionnaires, and a web service for processing the data, analyzing the
results and pooling.

The whole system, follows the so-called “Three Tier Layer” architecture, and is
organized in three areas (see Figure 1): the “Client Area” that acts as presentation tier, the
“Server Area” as business tier and data tier and the “Web Service Area” as a pure
business tier level. Each of these areas is independent of the others and can operate with
other information systems using common standards. In summary, the “Client Area” aims
to collect data and presents an elaboration of the results; the “Server Area” to manage, to
store and to retrieve data; the “Web Service Area” to process raw data and transform it
from the judgment matrix to relative importance weights. Moreover, in this area, a web
service analyzes data regarding respondent experience and, following the system
described above, executes the data pooling.

Figure 1 Three “Areas” of the web-based system: Client, Server and Web Services

2.7 Data pooling
We pooled global priorities using a weighted average of the judgment of each respondent.
We weighted each respondent ( rW ) based on her/his experience, taking into account the
following information about respondents: years since specialization, level of education,
area of work. These three features were considered equally important, while Table 2
presents the weights assigned to each element of each feature. This assignment was
chosen according to the hierarchy proposed by Saaty (Saaty, 2010). The “Relative
Importance Weight” is defined as Wr/min(Wr), so that it is clear that a Ph.D. is

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considered about 12 times more important than a professional qualification. Although this
normalization is more sensible to variation in case new features are inserted, it is much
easier to communicate to respondents and decision-makers not skilled in mathematical
methods, which was the priority in this study.

Table 2
Weighting assigned according to time since qualifying, highest educational qualification
and area of work

Feature Weight ( rW ) Relative Importance Weight
Years since qualification

>15 0.61 15.3
6-15 0.25 6.3
3-6 0.10 2.5
1-2 0.04 1.0

Education

Ph.D., MD, or equivalent 0.59 11.8
MSc or equivalent 0.25 5.0
BCS or equivalent 0.11 2.2
Professional Qualification 0.05 1.0

Area of Work

Falls health services/studies 0.57 4.1
Elderly health services/studies 0.29 2.1
Other 0.14 1.0

2.8 Correction of respondents relative importance in case of not perfect coherence
As described above, we submitted the questionnaires to the respondents, who were not in
a single location. At this point, we could not ask them to resolve divergent judgments in
order to achieve a consensus. Moreover, we preferred not to exclude respondents neither
to ask them to complete the questions again, because of the limited time they had
available. For these reasons we introduced a correction method in order to accept
respondents with a CR over the suggested threshold of 0.1. Then we used the exceeding
ΔCR to correct the relative importance weight ( *rW ) of respondents using the formula
(3).

( ) ] ]






∈∆∆∗−∗=

≤∆=

−=∆

1.0;0101

0
1.0

CRifCRWW
CRifWW

CRCR

(4)

We adopted a threshold of 0.1 because the maximum size of elements compared in one
category is seven (Saaty, 2003, Saaty, 2010). Nonetheless, this threshold could in future
be related to the size of the matrix.

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3. Results and Discussion
3.1 Hierarchy of Risk Factors
From the research literature, we individuated a set of 39 risk factors (Tinetti, 1996,
Tinetti. 1994, Gillespie, 2000), which was reduced to 35 during the pilot study, based on
feedback from the respondents. Five factors were excluded (“falls in the previous 12
months,” “capacity to describe causes of previous fall’s,” “loss of control,” “structural
diseases,” “cardiovascular medicine”) because they were considered confusing or
repetitive with respect to other factors and a two additional factors were introduced
(“poor self rated health” and “previous syncope”) at the suggestion of those participating
in the pilot study. We organized the 35 factors into categories and sub-categories by
developing a tree. In the research literature, various studies have investigated risk factors
for falls. However, few authors have proposed classifications to categorize risk factors
(Panel of Falls Prevention, 2001) and none is based on the opinion of experts from
different specializations. The tree we designed is shown in figure 2.

Figure 2 Tree of Risk Factors

We considered general risk factors (Table 3) to be those that might concern any older
person (including healthy older people), and which include environmental factors.

Table 3
General risk factors organized according to each sub-category

Physical Mental Socio-environmental
high body mass index (bmi) fear of falls need help toileting
loss of weight depression low family support
poor joint flexibility early stage dementia low social engagement
low walking speed loss of balance low social service support
low muscular strength low cognitive perception need to use stairs/steps in

home
low level of physical activity perceived risk of falls

poor self rated health

This category was further split into three sub-categories: physical, which includes those
factors associated with an individual’s stature and capacity; mental, which includes
psychological factors associated with aging; socio-environmental, which includes factors
related to the living arrangements of the person.

GENERAL

PHYSICAL PHYSICAL HEALTH MENTAL DRUGS
SOCIO

ENVIRONMENTAL
MEDICAL

CONDITION

CLINICAL

RISK FACTORS FOR FALLS

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Clinical risk factors concern frail older people with various health problems (Table 4).
This group includes three sub-categories called: physical health factors, which are, in
different proportions present in healthy, as well as in pathological subjects; drugs, which
embrace different medications; medical conditions, which include diseases typically
affecting elderly people.

Table 4
Clinical risk factors organized according to each sub-category

Physical health Drugs Medical condition
visual problems anti-depressives postural hypotension
continence problems anti-psychotics nervous system disease
dizziness beta-blockers musculoskeletal disease
mobility aids diuretics stroke
sleeping problems sedatives polypharmacy

previous syncope
taking any prescribed drugs

3.2 Questionnaires
As described above, we organized the 35 risk factors into 2 categories and six
subcategories. At this point, we needed seven questionnaires, six of which assessed local
weights and one to assess category weights. We first used a paper-based questionnaire in
order to pilot it in-lab. We then designed and implemented a web page for each
questionnaire to reach the highest number of respondents as described below. The time
taken to complete the paper version was almost double that for the web-based version:
the mean time to complete the electronic questionnaires was 20 (±12) minutes for the
respondents involved in the technical pilot, to 27(±14) minutes for the recruited experts,
compared to a mean time of 56(±16) minutes for the paper version. Additionally, we
encountered several errors in the completed paper versions, due perhaps to the limited
experience of the respondents with such a specific layout, even though we provided a
detailed explanation at the start of each questionnaire, including full examples as shown
in Figure 3.

Figure 3 Example provided during the piloting of the paper-version of the questionnaire

Example

For example, if you think that in public health initiatives to reduce the spread of HIV/AIDS, “promoting safe sex” is much more
important than “having a needle bank” then mark the two boxes as follows:

promoting safe sex > = < having a needle bank 1 2 3 4 5 6 7 8 9
Instead if you think that “having a needle bank” is between much more important and very much more important than “promoting
safe sex” then please mark the two boxes as follows:

promoting safe sex > = < having a needle bank 1 2 3 4 5 6 7 8 9
Or, if you think that “having a needle bank” is Equally important to “promoting safe sex” then please mark the two boxes as
follows:

promoting safe sex > = < having a needle bank 1 2 3 4 5 6 7 8 9

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In the electronic version no compilation errors were possible due to the use of
“combobox” objects (Figure 4), which allows only a natural scale to be used instead of
“sign and magnitude” to express pairwise judgments.

Figure 4 Combobox used to demonstrate responses.

In addition, we decided to randomize the order of pairwise comparisons to avoid
automatic responses from respondents who might get tired of completing a long
questionnaire. Moreover, we ensured that we had the same number of recurrences of each
risk factor to the left and to the right of the comparison. We did this in order to reduce
possible biases due to the tendency of inattentive respondents to correlate the importance
of factors to their usual reading. Figure 5 and Figure 6 show the same questions
implemented in the paper version and in the electronic one respectively.

Figure 5 Paper version of questionnaire

One set of questions from the paper version is shown in Figure 5. We randomized the
order of pair wise comparisons and ensured that each factor was twice on the left and
twice on the right.

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Figure 6 Electronic version of questionnaire

The same set of questions in Figure 5 is shown as they are implemented in the electronic
version in Figure 6. The drop-down boxes provide options for the respondents to select
the appropriate response category.

Finally, the elaboration of responses performed via the web services, as described further
in the paper, allowed the post-elaboration time and the risk of error due to manual
transcription to be reduced; this was especially important with this number of
respondents.

It is well known that the wording of the questions, the order in which they are asked, and
the number and form of alternative answers offered can influence the results of surveys.
This is particularly important when the questionnaire is submitted via the web with no
direct feedback from the responders. For this reason, we tried to reduce wording bias by
adopting some forethought. As is evident in Figures 5 and 6, in each section of the
questionnaire all the RFs appear the same number of times on the right and on the left, so
that the respondent could be not influenced by the impression of comparing the RF with
the “other.” Also the order of the questions is random and neither the same RF appears in
two consecutive questions, so that the respondent could be not influenced because of
comparing a RF in sequence with all the remaining RFs. All the words used in the
questionnaire are technical and selected from literature, so that their meanings and
connotations could be clear and familiar to respondents. In order to minimize non-
response bias, we recruited experts through the “Falls” section of national scientific
societies of geriatricians (British Geriatrics Society) and physiotherapists (AGILE). We
have no reason to believe that those specialists who did not respond are any different
from the ones who did respond. Therefore, we feel it is reasonable to assume that the

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final results are minimally affected by non-response bias related to the respondents’
professional background.

3.3 Respondents and execution of the study
Research ethics approval was obtained for this study from the University of Sheffield. A
technical pilot study involving 32 respondents was first performed in our labs to define
the editorial model while trying to minimize the risk of errors. A scientific pilot study
involving a group of nine experts, with different backgrounds and specializations, then
completed the questionnaires independently. All nine respondents had working
experience in the field of falls in the care of elderly people. Four physicians (comprising
a consultant geriatrician with 11 years’ experience, a general practitioners/family
doctors with 28 years’ experience, a MD who specialized as a gerontologist with 28
years’ experience, and a geriatrician with 22), four physiotherapists (with 10, 12, 13
and 13 years’ experience) and one professor of physiotherapy comprised the group. An
invitation letter, containing a link to the questionnaire, was sent by email via the
moderator of the email distribution list for the British Geriatrics Society (BGS) Falls
special interest group, the AGILA Chartered Society of Physiotherapy working with
older people, and to a program of work focused on falls preventions called the
“Preventing Falls Program.” The link contained a “get” variable to track the association
of the respondent, so we know that, from the 196 final respondents who visited the web
questionnaire, 163 were experts from these groups. Of these, 68 (41.7%) completed the
questionnaires. Table 5 gives details about all respondent background.

Table 5
Number of respondents during piloting and the final group of “consistent” respondents.

Technical
Piloting Scientific Piloting Final respondent experts

University 31 1 2
Physicians 1 4 12
Physiotherapists - 4 44
Nurses - - 10
Total 32 9 68

From the group of “final respondent experts” and the “scientific piloting group”, 29%
worked in “falls services” and 42% worked within “general elderly care services”. 16%
reported having an MSc and 8% reported having a Ph.D. or MD. The mean number of
“years since qualification” was 18.9 (±10.56).

Of the 68 final respondents, 10 (14.7%) completed the questionnaire consistently with a
CR <0.1, as suggested by Saaty, in all subcategories. Moreover 24 (35.3%) exceeded the
recommended threshold level in just one section out of seven, with a CR mean of
0.14(±0.03). As explained above, because we preferred neither to exclude respondents

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nor to ask them to answer again, we used a correction method for the respondents who
answered with a ( )2.0;1.0∈CR . We increased the CR level, using the ΔCR to correct the
relative importance of respondents as described in formula (3). We also included
respondents with a CR≤0.2, (n=37; 54.5%) with such a CR in all seven sections of the
questionnaires, and 62 (91.2%) if we include the ones that achieved CR in six of the
seven sections of the questionnaires.

3.4 The web system
The aim of the web-based system was to reach as wide a range of respondents as
possible. We designed the complete system using .NET web technologies, particularly so
that we could easily implement controls to avoid compilation errors. For example, the
system did not allow a respondent to proceed to the following section of the questionnaire
if they had not answered all of the questions in the current section.

Figure 7 summarizes the architecture of the implemented platform and the logic of the
system, which follows the three-tier level model outlined in Figure 1.

First, information about the respondent is requested. The system uses this information to
calculate the weighting for the respondent. This weighting is further corrected (reduced)
if the respondent’s CR is between 0.1 and 0.2, using formula 3 presented above.

The respondent was then asked to prioritize risk factors within each sub-class (first the
general risk factors followed by the clinical ones). Finally, she/he is asked to prioritize
each sub-class and class. The system uses the responses to compose the priority matrices,
from which it calculates relative priority weights and CR. If the CR is greater than the
threshold of 0.2 in at least one matrix, the respondent is excluded from the final pooling.
If the CR is between 0.1 and 0.2 in at least one matrix, the respondent’s weighting is
lowered according to formula 4. By weighting the priority of risk factors according to the
relative importance of the respondent, the system computes and stores the Global
Weights of each factor.

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Figure 7 Web system architecture and service logic

3.5 Data Pooling
As discussed in the previous paragraphs, to pool the results obtained from different
experts it is important to weight each feature of the respondent. The adopted weighting
system is summarized in Table 2. We assumed that the three features could be considered
to be of equally importance.

3.6 Fully coherent respondents
The results from the 10 respondents with a CR <0.1 in each matrix are presented in Table
6. In this table for each sub-category we reported: its parent category (see Figure 2); the
mean among respondents of the relative importance normalized using the distributive
mode; the range among respondents of the relative importance normalized using the
distributive mode; its global weight (GW), which is the mean value among respondents
of the relative importance of the sub-category, after weighting each respondent with the
scoring system introduced in section 2.7; its relative importance weight (RIW), which is
the GW normalized with the minimum the GWs among all the sub-categories
[GW/min(GW)].

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Table 6
Global weights of sub-categories of Risk Factors

Sub-Category Category Mean
(%)

Range
(%)

GW
(%)

RIW

Mental General 19.1 12-26 20.2 1.5
Physical General 19.1 12-26 20.2 1.5
Physical Health Clinical 16.4 11-22 15.5 1.2
Drugs Clinical 16.2 10-23 15.3 1.2
Medical Clinical 13.7 7-21 13.1 1.0
Socio-environmental General 15.6 10-21 15.6 1.2
GW: Global Weight; RIW: Relative Importance Weight.

Table 6 shows that, for all the sub-categories, a score (the “inter-categorical weights”)
was evaluated for each respondent and then mediated (Mean) among all respondents.
These values were then weighted with the relative importance of each respondent to
obtain the Global Weight (GW) of each sub-category. The Relative Importance Weight
(RIW) was estimated by dividing the GWs for the minimum sub-category, which is
“clinical-medical subcategories” in this case. The RIW reflects how much, in the opinion
of respondents, each sub-category is more important than the less important one.
Although this normalization is less stable than is ideal in case one element in the
hierarchy is changed, its results are easier to communicate to physicians. Finally, the
range gives an indication of the data dispersion, which reflects the differences in the
opinions of the respondents. These differences are also due to the general nature of the
questions asked in this study; for example, if the questions were more focused on a
particular case (for example, a patient suffering from specific condition, or using a more
specific definition of a fall), it is possible that the respondents’ opinions may have been
less diverse. In fact, different groups of community-dwelling older people could have
relatively different risk factors for falls. Nonetheless, the design of the questionnaire was
done in such way because we were interested in any kind of falls. Furthermore, measure
divergence among the respondents’ opinions using AHP is a primary outcome of the
study.

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Table 7
Risk Factors

Risk Factor Category Sub-Category Mean
(%)

Range
(%)

GW
(%)

RIW

low muscular strength general physical 1.77 1.00-2.54 1.89 5.9
low level of physical activity general physical 1.61 0.93-2.29 1.72 5.3
loss of balance general mental 1.53 0.70-2.37 1.62 5.0
need help toileting general socio-environmental 1.56 0.67-2.46 1.59 4.9
fear of falls general mental 1.34 0.55-2.13 1.40 4.3
low walking speed general physical 1.03 0.27-1.78 1.13 3.5
poor joint flexibility general physical 1.12 0.75-1.49 1.12 3.5
use of sedatives clinical drugs 1.11 0.57-1.66 1.10 3.4
use of antipsychotics clinical drugs 1.07 0.58-1.57 1.08 3.3
early stage dementia general mental 0.96 0.38-1.53 1.07 3.3
use of anti-depressives clinical drugs 1.07 0.50-1.64 1.06 3.3
low cognitive perception general mental 0.97 0.62-1.33 1.03 3.2
dizziness clinical health physical 1.09 0.57-1.61 1.01 3.1
perceived risk of falls general mental 0.96 0.32-1.60 1.01 3.1
visual problems clinical health physical 1.06 0.59-1.53 1.00 3.1

Table 7 presents the relative importance of the first 15 individual risk factors. We
evaluated the same synthetic parameters described above. RIW expresses the relative
importance of each Risk Factor normalized to the least important factor (“low social
services support”).

The range shown in the previous tables is too high to identify clearly the classification
between each consecutive risk factor. This may also be due to the high number of risk
factors. Nonetheless, it is clearly discernible that there is consensus that some factors are
much more important than others. An additional investigation could focus on these
factors in order to provide a classification that is more selective.

3.7 Correction of respondents’ relative importance in case of not perfect coherence
By applying the correction introduced above, we included 62 respondents obtaining the
following results for the sub categories, as shown in Tables 8 and 9.

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Table 8
Global weights of sub-categories of Risk Factors
Sub Category Category Mean

(%)
Range

(%)
GW
(%)

RIW

Mental General 22.6 13-32 23.1 1.8
Physical General 18.0 11-25 18.3 1.4
Physical Health Clinical 18.0 11-26 16.7 1.3
Drugs Clinical 16.1 11-22 15.5 1.2
Medical Clinical 13.2 7-20 13.6 1.1
Socio-environmental General 12.0 7-17 12.8 1.0

Comparing Table 9 with Table 7 demonstrates that the ranks of classified categories of
RFs do not change much with the exception of “Socio-environmental”. In fact, the first
five categories are significantly correlated with a Spearman’s rank correlation coefficient
of 97% (p<0.05). Nevertheless, the GWs of consecutive categories are too close, in
comparison to the wide ranges observed (third columns in Table 7 and 9), which reflect
divergence in the opinion of the respondents. Divergence among the respondents’
opinions is a primary outcome of the study, which was revealed by the AHP.

Table 9
First 15 risk factors with error corrections

Risk Factor Category Sub-Category Mean
(%)

Range
(%)

GW
(%)

RIW

loss of balance general mental 1.90 0.61-3.20 2.10 5.9
fear of falls general mental 1.79 0.82-2.76 1.75 4.9
low muscular strength general physical 1.65 0.86-2.44 1.68 4.7
low level of physical activity general physical 1.33 0.68-1.98 1.40 3.9
need help toileting general socio-environmental 1.17 0.53-1.82 1.28 3.6
Sedatives clinical drugs 1.32 0.84-1.80 1.23 3.4
perceived risk of falls general mental 1.22 0.56-1.88 1.19 3.3
dizziness clinical health physical 1.31 0.43-2.20 1.16 3.2
visual problems clinical health physical 1.31 0.56-2.06 1.15 3.2
antipsychotics clinical drugs 1.06 0.61-1.51 1.09 3.0
poor joint flexibility general physical 1.14 0.44-1.83 1.06 3.0
early stage dementia general mental 1.07 0.24-1.90 1.06 3.0
low cognitive perception general mental 0.99 0.55-1.43 1.02 2.8
low walking speed general physical 0.94 0.30-1.58 1.00 2.8
postural hypotension clinical medical 0.98 0.39-1.57 0.99 2.8

In addition, the results on Risk factors prioritization do not change substantially, when
comparing Table 9 with Table 7. Among the first 15 risk factors, 14 are the same in both
groups of respondents. The first five are almost in the same order. Nonetheless, the
difference between the RIWs of consecutive factors is minor, and comparable, to the
range. This leads us to conclude that a detailed classification of all the factors could be
not fully statistically significant, due to the divergence in the opinions of respondents.

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Moreover, both groups of respondent were in agreement in classifying drugs “high bmi”
and “Taking any prescribed drugs” as the two factors with the lowest priority for falls
risk in elderly people, and the final ten factors are the same.

3.8 Comparison with previous studies
A limited number of studies (Rubenstein, 1996, Rubenstein, 2006, Masud 2001) have
proposed a classification of the most likely causes of falls in elderly people, based on
hospital records. They based their classification on the mean percentage of a cause’s
prevalence, calculated from the 3,628 falls reported across 12 studies. These studies
considered only few of the RFs that we included in our hierarchy. Among these,
particularly important causes of falls reported were (in decreasing order of importance):
(1) gait/balance disorders or weakness (prevalence 17%, range among studies 4-39%); (2)
dizziness/vertigo (13%, 0-30%); (3) confusion (5%, 0-14%); (4) postural hypotension
(3%, 0-24%); (5) Visual disorders (2%, 0-5%).

Comparison of our results with this classification is not straightforward. One of the
reasons for this is that causes of falls can also be the dependent on other risk factors. An
example is drug consumption, which is not considered in these studies, but which may
cause vertigo, and which is itself a risk factor. Nonetheless, it is possible to estimate the
GWs of these five causes using Tables 7 and 9. In fact, “balance disorders or weakness”
are related to other risk factors such as “low muscular strength,” and “loss of balance.”
Therefore, the GW of these would be 3.51 or 4.00, by summing the GWs of these two
risk factors from Tables 7 and 9, respectively. Similarly, “dizziness/vertigo” is related to
the risk factor “dizziness” and can be caused by “use of sedatives.” Therefore, the GW of
this would be 2.11 or 2.39, by summing the GWs of these two risk factors from Tables 7
and 9, respectively. Moreover, “confusion” is related to “low cognitive perception” and
can be caused by “early stage dementia.” Therefore, the GW of would be 2.10 or 2.08, by
summing the GWs of these two risk factors from Tables 7 and 9 respectively. We
considered “postural hypotension” and “visual problems” as independent RF, but in this
case there is an inversion between these two RFs between our classifications and the one
proposed in previous studies. In fact, postural hypotension is not in the first fifteen RFs of
Table 7, and is considered less important than visual problems in Table 9. Although it is
not possible to compare our results with previous classifications directly, this proposed
prioritization, shows empirically that our results are broadly consistent with ones
obtained from previous studies, at least regarding the most important causes of falls.
Moreover, our research provides further insights regarding the hierarchy of risk factors
and produces a measure of the divergence of opinion among experts.

3.9 Limitations of the study
As noted in section 3.2, the wording of the questions can influence the results of surveys.
This is of particular importance when the questionnaire is submitted via the web with no
direct feedback or contact with the respondents. For this reason, we tried to reduce any

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bias in the wording by editing the questionnaire as described in section 3.2. Nonetheless,
possible bias in the wording, the sample size and not re-submitting the questionnaires to
respondents with inconsistent responses, are the main limitations of this study. Further
research could use a focus group with smaller number of experts to reach consensus using
a more iterative approach.

4. Conclusions
In the study described in this paper, we investigated an adaptation of the AHP and how it
could contribute to research assessing the priority of risk factors for falls in home-
dwelling elderly people. Our conclusions are that the AHP can contribute to assessing the
hierarchy of these risk factors. Moreover, it is useful to investigate a relatively broad
spectrum of opinions across respondents. This could be due to the different backgrounds
of the respondents, and we are investigating this hypothesis in an attempt to quantify any
differences. The high number of risk factor individuated, the low difference between
consecutive RIWs, and the relative high spread between the respondents’ opinions do not
allow us to identify a statistically significant punctual-scale of risk factors. Nonetheless,
this study allows us clearly to individuate the factors considered the more relevant for
falls compared with the less relevant ones. Further research could ask respondents to
prioritize the most important risk factors. Nonetheless, the difference of opinion between
respondents is in itself a primary outcome of this study. Further studies should try to
investigate the reasons for this.

The implementation of the web system to submit blind questionnaires, allows a wide
number of respondents to be reached. In addition, the time to complete the questionnaire
was almost halved when the electronic version was used. Finally, no errors of
compilation were registered, and users who completed both versions reported that the
electronic version was more user-friendly and easier to use than the paper version.

The method suggested to correct the weights attributed to each respondent on the basis of
its consistency (CR), allowed us to include a wider number of respondent without
dramatic loss of significance in the final scale.

The next version of the web system will support a control of coherence, which in real
time will suggest and underline respondents’ inconsistencies. This control will ask
respondents to review the comparison which presents the highest error, by comparing the
ratio of the two corresponding elements of the eigenvectors to the corresponding value of
the judgments matrix, as suggested by Saaty (1980, 1996).

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