11/9/04
The Vulnerable and Their Potential Disadvantages
Albert I. Hermalin and Mary Beth Ofstedal
Population Studies Center
Institute for Social Research
University of Michigan
This is a slightly revised version of the presentation for the Annual Meeting of the Population
Association of America, Atlanta, GA, May 9-11, 2002
The analysis presented constitutes a major portion of Chapter 11, The Vulnerable and their
Potential Disadvantages (A. Hermalin, M. B. Ofstedal, K. Mehta) of the forthcoming
monograph, The Well-Being of the Elderly in Asia: A Four-Country Comparative Study, Albert I.
Hermalin, editor, to be published by the University of Michigan Press, Winter 2002. Citations
should be to the forthcoming volume.
Acknowledgements: Partial support for this research was provided by a National Institute on
Aging grant (R37 AG07637). The authors appreciate the input of John Knodel and Kalyani
Mehta, and the assistance of Ingrid Naaman in preparing the manuscript.
Abstract
Identifying the Vulnerable Elderly in Asia
and Their Level of Disadvantage
Albert I. Hermalin
Mary Beth Ofstedal
The vulnerability of the older population is a persistent theme within gerontology, arising
from consideration of biological processes as well as underlying socioeconomic dynamics.
These concerns often translate into conjectures, without explicit measurement, of the groups
among the elderly who are most vulnerable and who may be at greatest disadvantage, such as the
oldest-old and those with the most limited economic resources and support.
This paper introduces a new methodology for examining this issue by developing a risk
factor for potentially vulnerable groups which measures their degree of disadvantage relative to
those not in the group, and which is independent of group size or other compositional elements.
This measure is used to compare profiles of disadvantage in economic, health, and social support
outcomes for 12 vulnerable sociodemographic groups in four Asian countries: the Philippines,
Singapore, Taiwan, and Thailand. Data come from representative surveys of older adults in each
country from the mid-1990s.
Results indicate wide variation among the vulnerable groups in the degree and extent of
their disadvantage. Some groups show higher relative disadvantage on only a few indicators of
well-being while others face problems across the board.
Identifying the Vulnerable Elderly in Asia and Their Level of Disadvantage
Background
As the analysis we are about to present differs in structure from the more usual regression
framework, a few words of background on how we arrived at this approach may be in order. It
also allows us to plug the monograph on a comparative study of aging in Asia that my colleagues
and I recently completed. The goal of the monograph was to explore the well-being of the
elderly on several dimensions—economic, health and work and leisure—in the face of the rapid
demographic, social and economic changes occurring in much of East and Southeast Asia.
In pursuing these goals we devoted chapters to each dimension of well-being using a
variety of measures as dependent variables and existing theory and literature to identify
potentially influential independent variables, and examined their effects through both descriptive
and multivariate analyses. But it occurred to us that these analyses, however illuminating they
might be, did not fully address a persistent theme within gerontology and one which surfaces
frequently in popular and media discussion of population aging: namely, which groups of older
people are particularly vulnerable to the social, economic and physical ills that often arise with
aging and how disadvantaged are they compared to others. For example, the NY Times reporting
on the opening of United Nations’ Second Assembly on Aging states, “But for many millions of
older people, especially the rural poor in developing countries (emphasis added), food, water,
electricity, medical care and security are still in scarce supply.” And further on, talking of the
influence of modernizing and other forces they talk of many older people, especially women,
[forced] into extreme poverty and isolation. (NY Times, April 9, 2002)
2
Note that as posed, these questions denote a shift in focus from the regression framework
where the emphasis is on specific variables (or characteristics of individuals) to one on groups of
individuals identified by one or more characteristics, but with each encompassing a host of
characteristics. This distinction is worth stressing because in studies devoted to gender, ethnic
and other differentials, the strategy sometimes is to divide people by the identifying
characteristic and compare group differences, versus trying to isolate the independent or net
effect of the characteristic in contrast to other influences on the outcome of interest. We do not
mean to suggest that one strategy is superior to another. They address different questions and
have different potential uses in terms of policy and program implications.
The Methodology Employed
The methodology we developed in trying to identify the vulnerable elderly and to measure the
nature and extent of their disadvantages may be best viewed structurally as akin to undertaking a
medical screening for certain conditions or diseases. For screening, one must decide who will be
tested, for which conditions, and what diagnostic tests will be employed. Similarly, these three
elements are critical to the goal of identifying the vulnerable groups and measuring the degree of
their disadvantage: defining the sociodemographic groups to be examined; selecting from among
the disadvantages those to which they are most vulnerable; and establishing indicators to test the
degree to which they are disadvantaged relative to the total older population or other groups.
Table 1 lists the vulnerable groups, which represent demographic and socioeconomic
categories of people likely to have above-average levels of one or more disadvantages. These
groups are identified on the basis of a priori knowledge about the process of aging, previous
3
studies, or reports in the mass media. Also shown in the table is the percentage that a given group
represents of all the elderly in each of the four countries.
In terms of relative size, the percentages in Table 1 show that some of the groups are
currently major components of all the elderly, such as those age 70 or over, women, and rural
residents in Thailand and the Philippines, while others are relatively small proportions, such as
those living alone or without living children, widowed men, and otherwise unmarried men and
women. It is important to note that the groups are not mutually exclusive; many individuals will
fall into multiple categories, such as older, low-educated women living in rural areas. In addition,
the relative sizes of the groups and their composition are likely to change substantially over time
with continued socioeconomic development, and such changes must be taken into account in
considering policy and program implications.
Table 2 lists the indicators of economic, health, and social disadvantage used in the
analysis and shows their proportion among all elderly in each country. The indicators for
economic disadvantages include difficulty in meeting expenses (or dissatisfaction with income),
being at the lower end of the income scale for both personal and household income, reliance on
children as sole or main source of financial support, and a weak asset position. The indicators for
health disadvantage include self-rated health, presence of chronic conditions, and various types
of physical and cognitive impairments.
There were few comparable indicators of social
disadvantage across countries. The three shown in Table 2 focus on the frequency of visits with
children, the size of the social network, and measures of depression or loneliness.
The third component of the strategy is devising a measure of relative disadvantage that
will capture the differential vulnerabilities among the various groups. The measure used here is a
risk factor, defined as the ratio of the proportion disadvantaged in a specified sociodemographic
4
group relative to the proportion disadvantaged among those not in the group. A ratio of 1 means
that both those in and out of the group have the same risk for the particular disadvantage; ratios
greater than 1 indicate a proportionate level of heightened risk for those in the specified group;
ratios of less than 1 indicate a relative degree of diminished risk facing those in the group. The
appendix provides the formal derivation of the risk measure as well as several related measures
that can be derived from the data.
The risk factors were calculated for each of the sociodemographic groups listed in Table 1,
on each of the indicators of disadvantage listed in Table 2, resulting in a large matrix of risk
factors for each country. As illustration, Table 3 presents the first portion of this matrix, showing
for the Philippines the relative risk faced by each sociodemographic group on each of the
economic disadvantage indicators. In addition, the first row for each country presents the
percentage of all elderly in each group, while the first column presents the percentage of all
elderly with the stated disadvantage.
Using an example from this table, Filipinos age 70 years or older are 90 percent more
likely than those under age 70 to have no assets (risk factor equals 1.90), while the rural elderly
are only 63 percent as likely to hold no assets than those residing elsewhere.
The risk factors can be used in a number of ways: to examine the profile of risks facing a
given sociodemographic group within each country, to compare different groups within
countries, and to compare groups across countries. Given time constraints we briefly illustrate
the first two uses and then move to cross-country comparisons, making use of graphs to highlight
the selective risks across groups. Because there is substantial overlap in the sociodemographic
groups under study, we also estimated multivariate models and those results will be summarized
at the end.
5
Example of Country-specific Risk ProfileResearch Findings
Figure 1 presents the relative risks of economic disadvantages in the Philippines that were shown
in Table 3. The figure shows at first glance that only those with no education face significant
excess risk on each of the indicators of disadvantage. For the other groups, excess risk tends to
vary across indicators, illustrating the value of using multiple measures. Those age 70 or over
have higher risks of low income, lack of assets, and reliance on children as the sole source of
income. Rural residents face greater risk mainly for lack of household possessions and the
perception of inadequate income; they are less likely than urban dwellers to have no assets or to
rely on relatives for sole financial support. The results relating to gender and family dynamics
show that widowed women have a relatively high risk of relying solely on children for income,
having low income and lack of assets. By contrast, widowed men show minor levels of relative
disadvantage on these measures.
Similar graphs were prepared for the health and social
disadvantages and for each of the four countries, but in the interest of time we move on to crosscountry comparisons.
Cross-Country Profiles of Relative Risks
To highlight the cross-country patterns the relative risk measures for each type of disadvantage
are averaged, giving each sociodemographic group within a country a single value for each of the
economic, health, and social dimensions. These values are presented in Figure 2.
For each dimension of disadvantage, Figure 2 permits visual comparison of risk profiles
across countries by sociodemographic group. The top panel, which displays average risks
associated with economic disadvantage, shows a number of similarities and differences across
6
countries. The most striking difference is the extremely high economic risk of the rural
population in Thailand, compared to the Philippines and Taiwan. Another sharp difference is the
excess risk in Singapore for many of the fertility and family-based statuses—those living alone,
without living children, and never married, separated, or divorced women. In all countries, those
age 70 or older are at a relative disadvantage, as are widowed women and those with no
education.
The average health risks shown in the second panel display more similarity across
countries. The most clearly disadvantaged group, not surprisingly, are those age 70 or over, and
the magnitude of the disadvantage is similar across countries, [varying from 2.1 to 2.6]. The only
other groups consistently disadvantaged are those with no education and, to a lesser degree,
widowed and all women.
The profiles of social disadvantage shown in the third panel are also similar across
countries. In every case the groups with very high relative risks are those living alone and those
without living children. Family statuses related to these—men and women who never married,
separated, or divorced—also show a high average social risk, except among women in Taiwan.
The patterns are also similar for the remaining groups in the Philippines, Thailand and Taiwan,
with each of these countries showing somewhat higher risks among the age 70-plus group, those
with no education and, except in Taiwan, among women. By contrast, rural residents show
slightly lower average risks than their counterparts in these three countries.
Taken together the results show that the sociodemographic groups selected do indeed tend
to have excess risk on at least one of the three broad dimensions of disadvantage. Yet few of the
groups were disadvantaged on all of the dimensions, and there was also variation in risk level
across the detailed measures that comprise each disadvantage.
7
As alluded to earlier, there is large overlap in the sociodemographic groups and this limits
our ability in the preceding analyses to determine which individual characteristics are most
predisposed to disadvantage on the indicators under study. We thus use multivariate analyses to
identify the characteristics that appear most salient.
Multivariate Results
Moving to a multivariate framework requires a change in the measures of disadvantage
employed. The risk ratios used in the previous sections are measures of each sociodemographic
group’s vulnerability relative to its counterpart, and as such cannot be directly used as an
individual-level dependent variable. At the individual level, we could conduct logistic regression
analyses predicting the log-odds of having a specific disadvantage, and this would closely
approximate the risk ratio approach used in the descriptive analyses. However, running separate
logistic regression models for every disadvantage indicator for each country would produce an
unwieldy array of results that would be difficult to summarize. Instead we adopt two simpler
measures: (1) a count of the number of specific disadvantages a respondent reports within each
of the three broad dimensions; and (2) a count of the number of dimensions in which each
respondent reports at least one disadvantage. Because the indicators of economic and health
disadvantage differ in number across countries, the dependent variables used for those measures
differ in terms of their ranges.
We carried out four OLS regression models for each country: one for each of the
dependent variables listed here. The independent variables included in the models are the
characteristics for each of the sociodemographic groups. With respect to marital status, we
distinguish three groups: currently married versus widowed versus never-married, separated, or
8
divorced. Also, because we’re interested in examining whether widowhood affects men and
women differently with respect to economic, health, and social disadvantages, we included
interaction terms between gender and marital status in the models.
Summary of Disadvantages Faced by the Sociodemographic Groups
In Table 4 we provide a simple summary of the results from each model. An asterisk indicates
that a significant disadvantage was observed for that group for the specified domain of
disadvantage, and a question mark means that the significance was borderline.
The results indicate that each of the groups examined does experience a significant
disadvantage in at least one country on one or more dimensions. However, the groups differ
greatly in the frequency with which they encounter a disadvantage, and in the type of
disadvantage experienced. Those age 70 or over are disadvantaged on the health dimension
relative to those age 60-69 in every country, and they are also consistently disadvantaged on the
economic dimension. The most surprising result perhaps centers on the rural elderly. Despite
considerable concern often expressed about the isolated rural elderly in the face of heavy urban
migration of the young, they show no disadvantage on the social dimension, nor on health, and
show a disadvantage on the economic dimension only in the Philippines and Thailand. Those
with no formal education experience a significant disadvantage on each domain in nearly every
country. As expected, those living alone or without living children display a consistent social
disadvantage within each country, but only those living alone tend to experience a consistent
economic disadvantage. Neither trait, net of other factors, is associated with above average
health risks.
9
Women as a group most often experience a disadvantage in the realm of health, joining
those 70 years and older and those with no education as the only groups with above average risks
on this dimension. They also are likely to experience an economic disadvantage in Thailand and
Singapore. Widowhood is often associated with an economic disadvantage, and for those who
have never been married or are separated or divorced, both economic and social disadvantages
show up selectively across the countries. In both cases, it’s interesting to note that the
disadvantages are likely to affect men as well as the women in these statuses.
Despite the strong effects observed for many of the sociodemographic characteristics in
the regression models, taken together the groups and characteristics represented in the models
capture only a small amount of the variance across all the elderly. For example, for the health
dimension the amount of variance explained by the model (as represented by R2) ranges from 4
percent for Thailand to 11 percent for Taiwan, and for the economic dimension the explained
variance ranges between 5 and 16 percent. Thus, it is clear that for economic, health, and social
disadvantages as defined here, vulnerability is a much more complex phenomenon than often
thought. Although they do differentiate those at higher risk for certain disadvantages, the
characteristics often used to identify groups that are most vulnerable in old age tell only a small
part of the story.
Another implication of Table 4 is that the likelihood of a given group experiencing an
above average risk on each dimension is quite similar across countries. This suggests that these
heightened risks reflect either underlying bio-demographic factors (like older age on health) or
common socioeconomic dynamics across countries (such as the persistent disadvantage of those
with no education). These patterns and the dynamics that give rise to them must be considered in
advancing policies and programs that will address the heightened risks.
10
Conclusion
In summary, this analysis points up two important findings. The first is that there is a great deal
of variation across groups in terms of the number and types of disadvantages faced. The second
is that, while many groups have above average risks on one or more measures, collectively they
account for only a small amount of the variance in the disadvantages examined here.
Despite having philosophies that look to the family as the major provider of services and
support of elders, each of these countries have been developing programs intended to assist older
people and their caregivers in handling problems that tend to emerge late in life. As these
programs become established, it is important that appropriate evaluations guide improvements in
effectiveness and cost-efficiency. Program evaluation is often a complex, multi-faceted task, but
several relevant elements have been touched on in this paper. One is the clear identification of
the primary target groups and careful assessment of their needs.
Policymakers in these countries and others that have recently undergone rapid
socioeconomic change will also face the task of adjusting their policies and programs to the
changing characteristics of the future elderly. The gains in education and the movement to more
urbanized and industrial societies mean that future elderly will be more knowledgeable on
average, have experienced higher standards of living, and have different expectations and
orientations than the current elderly. In spite of these advantages, however, smaller family sizes
and higher rates of singlehood and divorce are likely to undermine traditional sources of social
support. These trends will challenge policymakers to adapt current programs and develop
innovative new programs to address changing needs.
11
REFERENCES
Calkins, Evan. 1999. New Ways to Care for Older People: Building Systems Based on Evidence.
New York: Springer Publishing.
Hermalin, Albert I. 1995. “Aging in Asia: Setting the Research Foundation.” Asia-Pacific
Research Reports, No. 4, East-West Center, Program on Population.
Kamnuansila, Peerasit, Supawatanokorn Wongthanavasu, John Bryant, and Aree Prohmmo.
2000. “An Assessment of the Thai Government’s Health Services for the Aged.” Asia-Pacific
Population Journal 15(1):3-18.
Rudkin, Laura. 1993. “Gender Differences in Economic Well-Being among the Elderly of Java.”
Demography 30(2):209-226.
Sheldon, Brian, and Rupatharshini Chilvers. 2000. Evidence-Based Social Care: A Study of
Prospects and Problems. Dorset, U.K.: Russell House Publishing.
Table 1 Vulnerable Sociodemographic Groups and Their Percentage of All
Elderly, by Country
Sociodemographic Group
Age 70 or over
Rural residents
No education
Live alone
No living children
Women
Widowed:
Women
Men
Philippines
Thailand
Taiwan
Singapore
43.6
56.6
19.4
5.5
4.4
58.2
38.1
82.0
31.0
4.3
4.4
54.5
41.3
29.2
40.9
9.0
4.2
45.6
42.3
n.a.
66.9
3.3
4.3
53.6
31.1
9.9
25.4
6.5
19.0
7.9
35.2
9.7
4.7
1.2
.9
4.8
1.9
2.5
Never married, separated or
divorced
Women
Men
3.9
1.1*
* Represents less than 25 cases and will not be analyzed separately.
n.a. = not applicable
Table 2 Indicators of Economic, Health and Social Disadvantage and Their
Percentage of All Elderly, by Country
Philippines
Thailand
Taiwan
Singapore
23.1
--
-28.0
4.1
--
10.1
--
10.8
6.3
23.1
4.0
26.1
55.0
19.5
21.8
10.9
37.0
11.7
21.4
26.4
33.4
13.2
--
14.6
29.3
8.9
20.9
10.7
5.8
10.8
27.5
6.1
--20.1
8.9
32.5
4.4
16.1
9.0
19.9
16.6
8.0
5.9
18.5
9.8
24.9
10.7
7.8
9.2
7.4
17.1
11.4
8.4
11.5
9.6
9.8
9.0
1.3
Economic Disadvantages
Inadequate income
Unsatisfied with economic
situation
Low personal and household
income
Child/other relative as sole /
main source of incomea
No assets
Few household possessions
Health Disadvantages
Poor self rated healthb
2 or more chronic conditions
1 or more ADL limitations
1 or more IADL limitations
Subnormal cognitive ability
Vision or hearing
impairmentc
Social Disadvantages
Fewer than monthly visits
with any childd
Small social network
Depressed mood/lonelye
n.a. = not applicable
-- = not available
a
Reflects Child/Other Relative (excluding spouse) as Sole Source for Philippines, Taiwan and Singapore;
Child as Main Source in Thailand
b
Measured as Self- Rated Health less than “good” in Singapore
c
Covers only Vision in Thailand
d
Includes respondents with no living children
e
Measured with partial CES-D scales in Philippines and Taiwan; question on “loneliness” in Thailand;
lack of confident or advisor in Singapore
Table 3
Profile of Economic Disadvantages
Country and Type of
Disadvantage
% of
All
Elderly
with
Stated
Disadvantage
Age
70+
Risk Factor for Specified Disadvantage
for Those in the Sociodemographic Group Relative to All Other Elderly
Never
No
Married,
Widowed
No
Lives
Living
Separated or
Education
Rural
Alone Children Women
Divorced
Women
Men
Women
Men
9.89
3.89
*
Philippines
43.59
56.57
19.38
5.54
4.43
58.23
31.09
23.06
1.07
1.51
1.77
0.85
0.97
1.10
1.15
0.99
0.64
*
10.76
2.44
1.08
2.12
1.52
1.96
1.93
2.44
1.55
1.77
*
26.11
1.75
0.89
1.24
1.27
--
1.70
2.36
1.14
0.44
*
10.92
1.90
0.63
1.69
0.58
2.89
1.46
1.60
1.48
3.14
*
36.95
1.02
2.27
1.65
2.03
0.80
0.73
0.99
1.13
0.72
*
All elderly
--
Inadequate income
Low personal and
household income
Child/other relatives
as sole source of
income
No assets
Few household
possessions
* Fewer than 25 cases in sociodemographic group
Table 4
Summary of Each Sociodemographic Group’s Significant Disadvantages, by Broad Dimension and Country
Socio-Demographic
Group
Age 70+
Rural
No education
Lives alone
No living children
Women
Economic
Phil.
*
*
*
Health
Thai. Taiw Sing.
.
*
*
*
*
*
*
*
*
*
n.a.
*
*
*
*
Phil.
*
Thai. Taiw Sing.
.
*
*
*
*
*
Social
*
*
*
n.a.
*
Phil.
Multiple
Thai. Taiw Sing.
.
*
Phil.
n.a.
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
Thai. Taiw Sing.
.
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
?
*
*
n.a.
*
*
*
*
Widowed
Women
Men
Never married,
separ. or
divorced
Women
Men
*
*
*
*
*
*
?
*
*
*
*
*
?
*
?
*
*
*
Notes: Sociodemographic groups exhibiting significant differences in the multivariate results (Tables 5-8) are indicated with *’s in the relevant cells.
Results that are indeterminate are indicated with ?s.
?
*
*
2
Figure 1
Philippines: Relative Risks of Economic Disadvantages for Sociodemographic Groups
Age 70+
Illiterate or No
Education
Rural
Lives Alone
Inadequate Income
Low Personal and
Household Income
Child/Other Relatives as
Sole Source of Income
No Assets
Few Household
Possessions
0
1
2
RATIO
3
0
1
2
3
0
1
RATIO
No Living Children
Widowed Men
2
3
0
1
2
RATIO
RATIO
Widowed Women
All Women
3
Inadequate Income
Low Personal and
Household Income
Child/Other Relatives as
Sole Source of Income
Not Applicable
No Assets
Few Household
Possessions
0
1
2
RATIO
3
0
1
2
RATIO
3
0
1
2
RATIO
3
0
1
2
RATIO
3
Figure 2
Average Relative Risks Associated with Each Dimension of Disadvantage,
by Sociodemographic Group and Country
Economic Disadvantage
Philippines
Thailand
Taiwan
Singapore
Age 70+
Not Applicable
3.07
Rural
No Education
Lives Alone
3.04
No Living Children
4.76
All Women
Widowed Women
Widowed Men
Never Married, Separated
or Divorced Women
Insufficient #
of Cases
Never Married, Separated
or Divorced Men
0
1
2
3
0
1
2
3
0
1
2
3
0
1
2
3
Health Disadvantage
Philippines
Thailand
Taiwan
Singapore
Age 70+
Rural
Not Applicable
No Education
Lives Alone
No Living Children
All Women
Widowed Women
Widowed Men
Never Married, Separated
or Divorced Women
Insufficient #
of Cases
Never Married, Separated
or Divorced Men
0
1
2
3
0
1
2
3
0
1
2
3
0
1
2
3
Figure 2 - continued
Social Disadvantage
Philippines
Thailand
Taiwan
Singapore
Age 70+
Rural
Not Applicable
No Education
Lives Alone
6.83
No Living Children
8.17
15.62
5.43
6.82
All Women
Widowed Women
Widowed Men
Never Married, Separated
or Divorced Women
Insufficient #
of Cases
Never Married, Separated
or Divorced Men
0
1
2
3
4
5
5.23
0
1
2
3
4
5
0
1
2
3
4
9.41
5
0
1
2
3
4
5
Appendix:
Derivation of Relative Risks for Sociodemographic Groups
and Related Measures
A. As stated in the text, the relative risk for a given sociodemographic group is the proportion
disadvantaged in that group relative to the proportion disadvantaged among those not in the
group. This is equivalent to the ratio of the odds of being in a specified sociodemographic group
among all those with a given disadvantage, to the odds of being in that group among the total
population. The notation and algebra below formalize these relationships.
In S-D Group
Not in S-D Group
Number in Each Group
V
O
Proportion Disadvantaged
kr
r
Number Disadvantaged
krV
rO
Percent of Disadvantaged in S-D Group
s =
krV
kV
=
krV + rO
kV + O
Percent of Total Population in S-D Group
p =
V
V
=
V+O
T
Relative Risk as Defined:
Total
T
krV + rO
kr
=k
r
This is equivalent to the ratio of the odds of being in S-D Group among All Disadvantaged to the
odds of being in the S-D Group among Total Population.
Odds of being in S-D Group among Disadvantaged:
(1)
Odds =
krV V
 k
rO
O
Odds of Being in S-D Group for Total Population:
(2)
Odds =
V/T V O V
=
=
O/T T T O
Odds Ratio:
V
k
(1) O
=
=
=k
(2) V/O
(3)
B. Percent of Socio-Demographic Group Who Experience a Given Disadvantage
Using the notation above, the percentage of a specified sociodemographic group who
experience a particular disadvantage is:
krV
= kr
V
This proportion can be derived from knowing k (the relative risk), the proportion of the
population in the sociodemographic group, and the percent of the total population disadvantaged,
as follows:
% of pop in S-D group = p =
V
T
% of pop not in S-D group = (1 - p) =
O
T
% of total population disadvantaged:
krV + rO
= krp + r(1 - p) = D
T
Then
r(kp +1 - p) = D
r[p(k - 1) +1] = D
D
p(k - 1) +1
kD
kr =
p(k - 1) +1
r=
which is a function of p (the percentage of the population in the S-D group), D (the percentage
of the total population who is disadvantaged), and k (the relative risk).
C. Percent of All with a Particular Disadvantage Who Are in a Given Sociodemographic
Group:
V
krV
p
T
=
=
s =
1
krV + rO V O 1
+
p + (1 - p)
T Tk
k
which is a function of the relative risk and the proportion in a given sociodemographic group.
D. Numerical Illustrations:
The interrelationships among the measures defined above may be illustrated with the data
presented in Table 3.
For the Philippines, the sociodemographic group of those who are illiterate or without
formal education, given in row 1, is 19.38 percent of all elderly. The first column indicates that
23.06 percent of all elderly have the disadvantage of inadequate income. The relative risk factor
of inadequate income for those without education is 1.77, as shown in the table entry. This
means that those without education are 77 percent more likely to have inadequate income than
those with education.
In terms of the notation developed above:
k = 1.77
p = proportion of population in S-D group = .1938
1 – p = proportion not in S-D group = .8062
D = proportion of total population disadvantaged = .2306
Then according to B above, the proportion of those without education that have inadequate
income is:
kr =
kD
1.77(.2306)
.408
=
=
= .355
p(k - 1) +1 .1938(1.77 - 1) +1 1.149
From C above, we can also derive the percent of all those with inadequate income who
have no education. This is given by:
s=
p
p + (1 - p)
1
k
=
.1938
.1938
=
= .298
.8062 .6492
.1938 +
1.77
Conversely, if s and p are know, then from A,
s
.298
k = 1 - s = .702 = 1.77
p
.1938
1 - p .8062