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```							Problem Set 2 Answer Key                                                        Fall 2006

1. In the “Global Burden of Disease: Summary” on your reading list, Murray and Lopez (1996)
introduce the concepts of Global Burden of Disease and DALYs. The basic equation for DALYs
is DALY = YLL + YLD.

a. In one sentence, please define the abbreviations YLL and YLD.

YLL are years of life lost and YLD are years of life lived with disability.

b. One DALY is one lost year of healthy life. Is this a positive or negative metric? (Hint:
Healthier populations would have greater values in positive metrics, such as average life
expectancy.)

DALY is a negative metric since it captures a loss of health. The more DALYs ascribed to a
region or country, the greater the disease burden, the worse the population health.

c. The article describes disease burden as “the gap between a population‟s actual health status
and some “ideal”, or reference status”. The mortality component captures premature death,
which is a death that occurs before the age to which the dying person could have expected to
survive if they were a member of a standardized model population.

- What country‟s life expectancy is used as a reference for the US population?
- How about the population of Zimbabwe?
- What does this mean for the calculation of the mortality component of the Burden of Disease in
both countries? (Hint: Will it be higher or lower in one country or the same?)

Japan is the world’s longest-surviving population. Male and female life expectancy from Japan
is used to calculate the years of life lost in both the US and Zimbabwe, although these two
countries differ significantly in average life expectancy. Since Zimbabwe has a lower average
life expectancy, it will have a greater number of years of life lost when compared to Japanese life
expectancy than the US with a much higher average life expectancy.

d. Imagine a two-car collision in Country X. In one car, all of the passengers are killed, a 10
year-old girl, a 12 year-old boy, a 43 year-old woman and a 47 year-old man. In the second car,
the sole 18 year-old male passenger is left as a quadriplegic for the rest of his life. The „ideal‟ life
expectancy for Country X is 82.5 for women and 80 for men, and the disability weight for
quadriplegia is 0.85. What are YLL and YLD? (To calculate YLD, please use the following
equation, and ignore age-weighting and discounting: YLD = I x DW x L, where I is the number
of new cases, DW is the disability weight, and L is the average duration of the disease)

If ideal life expectancy for women is 82.5, 72.5 years of life are lost due to the death of the young
girl and 39.5 years of life lost due to the death of the woman. If ideal life expectancy for men is
80, there are 68 years of life lost due to the death of the young boy and 33 years of life lost due to
the death of the man. In total, 213 years of life are lost in the car accident. If the disability
weight for quadriplegia is 0.85, and there is 1 case due to the car accident, and the man is
expected to live for another 62 years, the years lost to disability, YLD = I x DW X L, YLD = 1 x
0.85 x 62, 52.7 years are lost to disability from the car accident.

2. Imagine the following changes in infant mortality rates in a country.

Infant mortality rates (deaths per 1,000 live births)
Poorest 20%      Richest 20%
1945              200             125
2000               75              20

- What happens to absolute inequality between 1945 and 2000?
- What happens to relative inequality between 1945 and 2000?
- Has the country become less unequal with respect to infant mortality rates?

The difference in infant mortality rates between the poorest and richest 20% narrows from 75
deaths per 1,000 live births to 55 deaths per 1,000 live births, so absolute inequality of infant
mortality rates decreases. However, relative inequality of infant mortality rates increases
because the ratio of infant mortality rates between the poorest and richest 20% increases from
1.6 in 1945 to 3.75 in 2000. Since the absolute inequality has decreased, but relative inequality
has increased, we cannot say whether the population is less unequal with respect to infant
mortality rates.

However, the answer might be different if you were examining the survival probability. Survival
probability is 1 – mortality rate. Observing the infant mortality rates listed above would result in
the infant survival probabilities in the table listed below.

Infant survival probability (per 1,000 live births)
Poorest 20%       Richest 20%
1945             800                875
2000             925                980

Using survival rather than mortality, absolute inequality is decreasing over time, as the
difference in survival narrows from 75 per 1,000 to 55 per 1,000 live births. Relative inequality
is also decreasing, as the ratio of probability of survival moves from 800/875 or 0.914 to
925/980 or 0.943. Relative inequality is decreasing since the ratio is approaching 1, meaning
less of a difference in probability of survival across the two segments of the population. In this
case, we could say that inequality is decreasing. However, because the trend of relative
inequality can change depending on the metric, it can be a less preferable method to measure
inequality and for this reason, many experts in the field do not consider it.

3. In “Global and regional burden of disease and risk factors,” Lopez et al. (2006) provide a list
of the top ten causes of deaths for low- and middle-income countries, as well as the top ten
causes of the burden of disease in these countries.
- What is a leading cause of disease burden but NOT mortality in low- and middle-income
countries?
- What is a leading cause of mortality but not disease burden in low- and middle-income
countries?
- How does considering disease burden, as well as mortality, potentially change resource
allocation decisions?

Road traffic accidents are among the 10 leading cause of deaths in low- and middle-income
countries, but not disease burden. Similarly, unipolar depressive disorders are a leading cause
of disease burden but not mortality in these countries. When considering only deaths, one might
allocate more resources to road traffic accidents. However, when you consider both years of life
lost, as well as years lived with disability, unipolar depressive disorders become a more
significant health issue. If allocation decisions were made on the basis of mortality alone, health
issues such as unipolar depressive disorder may not receive funding commiserate with
contribution to disease burden.

4. Below are four population pyramids for the country of Mexico, for the years 1970, 2000,
2015, and 2030, available from the United Nations‟ Department of Economic and Social Affairs
at http://www.un.org/esa/population/publications/EGMPopAge/Partida_Figures.pdf.
a. In no more than a few sentences, please describe what has happened and what is projected to
happen to the relative size of different age cohorts in Mexico over time.

The four figures above are population pyramids for 1970 and 2000 and projections for 2015 and
2030. In 1970, the population pyramid is widest at the bottom, meaning that the youngest cohorts
make up a significant proportion of the population. However, in 2000, the youngest cohorts are
actually smaller than the slightly older age cohorts. This suggests a decline in fertility as
younger age cohorts in 2000 are smaller than previous cohorts. The projection to 2015 suggests
that this will continue with younger age cohorts declining in size and thus proportion of the
population. The projection for 2030 suggests this trend will continue, with the second curve in
the pyramid representing the children of the larger cohort proceeding through reproductive
years.

Group I: Communicable           Group II: Non-communicable       Group III: Injuries

80
Percentage of total deaths (%)

70

60

50

40
30

20

10

0
1955

1960

1965

1970

1975

1980

1985

1990

1995

2000
Year

Distribution of deaths across broad cause groups, Mexico 1955-2004. Group I comprises
communicable diseases, maternal and perinatal conditions, and nutritional deficiencies. Group II
comprises noncommunicable diseases, including cardiovascular disease and cancer. Group III comprises
injuries.

b. The figure above illustrates the number of deaths attributable to Group I, II and III diseases in
Mexico. In no more than a few sentences, please describe what has happened to the number of
deaths attributable to Group I and Group II diseases?

Group I diseases are communicable diseases, while Group II diseases are noncommunicable
diseases. According to the figure, the percentage of total deaths attributable to communicable
diseases has decreased over time, while the precentage of total deaths attributable to
noncommunicable diseases is increasing.
c. Given the changes to the population‟s age structure that you considered in part a of this
question, briefly explain what you expect the relative contributions of Group I and Group II
diseases to mortality to be in the future and why. (Hint: Your answer should relate to the
changing population age structure.)

As a population’s birth rate falls, the number of adults relative to children increases. The more
common health problems of the population will be those of adults, rather than children.
Accordingly, one would expect that as this happens, the percentage of deaths attributable to
Group I diseases will continue to decrease relative to the percentage of deaths attributable to
Group II diseases. This phenomenon has been characterized as the epidemiological transition,
where the changing population age structure shifts the disease burden towards health problems
common to adults and away from those common to children.

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