•
STATISTICS AND QUALITY OF LIFE:
THIRD WORLD PERSPECTIVES
by
PRANAB KUMAR SEN
Department of Biostatistics
University of North Carolina
Institute of Statistics
Mimeo Series No. 2148
..
May 1995
STATISTICS AND QUALITY OF LIFE: THIRD WORLD PERSPECTIVES
BY
•
PRANAB KUMAR SEN
SUMMARY
The socio-economics, standard of living (in the poverty/affluence differential)
reflects the quality of life, while in health care and management, physical, socioenvironmental, psychological and mental health perspectives dominate the scenario.
Chronic diseases, autism and other developmental disabilities, congenital anomalies,
occupational hazards related disabilities, prevalence of AIDS, cancer, arthritis, disorders
requirin~ organ transplants and major surgeries, and many other incurable
diseases/disorders have profound impact on quality of life not only for individuals
affected but also of a society/community/country where they live. Although, quality of
life standards and preserving measures vary from industrialized countries to the third
world ones, they all are confronted with the basic challenging task: Subject to
prevailing natural resources, socio-economic setups and technological advances, how to
maintain (and improve) the quality of life? Statistical perspectives in this complex task
are critically appraised with due emphasis on quality gap ratio and quality of life
deficiency concepts.
AMS Subject Classifications: 62P10, 92C60, 92D30.
•
Key words and phrases: Affluence; aging; AIDS; ARA-Scale; arthritis; autism; cancer;
chronic disease; competing risk; congenital anomalies; cost-benefit; cultural impact;
disabilities; ecology; (harmonic-) Gini coefficient; health services and resources;
Karnofsky-scale; mental health; poverty; psychology; public health; QAL; quality
gapratio; QOLD; religion, statistical issues and perspectives; utility; WHOQOL.
1. INTRODUCTION
It is difficult to prescribe a precise definition and quantitative interpretation of
Quality of Life (QOL) of a society/community/country, although in a specific context
and/or on a subgroup basis, QOL can be defined more formally. The genesis of QOL is
probably in the socio-economics, particularly, in the context of quantitative assessments
of standard of living and/or wealth or real income; the popular poverty indexes [viz,
A.K. Sen (1976)] and measures of income inequity have distinct QOL flavors. In this
sector, however, there is a significant impact of a complex of factors ranging from social,
cultural religious as well as mental health perspectives. although these undercurrents
have been well recognized for quite sometime, a concrete quantitative assessment of
their impact has yet to be made properly. Even in the economic sector, measures of
real income (wealth) and/or poverty/affluence hinge so much on various qualitative
factors that without proper identifications of all these traits, any assessment may only
be of some marginal interest. Essentially, in this setup, the QOL picture is grossly
incomplete and unrealistic too. This criticism may be labeled more particularly to third
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world countries where there is even a greater need for an assessment of QOL in the
socio-economic sector.
In health (care, services and management) and medicare sectors, particularly in the
industrailized countries, QOL has emerged as a workable measure of quality of life of
individuals who are already afflicted with a specific disease/disorder for which QOL is
Although
sought as a convenient tool for assessment of the aftermath.
poverty/ affluence and health care system are intimately relted to such a measure of
QOL, they may not have a one-to-one relationship with the prognosis of such diseases or
disorders. Therefore, the conventional poverty or income inequity indexes may not be
of much utility in the assessment of QOL in the health sector. Nevertheless, both the
approaches related albeit partially) to a general theme: How to assess the well being Qf
~ society/community/country not only in terms of economic conditions, but also with
respect to diverse sociological. cultural. religious, mental health, physical. socioenvironmental and psychological health aspects?
Viewed from this broader perspective, it appears that there is a genuine need to
amalgamate the QOL measures for various sectors with due emphasis on their linkage in
order to developing a more comprehensive measure of QOL for the entire population,
In this task, it may be noted that in view of the significant increase in the awareness of
public health, ecological and environmental aspects of QOL, a meaningful measure of
overall QOL needs to incorporate the full impact of all these ingradient factors. Thus,
the diverse measures of QOL for diverse diseases/disorders in the health sector and
indexes for real income/poverty in the socio-economic sector need to take into account
the complex interactive system of a society/community/country, so that they relate to
a more meaningful picture. In veiw of the gulf of differences in social, cultural and
religious patterns in the third world countries and the industrialized ones, this
interactive factor may emerge as the most important one in a proper assessment of
QOL of third world countries. Therefore, it has become necessary to analgamate the
entire battery of socio-economic, clinical, biomedical, biotechnological, public health,
environmental and ecological factors in the formulation of a valid, comprehensive and
workable measure of QOL. Yet, there are impasses along each of these avenues, and
statistics is in dispensible for achieving a meaningful resolution.
The Division of Mental Health of the World Health Organization (WHO) has
undertaken a project: WHOQOL, for measuring (and improving) QOL, and adopted
the following interpretation: "Quality of Life is defined as an individual's perception of
their position in life in the context of the culture and value systems in which they live
and in relation to their goals, expectations, standards and concerns. It is a broad
ranging concept affected in a complex way by the person's physical health,
psychological state, level of independence, social relationships, and their relationships to
salient features of their environment. The instrument is to measure quality of life
related to health and health care" [viz., WHOMNH/PSF/93.9].
Such an interpretation is certainly a novel and bold step towards a more
comprehensive view of QOL. Nevertheless, it has already been identified as a measure
primarily for the health sector with some emphasis on the socio-economic factors. The
WHOQOL definition works out well in cases where a jackup of QOL is needed following
the occurrence of a disease, such as the prostate cancer (for males), breast cancer (for
females), epilepsy, Parkinson's disease, or major surgeries, such as organ transpolants,
bypass surgeries, and other major medical treatments, where a "perfect repair model"
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may not sound very reasonable. This has led to the formulation of the concept of
Quality adjusted life (QAL) which is often adapted by the medical community as a
measure of the medical and psychological adjustments which are needed to induce an
affordable QOL for patients undergoing such health problems. The dual QOL/QAL
measures are being increasingly adopted as a convenient working rule by the medical
community, especially in the industrialized countries. However, the QOL/QAL concept
primarily relates to an individual's perception, whereas for a society/
community/country, any such measure should focus on the entire population which may
then be stratified into various sectors with due emphasis on their importance as well as
relevance. Thus, a composite QOL measure with due emphasis on the population
rather than the individuals seems to be more appropriate. Often, the various individual
or specific causes can not be treated in isolation. In statistical terminology, we refer to
a competin~ risk setup which incorporate such multiple factors, where the individuals
may be susceptible to a variety of (interacting) risk factors which should not be treated
in isolation. In WHOQOL framework, a good deal of diversity has been aimed at, and
the recent annotated bibliography [WHO /MNH/PSF/94.1] is an important source of
such vital developments. Special mention may also be made of the new journal:
Quality 2f Life Research, which started appearing in print only in 1993. About the
same time, Walker and Rosser's (1993) (edited)) monograph on the same topic has
enlisted important issues by prominent researches in this developing field. Yet, in all
these developments, the primary emphasis has been on clinical trials, oncology, health
The picture has mostly been drawn through
care and health management.
observational studies with specific dysfunctionings in mind and mostly treating them in
isolation. There is ample room for sound statistical reasonings to addressing the
underlying complexities in a valid and more comprehensive manner, and this is
intended to be explored here.
Statistical Science has its rats in all the disciplines relevant to the QOL assessment,
and yet, it has a characteristic ability to formulating a rational quantitative approach
towards blending the diverse concepts and interpretation in a workable manner. In this
statistical assessment, the a~in~ aspect of a society, its mental health, social and
economic environment, religious and cultural heritage all play a vital role.
Advancements in modern science and technology (with special emphasis on
biotechnology and computer-intensive technology) have created some challenging socioenvironmental problems and tasks, where statistics is indispensible. As such, in Section
2, the role of statistics in the assessment of QOL in a broader perspective is critically
appraised. The triple-E: economics, ecology and environment, deserve a thorough
discussion in this context, and Section 3 is devoted to this scheme. QOL in health care,
service and management has received due attention from the health sciences community
under the patronage of the WHO, and in Section 4 the main highlights are presented.
There is a need to foster more interaction between the two approaches. The last section
is devoted to a critical appraisal of the current status of QOL assessments and the
prospects for a more comprehensive resolution. In this context, the concepts of quality
~ ratio (QGR) and quality of life deficiency (QOLD) are formulated properly and
incorporated in the main statistical appraisal of the QOL picture. Throughout the
presentation, emphasis is laid down on third world perspectives; there is even a greater
need for such QOL assessments in the third world.
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2. WHITHER STATISTICS IN QOL
The QOL of a Society (\community\country) should reflect the quality for each
sector of its population as well as the impact of each force/factor governing the society;
the sectors may not necessarily be demercated by economic/social\cultural\religious
boundaries alone, and the impact of health and environmental strata should be clearly
incorporated in this formulation. Also, the measure of well being should not only be in
the conventional standard of living (i.e., economic sense) and in the health aspects, but
also be attentive to various other aspects having some relevance to QOL. The
complexities of a modern society whether occidnetal or oriental, the advent. of
industralization in a greater part of the world, the human endeaver to conquer the
Nature through the Biotechnological Revolution, and the environmental threats have
made the life on this planet far more complex than a few decades back. For this reason,
we need to draw a more composite picture of QOL. The following figure attempts to
depict the QOL foundation.
Fig. 1
The QOL Interface
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The cultural, religious and sociological perspectives in QOL have been recognized for
quite a long period of time, albeit these have been subdued to a greater extent by
economic perspectives leading to the formulation of standard of living (hinging
primarily on poverty/affluence differentials).
In this context, social economics,
developmental economics, and economic theory have all mingled to a certain extent
with adequate impacts from social, religious and cultural factors, and yet there is ample
room for more coordination of these social sciences for a proper assessment of QOL. In
this complex, aging aspects of a society as well as its mental health perspectives have
profound impacts, and, in turn, these are also related to ecology and environment. In
Section 3, such social sciences perspectives in QOL are appraised with due emphasis on
some aspects of environmental sciences which are closely related to social aspects.
Typically, the environmentrics are more visibly related to medicine, technology and
health sciences which occupy a prominant quarter in QOL. The complexities of modern
life have cropped up from all sectors: Industrialization to biotechnology leading to the
evolution of toxicology; ecological imbalance and disorders; the entire field of public
health where epidemiological and ecological under-currents have merged into health
care, services and maintenances; the amalgamation of computer incentive biotechnology
with major clinical sciences; and a lot of other interdisciplinary sciences. It is quite
inappropriate to treat these sectors in isolation, and perhaps, Figure 1 may make it
easier to comprehend some vital linkage between these apparently disjoint sectors.
These complex interactive factors are· inducing environmental evolution and, often,
deteriorations of QOL in rather indirect ways. For these reasons, the WHOQOL
project, albeit being very valuable in its own way, may not be adequate to provide a
total picture of QOL. The health sector is, however, the most complex one, and in
Section 4, we provide a broad review of some contemporary developments of QOL
assessments in this domain. The composite picture in Figure 1 calls for more intensive
examination of modern Statistical (planning and inference) methodology. The QOL
picture varies from society to society and over time in any society/country, and yet,
there is a genuine need to draw a composite picture with especial emphasis on third
world countries where there is even a greater need for assessment of QOL. This
assessment may enable us to bridge the widening gap between industrialized and
developing nations in their endeavor of reaching for a common platform to measuring
QOL as well as interpreting the standard of living in a rational manner. This is the
primary goal of this (statistical) overview.
3. SOCIO-ECONOMIC-CULTURAL PERSPECTIVES IN QOL
Assessment of real income on wealth of individual families or households has long
been an important yardstick for not only revenue (or taxation) purposes, but also for
depicting the overall well being (i.e., the poverty/affluence structure) of a
society/community/country. Yet, this has never been an easy task, even in the most
developed countries. The very definition and (broad) interpretation of wealth or real
income hinge on various arbitrations of social, cultural, religious and health
perspectives, and these factors call for a far more complex formulation than the usual
ones adopted in practice. For example, real incomes of households in the agricultural
sector and in industrial sectors may be quite different, and in this spectrum, the
rural/urban differential is also profound.
Moreoever, the socialistic blocks and
capitalistic ones have different income systems, and thereby there are additional
complications in a mutually agreeable formulation of real income for both the systems.
In this context, any prevailing health care system for a society as well as a social
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security system system may make the situation quite different. Religious attitudes and
beliefs may also call for adjustments: The Mormons in USA are known to have a
different life style atuned to their religious beliefs, while in a third world country, like
India, religious attitudes towards population control have significant impacts on QOL.
It is clear from the above discussion that the very formulation of real income is
based on the complex of interactive social, cultural religious and (public) health
perspectives.
Thus, farm income, salary and wages and other purely monetary
measures by themselves may not be adequate for this purpose. For this reason,
statistical considerations are of utmost importance in fortifying the foundations of real
income, which is a basic element for economic (and statistical) analysis of many socioeconomic models. In the socio-economic perspective, the standard of living is the
precursor of QOL. Like the real income, standard of living is also based on a multitude
of factors embracing economic, social, cultural, religious and health perspectives. In
this context, poverty is defined as the extent to which individuals in a
society/ community/ country fall below a minimal acceptable standard of living, so that
it can be quantified in terms of the proportion of the poor people and their income
inequity. In a similar manner, affluence is defined in terms of the proportion and
income inequity of the rich or affluent people whose real income or wealth are far above
the acceptable range of the middle class people who confirm to a median pattern in
standard of living. In these quantifications, not only a meaningful resolution of real
income of individuals/families in terms of a single quantitative criterion is essential, but
also arbitration of poverty and affluence lines in terms of real income is a key factor.
Moreover, some measure of concentration or dispersion of wealth among the poor (and
rich) people is needed to depict a more real picture of poverty/affluence beyond the
crude ones provided by the proportion of such people. As is the case of measurement of
real income, proper arbitration of poverty/affluence lines rests on various social cultural,
religious and psychological perspectives, which may vary considerably from a society to
another, and these differences are even more noticable in third world countries. The
standard of living in a third world country may not match an industrialized nation,
even when the real incomes are adjusted by monetary transaction rates or GNP factors.
There are basic qualitative differences with respect to prevailing cultural, social and
religious attitudes as well as social mental health well beings. More comments on it will
be made later on.
Suppose now that with proper safeguards on interpretation and mensuration of real
oncome (Y), we have an income distribution F(y), y ~ 0, for a society/community, and
p and 11' be the poverty and affluence lines, also fixed according to some well formulated
concepts and criteria. Then
a = a p = F(p) and / =
/11'
= 1 - F(1I') = F(1I')
(3.1)
be respectively the proportion of poor and affluent people. These are very crude
measures of pvoerty and affluence of society, as they do not take into account the
inequity within the class. Note that the income distribution of the poor is given by
Fa(Y) = a-1F(y) for y ~ p, and 1, for y ~ p. Thus, the average income 2f the poor is
equal to
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Pa
= Jg ydF a(y) = a-I Jg ydF(y)
=a- 1 {pF(p) -
= a- 1pa - a-I
=p -
Jg F(y) dy}
J g F(y)
dy
a-I JgF(y)dy.
Therefore the income
(3a
~
=
(3.2)
ratio of the poor is given by
(p -Pa)/P
=1
_(pa)-1
Jg F{y) dy.
(3.3)
Side by side, for an income distribution F, the Gini coefficient G{F) (of Income
inequality) is defined as
(3.4)
where y l' Y 2 are two independent random variables, each following the d.f.F. In the
same manner, we may define G a = G(F a) and G, = G(F,) for the poor and affluent
income distributions. Then, typically, an index of poverty is based on the triplet (a, (3a'
G a ). Based on a set of (mostly, economic) axions, A.K. Sen (1976) advocated the
following two indexes of poverty
(~) = a(3a = income gap ratio adjusted proportion of the poor;
(3.5)
(~)
(3.6)
= a {(3a
+ {I
- (3a) G a }·
There are some alternative measures, and, a modification of (~ is the following:
,
(~) =
(3.7)
a (31- G a ,
[viz., Sen (1986)], which is a geometric mean, instead of an arithmetric mean in (3.6).
Robustness aspects of these indexes were studied by Sen (1986). If follows that
o < (~) ~ (~) ~ (~) ~ (~)
(2 -
(3a)
~
a
(3.8)
A somewhat different formulation is made for the case of affluence indexes,
income distribution of the rich people is truncated from the left, i.e.,
F ( ) = {[F(Y) - F(1I"))/[1-F(1I")], Y ~ 11",
,y
0,
y < 11".
as
the
(3.9)
Thus, the average income of the rich is equal to
P,
= J~ ydF,(y) = ,-1 J~ ydF(y).
= ,-1{1I" F(1I") + J~ F(y) dy}
=11"+,-1
J~F(y)dy.
(3.10)
Since 11" is < P,' we need to define the affluent income gap ratio in a different manner.
Sen (1988) defined this as
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7r)/ Il, = 1 -7r/ Il,
[3, = (Il, -
= 1 - ,7r ( J ~ ydF(y)) - 1,
(3.11)
which has a distinct 'harmonic mean' flavor. In view of this for a left truncated
(censored) income distribution, a nonnegative utility function u(t 1 , t 2 ), nondecreasing in
each t 1 , t 2 , has been incorporated in the formulation of a utility-oriented Gini coefficient
(for a distribution F):
G * = {E[u(Y 1 , Y2 )IY 1
F
-
Y2 11/E[u(Y 1 , Y2 ) (Y 1
+ Y2 )]},
(3.12)
where thy independent Y 1 , Y 2 both have the d.f.F. In particular, on letting u(t 1 , t 2 )
(t 1 , t 2 ) - ,we have the harmonic Gini coefficient:
G~* = {E[lY1
Thus, for F
=F"
-
Y2 1/(Y1 , Y2 ,)1/E[Y 1
+ Y2 )/(Y 1 Y2 )]},
=
(3.13)
defined by (3.9), G~* is defined accordingly. Side by side, we may
,
introduce the harmonic mean income of the rich by
(3.14)
so that parallel to (3.11), we have an alternative measure
[3~
=1
- (7r/,)
(J ~ y -
1 dF(y)).
(3.15)
Thus, parallel to (3.5), (3.6) and (3.7), one may consider the affluence indexes:
(~1)
=
,[3~,
(3.16)
(3.17)
(3.18)
we may refer to Sen (1988) for some detailed motivation and discussion. In this
context, we may mention a closely related measure, known as the Gastwirth (1973)
coefficient, which may be defined as
(3.19)
F
Unlike the Gini coefficients, G may not be directly obtainable from the Lorenf C'Wve
(for F). Nevertheless, it has a nice invariance property that for boty Y and Y
,G F is
the same.
It is clear from the above discussion that these indexes depend on the underlying
income distribution (of the poor/rich) in a relatively complex manner (i.e., not simply
on the proportion a or , or the mean income Ila or Il ), and in that way, they try to
adjust better the income inequity within the sectors. This feature is far more important
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in the context of quality of life, as will be discussed in the next two sections. Another
basic feature of the indexes referred to before, not so advantageous for the current
study, is the fact that they entail a precise definition and interpretation of real income,
its reliable assessment for individual families, and proper demarcation of the
poverty/affluence lines. As we shall see later on that in the context of standard of
living (or, more generally, QOL), such interpretations and assessments constitute the
major statistical roadblocks, and hence, our main objective would be to address these
issues properly. We conclude this section with a final remark that although health
aspects occupy a prominant quarter in a broad interpretation of standard of living, in
the conventional setup, they are only taken into account in the definition of real income
(by allowing adjustments for health insurance, medical expenses and related items). As
such, in a proper interpretation of QOL, there is ample room for emphasizing the health
aspects along with the socio-economic ones.
4. QOL IN HEALTH PERPSECTIVES
It has been noted earlier that the WHOQOL interpretation emphasizes the
"individual's perception of their position in life in the context of culture and value
systems in which they live and in relation to their goals, expectations, standards and
concerns". The WHO aims to develop an instrument to measure QOL related to health
and health care, incorporating physical health, psychological state, level of
independence, social relationship and other socio-environmental considerations in a
broader, comprehensive and reliable manner. In this context, although "standard of
living" surfaces in each of the sectors referred to above, its primary emphasis on the
poverty--affluence differential is lost.
,
A few decades ago, physicians and clinical researchers noticed the inadequacy of
traditional measures of mortality and morbidity in their assessment of health status in
some chronic diseases. Such assessments were particularly pertinent in making a
decision, in a specific context (i.e., disease or patient groups), such as cancer,
cardiovascular disease and the elderly, for an individual's treatment. This led to the
evolution of some measures of "ill health" on an individual basis and for specific type of
diseases or disorders. The Karnofsky-Scale in cancer [viz., Karnofsky and Burchenal
(1949)] and the American Rheumatism Association (ARA- )Scale in arthritis [viz.,
Steinbrocker, Traeger and Battman (1949)] are notable examples of such precursors of
QOL. The National Center for Health Services Resources (USA) developed schemes for
studying effectiveness and economic costs of health services in USA, and sooner similar
studies were initiated in other developed countries; the picture is not so clear for a
majority of the third world countries, where there is even a greater need for such
assessments.
Developments of these QOL measures focus primarily on alternative uses of
resources and their benefits. In developed (industrialized) countries, inspite of having
adequate manpower and medical technology, the cost of health services and medicare is
escalating at an alarming rate, beyond the affordibility range for a greater sector of the
population, and hence, cost-benefit aspects of health care are on the forefront of
considerations by the health regulatory agencies and medical practitioners as well. In
this context, any alternative use of resources and its benefit naturally requires a close
scrutiny from medical, economical as well as social points of view, and QOL is the focal
issue in such explorations.
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At the present stage, the focus on assessment of QaL is primarily on specific
diseases (such as cancer, AIDS etc) and on the individuals afflicted by them. The first
and foremost task in this repsect has been the development of measurement tools for
QaL. The primary difficulties stem from the facts that there are generally many
outcome variables (or responses) which are needed to be taken into account in QaL
assessment; these response variables are, often, quite interacting and may even be
Thus, the question of synergism" remains pertinent to an
competing in nature.
assessment of QOL.
Furthermore, many of the response variates are either
binary/polychotomous or ordinal in nature. These may call for nonstandard statistical
modeling as well as analysis wherein measurement lli.Q!.§. and misclassification of states
are generally prevalent. The QaL assessments are generally made with respect to
specific objectives, and these are, often, not precisely formulated prior to data
collection, thus raising concern over the validity and reliability issues. For example,
standard QaL assessment questionnaires relate to a set of questions, with a 5 point
qualitative scale, divided into broad sectors: physical well-being, social/family wellbeing, functional well-being, emotional well-being and relationship with the attending
medical personnels: doctors, nurses, etc. Naturally, the picture may vary considerably
from one disease to another, and also may vary considerably with the age/sex and other
socio-economi. dors affecting the individuals under consideration. Therefore, there is
a genuine need tu emphasize properly on the most important and relevant questions for
the specific disease or disorder under focus.
It is very unlikely that the same
questionnaire may be appropriate for two or more disorders, even if they belong to a
common class. For example, for lung cancer, prostate cancer and breast/uterus/ovarian
cancer, the symptoms are somewhat different and so are the response variates.
Therefore, a first and foremost task is to identify (mostly, from medical and therapeutic
considerations) the most relevant factors and to frame the questionnaire in such a way
that it addresses them the most. Note that in order to be effective, a questionnaire
should be based in as much simple terms as possible, and, at the sametime, it should be
as brief as possible. In this quest, statistical planning (or design of a questionnaire) is
an essential task. Unfortunately, until very recently, this vital task has mostly been
overlooked by the medical/health care systems, and we can not simply ignore this
primary requirement.
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In the above mentioned setup, related to a specific disease or disorder, the
WHaQOL interpretation relates to an individual who is already affected by the same
and is expected to have a sub-standard QaL as well as reduced residual life. This
feature of QaL assessment relates to a multitude of factors:
(i)
Multiple response variates covering diverse aspect of the disorder;
(ii)
A follow-up scheme to judge the progress over time, resulting in repeated
measurement designs or the so called longitudinal studies;
(iii) Due to noncompliance or other factors, dropout or withdrawal is generally
common--and this incompleteness may not be taken for granted as purley random in
nature. Thus, random censoring schemes may not be that pertinent.
(iv) Due to the nature of response variates, as has been explained earlier, it may
be quite inappropriate to appeal to some standard parametric models for drawing
statistical conclusions. Even linear models. log-linear models and generalized linear
models are often judged inadequate in this context. The so called semi-parametric
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models are also subject to similar criticism. While nonparametrics appear to have a
greater scope for adoption in this context, it should be clearly kept in mind that the
usual regularity assumptions governing them may not be reliable here, and hence, extra
care may be needed to enhance reliability and validity aspects of such assessments. For
example, for the same individual, observations at successive points of time may not be
independent or identically distributed, and moreover, at each timepoint, there may be
multiple measurements which may be sensibly stochastically dependent on each other.
A comprehensive statistical measure should therefore address these issues carefully.
Multivariate nonparametric methods are potentially more useful in this respect.
(v) QOL assessments over a time-period (as is generally the case) should also
reflect the pattern of change over time, so that proper clinical adjustments are to be
made so as to update the QOL picture as far as feasible. Often, such medical ethics and
practice run contrary to statistical intuitions (as they are based on different
perspectives). Since biomedical undercurrents are more prominent in QaL assessments,
statisticians are therefore charged with the challenging task of developing appropriate
methodology and analysis schemes to handle such complex data.
(vi) As of now, mostly, such QOL assessments are geared towards alternative
health services resources and their benefits. However, as we shall see in the next
section, we encounter here a more complex objective when viewed from a
population/society perspective, and in view of this, most of the simple measures of
QOL, available in the literature, may need considerable modifications to suit our goals.
Keeping all these factors in mind, we consider the following formulation of a QaL
assessment model from an individual's perspective and relating to a single specific
disease/ disorder.
Broadly speaking, we have a four-phase QOL assessment scenario:
(i)
(ii)
(iii)
(iv)
Pre-therapy stage: QOL assessments often lead to a proper therapeutic
course.
On going therapy stage: Watch for toxicity/side-effects and emergency
options.
Post therapy stage, I: While being still under medical care, assessment of the
therapeutic actions on QOL.
Post-therapy stage, II: Long-range standing on QOL.
At each stage, WOL assessment involves a number of response variables (along
with some auxiliary variables as well as concomitant ones), all of which may not be
continuous in nature or may even be qualitative to a certain extent. Thus, we assume
that at the ith stage (i=I,2,3,4), we have a response vector ~. = (XiI' ... , Xi ), and a
set of concomitant variates ~.l = (Z'I' ... , Z· )" where p. ana q. are positivWintegers.
Moreover, ~e. have a variabie 0i_ 1,i \vhich rJ~es to th~ ~omplia~ce from stage i-I to
the stage 1, 1=1, ... , 4. thus, 00 1 = 1, whIle 1 2 IS equal to one only when the
individual enters to stage 2 from I'through compliance and survival; otherwise, we set
A similar interpretation is labelled to 62 3 and 2 4' Also, in general, the
1 2 = O. vector~.
covariate
may contain both non-stochastic (design' variates and stochastic
concomitant variates. If all the X·· are quantitative (i.e., discrete or continuous)
variates, it may be possible to introdJte suitable measures of central tendency to assess
the QaL on individual items. On the other hand, if for some j, Xij' is binary, a probit
°
°
°
11
or logit model can be adopted to quantify it in an appropriate manner. The situation is
slightly more complicated for polychotomores response variable, although Z (or normal-)
~ methodology from psychometry can be used with convenience in many situations.
In either case, there is a repeated measurement (assessment) flavor, and hence,
longitudinal data analysis models are often adopted for QOL assessments. Thus, at
stage 2, it may be quite natural to treat )5:2 as the (primary) response vector, while ~2'
~1' )5:1 are to be treated as covariates, ana in addition, the role of 8 2 should not Be
1
deempllasized. Similarly, at stage 3, )5:3 is the primary response vector, while )5:1' )5:2'
~1' ~2' ~3 are to be treated as covanates, and 81 _ , 8 3 are to be incorporated III
2 2
statistIcal modeling and analysis. The role of these~.. is not isomorphic to that of the
conventional missing variables, even when the latterI~re treated as random ones. For
such reasons, there has been some attempts to formulate suitable Markov (or
semiMarkov) models for such repeated QOL assessments. Nevertheless, because of the
high dimension of the )5:. and the ~i as well, such formulations are often quite complex
in nature. There are sobe other important considerations pertinent to this assessment
protocols:
(i)
QOL assessment for a individual relative to the group of individuals
experiencing a similar disorder, and
(ii) QOL assessment for an individual relative to the overall population belonging
to the same cohort group based on the covariates (viz., age, sex, etc.).
(iii) The emphases on QOL/QAL vs. length of life following the incidence of the
specific disorders.
Let us move to a more complex but statistically important problem. The QAL
picture relates to the life-style adjusted by the quality of various physical, social,
psychological and mental health perspectives following the incidence of a disorder. The
poverty/affluence differential, various poverty indexes, referred to earlier, not only
reflect the proportion of the poor people in their formulation, but also the "income gap
ratio", (Gini's) coefficients of income inequity and some other factors are incorporated
to induce various refinements. A very similar scenario relates to the QOL indexes as
well. With respect to each of the traits, the ability of a person to function adequately
or not, may either be represented by a binary response variable, or more generally, by
some polychotomores response variates. Thus, taking into account all the relevant
factors underlying QOL, we have generally a multiple polychotomres response vector.
Even for a multiple dichotomores response vector, interpretation and formulation of
suitable measures of association, central tendency and dispersion (of the underlying
traits) may require sophisticated statistical theory and methodology. On the top of that
formulation of "quality iM! ratio" and Gini-type measures of concentration for such
multiple polychotomores models may require even more sophisticated statistical
methodology. The setups of longitudinal data models and possible lack of compliance,
as have been discussed earlier, add more complexities in this formulation. Further, the
ARA-Scale or Karnofsky-Scale for arriving at an overall QOL measure (in the context of
a specific disorder/disease) from the multiple responses, may not be very suitable for
some other disorder, even if that may be related to the disorder for which such scales
are usually advocated. Even if the same (or a very similar) questionnaire is used to
assess QOL for two (possibly related) disorders/diseases, the relative weights to be
attached to the various components may depend on the specific case. Thus, for
designing such questionnaires, it is essential to take into account the various forms of
12
,
dysfunctionings which are likely to crop up in the post-therapy stages. Therefore,
standard statistical designs in agricultural, biometric or clinical studies may often be
inappropriate in QaL studies. In view of this, statistical analysis for QOL assessments
may often follow some non-standard routes. To illustrate this point, let us consider a
composite disease/disorder model. Like the misfortunes which always flock together,
various diseases or disorders affecting individuals in any society/community may also be
concordant. While addressing a primary source of disorder, it may be wise to take into
account possible secondary source(s), so that their impact on the QaL picture
pertaining to the primary source can be traced out to a greater extent, and proper
adjustments can thereby be made. This is a highly complex statistical task, not only in
terms of planning of the study but also from valid and efficient statistical analysis point
of view. Finally, health perspectives are closely related to social, cultural, religious and
economic perspectives, and hence, any QaL/QAL assessment in a health perspective
must take into account such undercurrents. In the third world, such undercurrents are
overwhelming, so that QaL assessments may face greater complexities and
uncertainties. The past few years have witnessed the growth of some statistical
literature on QaL assessments in clinical trials and cancer and related studies, and
some of these references were cited in the Bibliography. They provide us with a better
understanding of the QaL complex in the health sector, and we shall prOOOf"A to unify
them in a comprehensive manner, for a broader interpretation and working measure.
5. STATISTICAL ISSUES IN QOL AND COMMUNITY PERSPECTNES
It has been noted earlier that at the present state of developments, QOL measures
focus primarily on alternative uses of resources and their benefits, mostly in the health
care and management sector. Such an overall objective should not be limited to a
single source of disorder or disease, no matter how important it might be; nor, it should
treat such disorders/diseases in isolation and prescribe resolutions on a case by case
basis. Rather, the QaL assessment should encompass the spectrum of all major
disabilities, disorders and diseases, and, with due emphasis on their impact on the entire
society/ community, it should relate to specific as well as comprehensive overall
resolutions. Therefore, a comprehensive QaL assessment is highly sensitive to socioeconomic, cultural as well as religious factors governing the society, and hence, proper
safeguards are to be maintained in depicting such a complex and interactive
The QaL in socio-economic perspectives is indeed an important
phenomenon.
component of this omnibus task, specially in the third world countries, where poverty,
generally high illiteracy rate and other social roadblocks may severely limit the scope of
implementation of QaL measures in the health sector as well as its proper assessment
in a more comprehensive manner. QaL is interpretable in a socio-cultural sense where
the attitude towards life may itself be the most significant factor, and level of
education, socio-enviromental factors and religious beliefs may all be important
indicator-factors in this context. As such perspectives may vary considerably from
industrialized nations to third world countries, any assessment of QaL should pay
adequate attention to such socio-economic-cultural backgrounds.
The primary difference between individual and community perspectives in QaL
assessments is that a society/community should adopt a plan which can be
administered for the majority of its people, and not for only a fraction who can afford to
meet the expenses; therefore the QaL picture has to be assessed from a broader
perspective in a community plan. In this setup, it should be kept in mind that a
13
community may be suspectible to a variety of diseases, disorders and diverse disabilities
whose impacts are therefore to be judged from a population aspect (rather than
individual aspects). Thus, even if a QOL assessment is confined to the health sector
only, all these factors are to be taken into account, their relative impacts are to be
assessed, their interactions are to be carefully examined, and relative to such a complex
disorder-environment, QOL measures for individual sectors are to be formulated in a
valid (statistical) manner, and finally, they are to be "pooled" in a statistical fashion to
formulate some over all QOL measures for the society/community. There are various
statisH,,".! is~ues relating to such "pooling" of QOL's. For a society/community, the
compuslte sociv ,.conomic-cultural picture may change over time, so that time-series
models (albeit in a multivariate setup) remain quite pertinent in this context too. This
composite picture may also vary, often considerably, from region to region within a
countn~ as well as, from rural to suburban to urban areas in any region, so that "spatial
mout..", .aay also be pertinent. Two or more countries/societies may differ with respect
to their disease/disorder incidence mappings, so that for a valid statistical comparison
of their QOL measures, proper precautions are needed to implement statistical tools. In
this respect, the situation is quite comparable to (wholesale or consumer) price index
numbers which are wei~htf>d avc_use or "arious component index numbers (for different
sectors), an~ for different countries, S l ; l weights can be different (depending on the
rel(\+:.o:: importance attached to thearious sectors).
In QaL assessments too
arbitration of these relative weights may be a delicate task.
,
With respect to a composite QOL measure for a community or country, one may
confine attention to a broad sector, such as health services and management, or even to
an overall spectrum combining standard of living, social, education and cultural
standards as well as health aspects. In the former case, all other factors, not included in
the specific sector but having good impact on it, are to be incorporated as auxiliary
variables, while in the latter case, more complex multi-factor analysis and modeling
appear to be more appropriate. Therefore statistical modeling and analysis schemes for
QaL assessments are atuned to the general objectives of the QaL measures. We intend
to pursue the general statistical technicalities arising in such QaL assessments in future
communications.
In the rest of this section, we present a schematic statistical
formulation avoiding the technicalities to a greater extent.
We denote by GJ) the domain of sectors for which QOL assessments are to be made.
Typically, such a domain can be partitioned into a number of sectors, and we express
this as
GJ) = U GJ).,
(5.1)
iii 1
where GJ). refers to the domain of the ith sector, and I = {i} is a (finite) index set for
such seclors. For each i, we denote the members of the set GJ). by d.. , j ( J.. As a
scoeity/ community is susceptible to a multitude of factors, the d.~J may lactually
represent a combination of more elementary events (disorders etc). l.specifically, for
each d ij , one may formulate a QOL measure, and denote this as
11" •• ,
IJ
j ( J., i ( I.
1
(5.2)
The basic statistical problems are then the following:
(I)
How to formulate the 11" •• with due emphasis on other members within the
same GJ)i and also those not in the sJlne sector?
...
. 14
(II) How to incorporate the 1Ti" j { J j , to formulate a comprehensive measure for
the sector ':D.?
J
,
1
(III) Is it appropriate to '"pool" these comprehensive, measures (denoted by II., i (
I) for formulating an overall QOL measure (say nO) for the entire domain ':D?
1
"
The formulation of the individual 1T •• , j f. J.; i f. I, can be made on the basis of
suitabale parametric models (viz., the P-hreto (fncome) distribution for the response
variable) or by incorporating more robust, nonparametric or semi-parametric
methodology. Generally, it may be difficult to advocate a specific parametric model,
especially when some of the response or auxiliary variables may be binary or
polychotomores. Logistic regression models and other nonparametric regression models
may be used as alternatives to some standard parametric models.
In terms of
robustness nonparametric models are more appropriate, especially when the data sets
are larger to justify the regularity assumptions. Although, QOL has a predominant
qualitative flavor, statistical measures are more geared towards a quantification in
terms of some interpretable factors. The situation is quite comparable to the standard
of living assessment where poverty (or affluence) indexes go beyond the crude ratio of
poor (or rich) people in the entire population. Motivated by this, we may proceed as
follows.
For an element d·· (f. ':D.), let 0' •• be the proportion of the population subject to this
n
IJ
clause. Thus, for eachi
{ I, 1
O'i = ~jd. O'ij
(5.3)
1
J
is the porportion of the population, subject to the set of clauses ':D., and ~. T. 0'. = 1.
Typically, for each d .. , QOL assessment involves a set of scores (m6stly bal~a oW some
ordinal k( ~ 2) point l~cales). For di(or poly- )chotomores responses, there are various
statistical measures to derive such a quantitative score. For quantitative responses, the
problem of attaching such scores is comparatively simpler. Let there be rii such scores
(for the clause d.. ), and for each of these scores, we compute the mean scores, denoted
by Jl.. ,s=1, ... r... For each of these scores, if we consdier the "normal" population
(defiHe~ suitably) land denote the corresponding averages by
s' 5=1, ... , rij' then
typically in a QOL assessment problem,
,
:J
Jlij
,Vs=1, ... , r. ., jd1·, iii.
(5.4)
1J
Thus, we may literally define the quality ~ ratio (QGR) [as in the case of poverty
indexes] by letting
Jl"
IJ,S
(3..
IJ,S
= 1 -
$
Jl9.
IJ,S
Jl"
IJ ,s
/ Jl9.
IJ,S
,
s=1, ... , r .. , j { J.. , i
IJ
IJ
f.
I.
(5.5)
Next, for each (i,j), we define a composite (Ql QQ.R (39.
as a (weighted) average of the
1
,s=1, ... , r.. , where the weights are to be determin Jd by the relative importance of
tiksr.. componiAts. thus, we may set
(3..
IJ
(39. = ~
IJ
rij
rij
_ 1
1
Ws (3.. where ~s=1 Ws ,
s=
IJ,S
(5.6)
and the Ws may vary from one (i,j) to another, but for notational simplicity, the
subscripts are omitted. As in (3.5), we may then set a QGR-adjusted QOL measure for
•
15
d.. as
IJ
11"(1) =
IJ
a~
a ..
IJ
!J
J. i ( 1.
J' (
1J '
(5.7)
l'
It is also possible to introduce more refined measures analogous to (3.6) or (3.7), but for
the sake I,E simplicity of presentation, we shall not go into such complications. Next,
based on (5.7), we may define
1I"P) = E. J 11"(1)
J( . IJ'
1
i(I
1
(5.8)
,
and the overall QOL measure for the population as
11"(1) = E.
If
I
AI)
(5.9)
1.
In this
ipect, we may like to note some points of clarification. First, in (5.5), it has
been t
:-. taken for granted that the
/3..
IJ ,s
are all nonegative. although, this is very
much t" case when QOL assessments deal with various diseases or disorders which
reduces Ll.. e level of normal living and activity standards, the way we have formulated
the GJ.1 (ill), there may be some d..IJ , for which for some s, IJ"
is >
IJ~ • For example,
IJ,S
IJ,S
in Section 3, for the ?.ffluent class, the average income is greater than the population
mean income. In the content of QOL assessment it can therefore be taken for granted
that for any s for which
IJ"
IJ,S
is greater than IJ~ ,the corresponding /3..
IJ,S
IJ,S
is to be taken
as 0, i.e.,
/3..IJ ,s = (1 where a+
= max
(a,O).
IJ"
IJ ,s
Secondly, if /3..
.
IJ ,s
/IJ~
)+,
IJ ,s
'tis,
i, j
(5.10)
is zero or nearly so, it implies that with
respect to that item-score, there is no major deterioration of QOL.
interpretation holds for the /3~ which will be
IJ
°(1)
A similar
only when all the component /3..
IJ,S
are
equal to 0. Judged from that point of view, 1I"ij in (5.7) is really a measure of the
QOL-deficiency (QOLD) due to the clause d ij , for j ( Ji , i (1. In this respect, the
similarity between the poverty indexes studied in Section 3 and (5.7) may be quite
apparent, although (5.7) is of more complex form due to the pooling of the constituent
me~ures.
In this sense, QOLD has a natural interpretation:
QOLD =
Average compromise of QOL due to
to the clause d ij , for j ( J i , i ( 1.
(5.11)
Thirdly, this QOLD interpretation in (5.11) extends directly to (5.8) and (5.9). There
is, however, a profound need for more statistical work in this respect. The basic
concern is: Can we combine the constituent indexes /3.. into an overall one (/3ft) in a
meaningful way? Further, if this is possible, what1J fs a most convenient way of
16
..
•
.J
)
•
•
implementing this? Both the answers are in the positive node, although the actual
implementation depends on a skillful choice of the constituent scales for each clause d..
so that they convey combinable information), and also for the chosen scales (which maY
not always be continuous or even quantitative), extraction of statistical measures may
often require sophisticated statistical analysis. Finally, the combinations in (5.8) and
(5.9) both belong to the domain of meta-analysis. It is very possible that the QOLD
measures may differ considerably from one d·· to another (within a GJ).) and also from
one GJ). to another (i (I). Nevertheelss, theSJ are inter-related in a ilJ. a well defined
statist1cal sense. Thus, the basic philosophy, of meta analysis spans to this complex
field as well. On the other hand, for different d·· or GJ)., generally the measurement
scales may be quite different (i.e., a common quesHonnaite may not be satisfactory for
all such clauses), so that from a statistical perspective it may be quite necessary to
provide standardized questionnaires which would remain more usable and interpretable
for subgroups GJ). or the entire complex. This challenging task requires, in turn, a
complete coordirlation of statistical outlook with that of the scientists and researchers
from all the other pertinent sectors in QOL assessments. In this respect, the mapping
of the individual clauses d.. , the sectors GJ). and the overall domain pertaining to a QOL
assessment task need to b~ done very juJiciously. The assessment of QOL for each of
these sectors may need somewhat different techniques, and these are not so much
statistically harmonious. For example, in the health sector, the particular nature of a
disorder/disease may call for some specific type of assessment tools, and statisticants
may be confronted with the perplexing task of combining information from such diverse
setups into a common channel which could be used for an overall assessment in an
effective manner. A more statistically important factor is the attachment of the
relative weights for the different GJ). (or the di.i within a GJ).), so that in (5.8) or (5.9), a
weighted average may appear to ble valid ana appropriatJ from pooling of information
point of view.
We conclude this section with some general remarks pertaining to the third world
perspectives in this context. A satisfactory resolution of a QOL assessment task can
only be made through an interdisciplinary approach, as has been pointed out in Sections
1 and 2. Statistical considerations are, however, quite overwhelming in this respect.
For the third world, setting up of such an interdisciplinary organization to pursue the
QOL assessment task may itself be a big step, and on the top of that implementation of
sophisticated statistical tools may even be harder. The partitioning {GJ)., i ( I} may itself
vary from country to country or society to society, and this has to be rhade with utmost
understanding of the underlying socio-economic, cultural, religious, socio-environmental
as well as physical, psychological and mental health perspectives. This requires the
setting up of various constituent regulatory agencies which, in turn, should be
interactive in the collection of relevant information and their exchanges for a healthy
resolution. While in most of the industrialized nations, there are such regulatory
agencies or institutions, in the third world, this task remains to be accomplished. No
QOL assessment can be made without the actual planning of a study, collection of
relevant statistical information, checking the quality and reliability of collected
statistical data sets, and finally, implementing reliable statistical analysis tools for
drawing valid conclusions. In this respect, the WHOQOL interpretation (mostly
relating to the health sector), the FAO (Food and Agricultural Organization)
interpretation (with emphasis on nutrition and rural economy) and the UNESCO
approach (encompassing various cultural, religious, education and socio-economic
aspects) should all be blended into a common overall one which would provide a
comprehensive picture. Undoubtedly, statistics is the key technology in this quest.
. 17
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