Applied Research in Quality of Life

, Volume 6, Issue 4, pp 349–361

Determination of Weights for Health Related Quality of Life Indicators among Kidney Patients: A Fuzzy Decision Making Method

Authors

    • Department of Mathematics, Faculty of Science and TechnologyUniversity of Malaysia Terengganu
  • Noor Jamalina Jamal
    • Department of Mathematics, Faculty of Science and TechnologyUniversity of Malaysia Terengganu
Article

DOI: 10.1007/s11482-010-9133-3

Cite this article as:
Abdullah, L. & Jamal, N.J. Applied Research Quality Life (2011) 6: 349. doi:10.1007/s11482-010-9133-3

Abstract

Health-Related Quality of Life (HRQoL) is one of the significant current discussions in the health fraternity. It encompasses multidimensional indicators and serves the purpose of evaluating health quality among patients. Patients’ perceptions of the impact of disease and treatment and the indicators such as physical, psychological, social function and well being are normally investigated. However there is no clear suggestion of which indicators contributed more than others. The arbitrary nature of HRQoL paves the way for fuzzy theory in evaluation of indicators. This paper describes the application of a fuzzy decision making method in ranking indicators of HRQoL among kidney patients. Four experts in health fraternity were selected as decision makers to elicit information regarding health related status of chronic kidney disease patients over eight HRQoL indicators. The decision makers were required to rate the regularity of experiencing health-related problems in linguistic judgment among the patients. The five linguistics variables were used as input data to a modified version of Fuzzy Simple Additive Weight decision making model. The modified six-step method was possible to tap the extent of decision makers’ opinions on the severity of HRQoL experienced by the patients. It is shown that the indicator of role-physical recorded the lowest problematic level while the indicator of mental health recorded the highest problematic level experienced by the patients. The ranking signifies the impact of the indicators to health quality specifically the chronic kidney disease patients.

Keywords

Fuzzy setsFuzzy numbersHealth indicatorsDecision makingKidney patients

Introduction

Quality of life (QoL) has been gaining momentum in recent years with increasing awareness efforts made to create a higher quality living environment. The conceptual definition of QoL varies depending on social status and local preferences. Some of the definitions of QoL are extended specifically to health related issues and is referred to as health related quality of life (HRQoL). Guyatt et al. (1993) classified HRQoL into two types which are generic and specific. Generic HRQoL measures the QoL of well-being in general while specific HRQoL measures by specific condition or disease. Occasionally QoL and HRQoL are used interchangeably with little distinction between the two concepts. But a loose distinction between these two concepts can be drawn by giving more emphasis on health related rather than the general outlook of quality in human lives. HRQoL is often defined as a multidimensional concept that reflects a person’s perception of their physical, psychological, and social function and health status (Phillips 2006), (Bowling 1995). HRQoL is also variously referred as patient-assisted outcome measure, health status, and functional status or just as outcome measure. Sharma (2004) defines HRQoL as a multidimensional dynamic concept that has developed from the need to estimate the impact of diseases, which includes economic welfare, characteristic of community and environment, and health status. Bowling (1995) defines HRQoL as optimum level of physical role (e.g. work, career, parent etc) and social functioning, including relationships and perceptions of health, fitness, life satisfaction and well-being. Most of the conceptual definitions of HRQoL refer to a person or group’s perception of their physical and mental health.

There are many thoughts and notes about what is HRQoL and how it being measured. McCall (1975) postulates measure of HRQoL was the extent to which people’s happiness requirements are met. Some relate measures of HRQoL with their defined indicators. It comprises the indicators of ability, adaptation, appreciation, basic needs, belonging, control, demands and responsibilities, enjoyment, happiness, needs, knowledge, as far as pleasure and politics. The intangible and subjective definitions of HRQoL imply the need to embark to a subjective evaluation. Broad and arbitrary definitions of HRQoL motivate a new approach to its measurement. Each indicator contributes to one’s overall assessment of HRQoL. Perhaps the key indicators of HRQoL may include physical functions, sensations, self-care, cognition pain/discomfort and emotional/psychological well-being. Understanding HRQoL in today’s environment is particularly important in health care where monetary or material measures are temporarily excluded. Decisions on human activities are closely related to their effects on HRQoL. Thus concept of HRQoL is used as an important parameter for measuring outcome in modern medicine. This can be used as discriminative as well as an evaluative indicator.

Currently, there is a growing field of research concerned with the development, evaluation and application of HRQoL measures within health related research. Many of this research focus on the measurement of HRQoL rather than a more global conceptualization of QoL. Measurement of HRQoL is made from the perspective of the patient and thus takes the form of self completed questionnaires. For example, Varni et al. (2007) conducted a study to compare generic HRQoL across ten chronic disease clusters and 33 disease categories/severities from the perspectives of patients and parents. The analysis were based on over 2,500 pediatric patients from 10 physician-diagnosed disease clusters and 33 disease categories/severities over 9,500 healthy children utilizing the PedsQL™ 4.0 Generic Core Scales. The Generic Score Scale also used by Hill et al. (2007) to demonstrate the value of categorical confirmatory factor analysis and Item Response Theory in examining a HRQoL in children and adolescents. Researches in HRQoL were varied in approaches and studied across genders, age groups and type of diseases. Barr et al. (2007) conducted a research of HRQoL in children to determine if HRQoL is affected in children with velopharyngeal insufficiency by using statistical analysis such as means, standard deviations and covariance. Wong et al. (2009) conducted a research on visual impairment and its impact on HRQoL among adolescents. They used descriptive statistics measures such as means, standard deviations, confidence interval, and P-value to describe results.

In the midst of many type of diseases, chronic kidney disease (CKD) is one of the most common chronic diseases that impact to HRQoL. Monitoring a patient’s functional status and their subjective well being is importance in patients with CKD. The concept of QoL in dialysis has evolved since the inception of renal replacement therapy from simple survival to enjoying life (Zadeh and Unruh 2005). National Institutes of Health reported that dialysis left patients feeling washed out. Patients suffered from the side disease caused by CKD such as disabling bone disease, dementia caused by aluminum intoxication, and severe fatigue from uncontrollable anemia. High cardiovascular disease death rates limited life expectancy. Some patients were lucky enough to get a kidney transplant, which greatly improved their quality of life and life expectancy (National Institute of Health 2010). In Malaysia, more than 3,500 people develop end stage renal failure every year, increasing the number of patients requiring dialysis. The Malaysian Society of Nephrology reported that CKD affects about 8 to 10 percent of the population and currently the number of patients requiring dialysis in Malaysia is growing by 5 to 7 percent annually (Jamal 2010). As awareness of the importance of HRQoL measurement in chronic disease has increased, several studies have been conducted in the CKD populations. The largest study to date regarding HRQOL in patients with CKD comes from the Dialysis Outcomes and Practice Pattern Study (DOPPS) (Goodkin et al. 2001). DOPPS was a multinational, prospective, observational study of haemodialysis patients focusing on practice patterns and outcomes. In a racial and ethnic study, Lopes et al. (2003) examined HRQoL and associated outcomes among different racial and ethnic groups in the U.S. cohort within DOPPS. The study concluded that significant differences were found in HRQOL scores among different racial and ethnic groups, even when subjects were clinically similar in other respects, including age, comorbidities, and length of time dialysis. In another research, Kimmel and Patel (2006)] conducted a research on QoL in patients with CKD and focused on the patients who undergo the hemodialysis treatment and determined differential perception of QoL from these patients. Every CKD patient, especially those who undergo renal replacement therapy as opposed to these who undergo hemodialysis and peritoneal dialysis, will have the major changes in their way of living and lead to the changes in their QoL (Guo et al. 2002).

Most of data in the research were assessed and measured using descriptive and inferential statistics approaches which is fundamentally dependant on data collection via questionnaire. With statistical techniques, health related indicators are measured based on data collected via a questionnaire that handed to the patients or respondents. Other forms of health related research may opt to qualitative nature research such as interviews and observations. The present research takes neither qualitative nor quantitative approach to evaluate indicators of HRQoL. Instead a fuzzy decision making approach is employed. Evaluation of HRQoL indicators is done in tandem with the arbitrary, vague and uncertain definitions of HRQoL. In fuzzy decision making approach, data in form of linguistic judgment are collected via a group of expert which normally referred as decision makers. The applications of fuzzy decision making in health sciences and well being are not something new. For example, the theory has been applied in medical decision making (Reyna 2008; Torres and Nieto 2006; Phuonga and Kreinovich 2001) and also in measuring quality of life (Lazim and Abu Osman 2008, 2009). One of the most popular methods in fuzzy decision making is fuzzy simple additive weight (FSAW) method. This weighted sum method is the most widely used in multiple criteria decision making (Hwang and Yoon 1981, Chang and Yeh 2001) and (Virvou and Kabassi 2004). Against this background, the purpose of this paper is to rank the eight indicators of HRQoL using a modified version of FSAW among CKD patients. In other words, the theory of fuzzy sets in decision making is utilized to describe the extent of health related problematic status experienced by CKD patients.

Preliminaries

In order to comprehend the method, some definitions and properties of fuzzy sets and its affiliates are presented.

Definition 1

Fuzzy Sets (Zadeh 1965). In a universe of discourse X, a fuzzy subset \( \widetilde{A} \) of X is defined with a membership function \( {\mu_{{\widetilde{A}}}}(x) \) that maps each elements x in X to a real number in the interval [0,1]. The function value of \( {\mu_{{\widetilde{A}}}}(x) \) signifies the grade of membership of x in \( \widetilde{A} \).

Definition 2

Trapezoidal Fuzzy Number (TFN) (Dubois and Prade 1978; Keufmann and Gupta 1991). A fuzzy set \( \widetilde{A} = \left( {a,b,c,d} \right) \) on R, a<b<c<d, is called a trapezoidal fuzzy number if its membership function is
$$ {\mu_{{\tilde{A}}}}(x) = \left\{ {\begin{array}{*{20}{c}} {\frac{{\left( {x - a} \right)}}{{\left( {b - a} \right)}},} & {a \leqslant x \leqslant b,} \\{1,} & {b \leqslant x \leqslant c,} \\{\frac{{\left( {x - d} \right)}}{{\left( {c - d} \right)}},} & {c \leqslant x \leqslant d,} \\{0,} & {otherwise,} \\\end{array} } \right. $$
where a, b, c, d are real numbers. The TFN can be denoted by (a, b, c, d). The x in interval [b, c] gives the maximal grade of \( {\mu_{{\widetilde{A}}}}(x) \) i.e., \( {\mu_{{\widetilde{A}}}}(x) = 1 \); it is the most probable value of the evaluation data. Constants c and d are the lower and upper bounds of the available area for the evaluation data. These constants reflect the fuzziness of the evaluation data.

In fuzzy arithmetic operations, the TFN applies the following properties (Keufmann and Gupta 1991; Liang and Wang 1991; Chen and Hwang 1992; Chiou et al. 2005).

Property 1

Given two trapezoidal fuzzy numbers \( \widetilde{A} = \left( {a,b,c,d} \right) \) and \( \widetilde{B} = \left( {e,f,g,h} \right) \), four main operations of these two fuzzy numbers can be expressed as follows:
  1. (1)
    Addition of two trapezoidal fuzzy numbers ⊕
    $$ \begin{array}{*{20}{c}} {\widetilde{A} \oplus \widetilde{B} = \left( {a + e,b + f,c + g,d + h} \right),} \hfill & {a \geqslant 0,e \geqslant 0.} \hfill \\\end{array} $$
     
  2. (2)
    Multiplication of two trapezoidal fuzzy numbers ⊗
    $$ \begin{array}{*{20}{c}} {\widetilde{A} \otimes \widetilde{B} = \left( {ae,bf,cg,dh} \right),} \hfill & {a \geqslant 0,e \geqslant 0.} \hfill \\\end{array} $$
     
  3. (3)
    Multiplication of any real number k and a trapezoidal fuzzy number ⊗
    $$ \begin{array}{*{20}{c}} {k \otimes \widetilde{A} = \left( {ka,kb,kc,kd} \right),} \hfill & {a \geqslant 0,k \geqslant 0.} \hfill \\\end{array} $$
     
  4. (4)
    Division of two trapezoidal fuzzy numbers /
    $$ \begin{array}{*{20}{c}} {\widetilde{A}/\widetilde{B} = \left( {\frac{a}{h},\frac{b}{g},\frac{c}{f},\frac{d}{e}} \right),} \hfill & {a \geqslant 0,e \geqslant 0.} \hfill \\\end{array} $$
     

Property 2

Given any real number k and a trapezoidal fuzzy number \( \widetilde{A} = \left( {a,b,c,d} \right) \), the division operation (/) of the two numbers can be expressed as follows:
  1. (1)
    Division of any real number k and a fuzzy number /
    $$ \begin{array}{*{20}{c}} {k/\widetilde{A} = \left( {\frac{k}{d},\frac{k}{c},\frac{k}{b},\frac{k}{a}} \right),} \hfill & {a \geqslant 0,k \geqslant 0.} \hfill \\\end{array} $$
     
  2. (2)
    Division of trapezoidal fuzzy number and any real number k/
    $$ \begin{array}{*{20}{c}} {\widetilde{A}/k = \left( {\frac{a}{k},\frac{b}{k},\frac{c}{k},\frac{d}{k}} \right) = \frac{1}{k} \otimes \widetilde{A},} \hfill & {a \geqslant 0,k \geqslant 0.} \hfill \\\end{array} $$
     

Property 3

Given two trapezoidal fuzzy numbers \( \widetilde{A} = \left( {a,b,c,d} \right) \), \( \widetilde{B} = \left( {e,f,g,h} \right) \) and any real number k, four commutative operations of these two numbers can be expressed as follows:
$$ \widetilde{A} \oplus \widetilde{B} = \widetilde{B} \oplus \widetilde{A}, $$
$$ k \oplus \widetilde{A} = A \oplus k, $$
$$ \widetilde{A} \otimes \widetilde{B} = \widetilde{B} \otimes \widetilde{A}, $$
$$ k \otimes \widetilde{A} = \widetilde{A} \otimes k, $$
if k ≥ 0, a ≥ 0, e ≥ 0.

The definitions and properties are required prior to proposing the computational method.

The Proposed Decision Making Method

The proposed method is a modified version of the Fuzzy Simple Additive Weight (FSAW) proposed by Chou et al. (2008). Modifications are made to accommodate the objective of the research and also to simplify the computational procedures without losing the novelty of FSAW. This experiment defines all the decision makers (DMs) are equally importance thus should carry the equivalent weight. The proposed method also considers one layer structure in which criteria and alternatives are replaced with indicators. The proposed method is relatively straightforward and eventually reduces the computational cost. The step-wise procedure of the proposed method is given as follows.
  1. Step 1:

    Define Linguistic Variables

     
The indicators of the subject are selected. The DMs are selected to determine the number of indicators that influence or affected their lives. The indicators are defined qualitatively and assessed in linguistic terms represented by fuzzy numbers.
  1. Step 2:

    Introduce linguistic weighting variables for DMs to assess the importance of indicators.

     
  2. Step 3:

    Compute aggregated fuzzy weights of each indicators.

     
Let \( {\widetilde{W}_{{jt}}} = \left( {{a_{{jt}}},{b_{{jt}}},{c_{{jt}}},{d_{{jt}}}} \right),j = 1,2, \ldots, n;t = 1,2, \ldots, k, \) be the linguistic weight given to the indicators C1, C2, ..., Ch. The aggregated fuzzy attribute weight, \( {\widetilde{W}_j} = \left( {{a_j},{b_j},{c_j},{d_j}} \right),j = 1,2, \ldots, n, \) of indicators Cj assessed by the respondents is defined as
$$ {\widetilde{W}_j} = \left( {{I_1} \otimes {{\widetilde{W}}_{{j1}}}} \right) \oplus \left( {{I_2} \otimes {{\widetilde{W}}_{{j2}}}} \right) \oplus \ldots \oplus \left( {{I_k} \otimes {{\widetilde{W}}_{{jk}}}} \right), $$
(1)
where \( {a_j} = \sum\nolimits_{{t = 1}}^k {{I_t}{a_{{jt}}},{b_j} = \sum\nolimits_{{t = 1}}^k {{I_t}{b_{{jt}}},{c_j} = \sum\nolimits_{{t = 1}}^k {{I_t}{c_{{jt}}},{d_j} = \sum\nolimits_{{t = 1}}^k {{I_t}{d_{{jt}}}} } } } \).
The degrees of importance (or reliability) of decision-makers are It, t = 1, 2, ..., k where It ∈ [0, 1] and \( \sum\nolimits_{{t = 1}}^k {{I_t} = 1} \). In this paper, all decision-makers are carried an equal importance and reliability (since this committee is considered as homogeneous group) and the value of It, t = 1, 2, ..., k where k is number of the decision-makers is \( {I_1} = {I_2} = {I_3} = {I_4} = \frac{1}{4} \).
  1. Step 4:

    Defuzzify the fuzzy weights of individual indicators.

     
To defuzzify the weights for the fuzzy indicators, the signed distance is adopted from (Yao and Wu 2000). The signed distance of trapezoidal fuzzy number \( \widetilde{A} = \left( {a,b,c,d} \right) \) is defined as
$$ d\left( {\widetilde{A}} \right) = \frac{1}{4}\left( {a + b + c + d} \right). $$
The defuzzification of \( {\widetilde{W}_j}, \) denoted as \( d\left( {{{\widetilde{W}}_j}} \right), \) therefore given by
$$ d\left( {{{\widetilde{W}}_j}} \right) = \frac{1}{n}\left( {{a_j} + {b_j} + {c_j} + {d_j}} \right),j = 1,2, \ldots n. $$
(2)
From the perspective of membership grade, the signed distance method is superior to the centroid method for defuzzifying a fuzzy number (Yao and Chiang 2003).
  1. Step 5:

    Compute the normalized weights and construct the weight vector.

     
The crisp value of the normalized weight for indicators Cj, denoted as Wj is given by
$$ {W_j} = \frac{{d\left( {{{\widetilde{W}}_j}} \right)}}{{\sum\nolimits_{{j = 1}}^n {d\left( {{{\widetilde{W}}_j}} \right)} }},j = 1,2, \ldots, n, $$
(3)
where \( \sum\nolimits_{{j = 1}}^n {{W_j} = 1} \). The weight vector W = [W1, W2,..., Wn] is therefore formed.
  1. Step 6:

    Establish ranking order of indicators’ weights.

     

The six-stepwise procedure is applied in computation of the following experiment.

An Experiment

An experiment was conducted to elicit linguistic judgment over the health related status of CKD patients. Four DMs composed of a medical officer (D1) and three nurses (D2, D3, D4) were voluntarily formed the group of experts. All DMs are employed at a kidney patient ward in a Malaysian government funded hospital. DMs were asked to express their opinion in health related problem among the patients based on a guided interview. The closed ended questions of the interviewing process were developed by the authors, based on literature in HRQoL and also based on the SF-36 questionnaire proposed by Hill et al. (2007). There were eight indicators of HRQoL in the questionnaire and DMs need to make their decisions about the health related problem with respect to the eight health related indicators among CKD patients.

DMs need to respond in five linguistic scales from ‘never has a problem’ to ‘always has a problem’ to indicate their views over experiences of health related symptoms of eight indicators among CKD patients. Linguistic scales and their respective trapezoidal fuzzy numbers are given in Table 1.
Table 1

Linguistic variables and fuzzy numbers for the importance weights

Linguistic variables

Trapezoidal fuzzy numbers

Never (N)

(1,1,1,2)

Almost Never (AN)

(1,2,2,3)

Often (O)

(2,3,3,4)

Sometimes (S)

(3,4,4,5)

Almost Always (AA)

(4,5,5,5)

Analogously, fuzziness of judgments among the group of DMs can be translated to TFNs. The flexibility of linguistic judgment and their TFNs for the indicators can be observed in Fig. 1.
https://static-content.springer.com/image/art%3A10.1007%2Fs11482-010-9133-3/MediaObjects/11482_2010_9133_Fig1_HTML.gif
Fig. 1

Trapezoidal fuzzy numbers (TFN) to represent judgment score of the indicators

The eight indicators that used in the research are physical functioning (C1), role-physical (C2), bodily pain (C3), general health (C4), vitality (C5), social functioning (C6), role-emotional (C7) and mental health (C8). The Physical functioning (C1) is a ten-question scale that captures abilities to deal with the physical requirement of life, such as attending to personal needs, walking, and flexibility. Role-physical (C2) is a four-item scale that evaluates the extent to which physical capabilities limit activity. The bodily pain indicator (C3) is a two-item scale that evaluates the perceived amount of pain experienced during the previous 4 weeks and the extent to which that pain interfered with normal work activities. The indicator of general health (C4) is a five-item scale that evaluates general health in terms of personal perceptions. Vitality (C5) is a four-item scale that evaluates feelings of pep, energy, and fatigue. Social functioning (C6) is a two-item scale that evaluates the extent and amount of time, if any, that physical health or emotional problems interfered with family, friends and other social interactions during the previous 4 weeks. The indicator of role emotional (C2) is a three-item scale that evaluates the extent, if any, to which emotional factors interfere with work or other activities. Lastly mental health (C8) is a five-item scale that evaluates feelings principally of anxiety and depression. The eight indicators are highly considered as an essential elements in measuring impact of health related problems to the CKD patients.

The proposed step-wise procedure (see The Proposed Decision Making Method) is developed after considering two states of the experiments. The first state is rating and the second state is aggregation. In the rating state, DMs express their opinions (or performance ratings) of indicators with respect to their patients quality of life using via a guided interview. These ratings are fuzzy data that can be linguistic terms or verbal assessment. This state aims to convert fuzzy data into trapezoidal fuzzy numbers. In the aggregation state, fuzzy numbers of the indicators are aggregated to obtain the indicators’ weights. In short, aggregation state is a prerequisite process in finding weights.

Summarily, flow of the experiment can be depicted in Fig. 2.
https://static-content.springer.com/image/art%3A10.1007%2Fs11482-010-9133-3/MediaObjects/11482_2010_9133_Fig2_HTML.gif
Fig. 2

The conceptual model of the experiment

The vital part of this conceptual model is how the computation is carried out. Details of computational steps and results are explained in the following section.

Computations and Results

The steps proposed in “The Proposed Decision Making Method” are executed in the following manner.
  1. Step 1:

    Define Linguistic Variables

     
Linguistic variables and their respective fuzzy numbers are defined (see Table 1).
  1. Step 2:

    Introduce the importance weights of Indicators

     
Four decision makers are sought to provide importance weight for each indicator in linguistic variables. Inputs from decision makers are given in Table 2.
Table 2

The importance weights of the indicators

Indicators

Decision makers

D1

D2

D3

D4

C1

N

N

O

AN

C2

N

AN

AN

N

C3

AN

O

S

N

C4

O

AN

O

AN

C5

N

AN

O

O

C6

N

N

O

AN

C7

AN

AN

O

O

C8

S

AN

O

AN

  1. Step 3:

    Compute Aggregate Fuzzy Weights (AFW)

     
Based on the assessment values in Table 2, fuzzy weights of individual indicator are computed using Eq. 1. Aggregated fuzzy weights are obtained as Table 3.
Table 3

The fuzzy weights of the indicators and the aggregated fuzzy weights

Indicators

Decision makers

AFW

D1

D2

D3

D4

C1

(1,1,1,2)

(1,1,1,2)

(2,3,3,4)

(1,2,2,3)

(1.25,1.75,1.75,2.75)

C2

(1,1,12)

(1,2,2,3)

(1,2,2,3)

(1,1,1,2)

(1,1.5,1.5,2.5)

C3

(1,2,2,3)

(2,3,3,4)

(3,4,4,5)

(1,1,1,2)

(1.75,2.5,2.5,3.5)

C4

(2,3,3,4)

(1,2,2,3)

(2,3,3,4)

(1,2,2,3)

(1.5,2.5,2.5,3.5)

C5

(1,1,1,2)

(1,2,2,3)

(2,3,3,4)

(2,3,3,4)

(1.5,2.25,2.25,3.25)

C6

(1,1,1,2)

(1,1,1,2)

(2,3,3,4)

(1,2,2,3)

(1.25,1.75,1.75,2.75)

C7

(1,2,2,3)

(1,2,2,3)

(2,3,3,4)

(2,3,3,4)

(1.5,2.5,2.5,3.5)

C8

(3,4,4,5)

(1,2,2,3)

(2,3,3,4)

(1,2,2,3)

(1.75,2.75,2.75,3.75)

  1. Step 4:

    Defuzzify the AFWs

     
Compute the defuzzified values of the AFWs using Eq. 2. The defuzzified values for each indicator are given in Table 4.
Table 4

The defuzzified values of the aggregated fuzzy weight

Indicators

C1

C2

C3

C4

C5

C6

C7

C8

Defuzzified values

1.875

1.625

2.5625

2.5

2.3125

1.875

2.5

2.75

  1. Step 5:

    Normalized the Fuzzy Weights

     
Normalization of indicators can be made using the Eq. 3. The normalized weights are given in Table 5.
Table 5

The normalized weights of indicators

Indicators

C1

C2

C3

C4

C5

C6

C7

C8

Normalized weights

0.1042

0.0903

0.1424

0.1388

0.1285

0.1042

0.1388

0.1528

  1. Step 6:

    Establish Ranking Order for Indicators

     
The normalized weights for indicators are finally ranked. The weights of indicators and ranking order can be seen in Table 6.
Table 6

Weights and ranking order for the indicators

Indicators

Weights

Ranking order

Physical Functioning

0.1042

2

Role-physical

0.0903

1

Bodily pain

0.1424

5

General health

0.1388

3

Vitality

0.1285

4

Social functioning

0.1042

2

Role-emotional

0.1388

3

Mental health

0.1528

6

Table 6 shows the weights and ranking order of the indicators for the health-related quality of life among CKD patients. The indicator C8 poses the most problematic indicator to the CKD patients. It should noted that mental health indicator (C8) consist of five-item scale that evaluates principally feelings of anxiety and depression. CKD patients’ especially elderly people who already burdened by the disease that they have will easily fall into depression and feelings of anxiety caused by their self-administration that may be more difficult (Zadeh and Unruh 2005). Meanwhile, C2, which is the role-physical indicator, gives the smallest impact to the CKD patients to their health quality. This means that the patients did not care too much about their role-physical and had the least impact to their quality of life. The results also show the same ranking order for physical functioning (C1) and social functioning (C6). The other two indicators general health (C4) and role-emotional (C7) also shared the same ranking order.

Conclusion

There are many approaches that have explored health related quality of life indicators. This paper has developed a decision making approach based on fuzzy linguistic judgment to evaluate health related quality of life among chronic kidney disease patients. The simplified version of Fuzzy Simple Additive Weight was employed to decide weights for the eight indicators of health related quality of life. A group of decision makers was assigned to evaluate the status among chronic kidney disease patients over the eight indicators using the five linguistic judgments. The proposed six-stepwise method has successfully identified the weights for indicators. Of the eight indicators, mental health received the highest weight followed by bodily pain. The results indicate that heath related status among chronic kidney disease patients were heavily burden by mental depression and anxiety. Normal work activities among patients were also limited due to their bodily pain. The weights for indicators emphasize the feasibility of using a decision making approach in manipulating expert experiences and judgments in order to fully understand the severity of health related problems among chronic kidney disease patients. The practical implication of these findings is that perhaps equal attention should be focused not only to improvement of their physical pains but could be extended to their mental or psychological status. The advantage of this study lies upon the decision making approach used where the patients are not directly the sample of the study. Therefore making inference to general sample of patients or of the general population is apparently a limitation of this study.

Acknowledgements

The authors thank to the Ministry of Higher Education, Malaysia under the Fundamental Research Grant Scheme, no. 59148 for financing this project.

Copyright information

© Springer Science+Business Media B.V./The International Society for Quality-of-Life Studies (ISQOLS) 2010