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Lectures Public Health Economics
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This document summarizes all lectures of the course Public Health Economics for the academic year .
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Video Lecture 1.1 – Population Health MeasurementSummary measures of population health allow for comparisons of different countries, different subgroups
within countries (for instance, based on socioeconomic status), and countries over time. The global goal
of summary measures of population health is to measure progress over time, to measure the impact of
interventions, and to identify disadvantaged populations or subgroups.
The death rate is a very crude measure to say something about mortality differences between countries,
for instance because it is not corrected for differences in the age composition of countries. Alternatively,
you could look at how a mortality rate is divided across different age groups. This allows you to see what
share of all deaths occur, for instance, at an age below 14, between 15 and 59, and above 60. You can
make comparisons between different regions in the world. The share of deaths among people of an age
below 14 is much higher in Africa than in Europe. However, there is also a relatively high number of young
people, which could partly explain the large number of deaths at a young age. To compare countries in
terms of health, you could also look at the infant mortality rates (or mortality rates for other age groups).
You could also compare time trends in health for particular age groups across countries.
Counting the deaths says something, but it does not tell the whole story. It does not include a time
perspective. We want to see how mortality risks play out over lifetimes. Life expectancy is a simple
measure to compare mortality over time and across countries. It translates mortality risks at different
ages into time. More specifically, we use mortality risks at different ages to calculate the average number
of years lived. This allows us to make lifetime comparisons in health across countries, within countries
over time, and between different subgroups.
Video Lecture 1.2 – The Life Table (A)
The life table is a useful tool to summarize mortality probabilities. It is at the heart of modeling the impact
of public health interventions. The life table is a simple way to create survival curves and to calculate life
expectancy. Life tables can be extended to calculate disability-free life expectancy or quality-adjusted life
expectancy and expected lifetime health care expenditures.
A survival curve has age on the x-axis and survival probability on the y-axis. The curve is downward-sloping
and shows for each age the probability that someone aged 0 survives up to (at least) that age. Life
expectancy at birth is the area under the survival curve. If you want to know the remaining life expectancy
at an age of 20, then you need to look at the area under the survival curve after an age of 20 and divide
that by the probability that someone is still alive at an age of 20.
The mortality rate is the ratio of
people dying within a certain period
and the amount of time lived. The
survival curve gives the mortality
probability (which is equal to 1 minus
the survival probability). In the figure
on the right, the mortality rate would
be equal to line A divided by area B.
,We often assume that the mortality rate
is constant over time; for each age
interval, the mortality probability
divided by the number of years lived is
constant. In the figure on the right, this
means that line A divided by area B is
the same in both cases. This assumption
will help us to convert mortality rates
into survival probabilities.
Video Lecture 1.3 – The Life Table (B)
A life table is a collection of age-specific mortality probabilities. Such a table shows, for each age, what
the probability is that a person of that age will die before his or her next birthday. From this starting point,
a number of statistics can be derived that are also included in the life table. These statistics include the
probability of surviving any particular year of age, the remaining life expectancy for people at different
ages, the proportion of the original birth cohort still alive at each age and estimates of a cohort’s longevity
characteristics.
On the right, you see how a life
table (for dogs) looks like.
Mortality risk for x to x+1 gives
the probability that a dog dies,
for instance, between its fifth
and sixth birthday. Survivors as x
gives the number of dogs that
are still alive at consecutive ages
(out of the 1,000 dogs we start
with). Deceased in x to x+1 gives
the number of dogs that die at
each year. Years lived in x to x+1
refers to the number of years
lived in each year. Total years
lived after x gives the total
number of years lived after a
certain age. Life expectancy at x gives the life expectancy at each age; for instance, a dog that is 10 years
old will, on average, live for another 3.29 years. The life expectancy at a certain age is calculated as the
average total number of years lived per dog. Hence, you calculate it by dividing total years after x by
survivors at x. In the table, life expectancy generally decreases. However, it increases when going from
age 0 to age 1. So, once a dog survives from age 0 to age 1, its life expectancy becomes higher. This is due
to the fact that the mortality risk at an age of 0 is relatively high.
In a life table, the starting number of the number of people alive at an age of 0, also referred to as the
radix, is usually set at 1,000 or 100,000. Suppose that x is the age in completed years (or birthdays) and
q(x) is the probability to die between x and x+1. Then, we can make the following calculations:
, • The number of survivors to age x: l(x)
o l(x) = l(x-1) × [1 – q(x-1)]
• The number of persons dying between x and x+1: d(x)
o d(x) = l(x) – l(x+1)
o d(x) = l(x) × q(x)
• The number of person-years lived between x and x+1: L(x)
o L(x) = l(x+1) + [0.5 × d(x)]
o L(x) = 0.5 × [l(x) + l(x+1)]
o To calculate the number of life years, we generally assume that death occurs uniformly
within the age interval; that is why we use the 0.5. But due to the uneven distribution of
deaths during the first year of life, 0.5 should be replaced by a lower value (like 0.2).
o Sometimes, the last age interval is not closed (suggesting that not everyone has died at
the last age interval). In that case, you take the number of people alive at the last age
interval that you have and divide this by the mortality rate: L(ω) = l(ω) / m(ω). This is the
exact estimate of life years lived under the assumption that mortality rates are constant.
o We generally work with life tables that have intervals of one year, but you can also have
age intervals of for instance 5 or 10 years. The calculation is the same as with normal life
tables, except: L(x,x+5) = [5 × l(x+5) + [2.5 × d(x,x+5)].
• The number of person-years lived after x: T(x)
o T(x) = L(x) + L(x+1) + L (x+2) + … + L(x=max)
• The average number of person-years lived after x: e(x)
o e(x) = T(x) / l(x)
o This is essentially the life expectancy at age x.
Mortality probabilities, q(x), are derived from observed or published mortality rates, m(x). If we assume
that mortality rates are constant across the age intervals, then we can use the following formula to
convert age-specific yearly mortality rates into mortality probabilities: 𝑞(𝑥) = 1 − 𝑒 −𝑚(𝑥) . So, q(x) equals
the number of deaths divided by the number of persons at the beginning of the age interval, whereas m(x)
equals the number of deaths divided by the number of person-years at risk during the age interval. In
other words, q(x) = d(x) / l(x) while m(x) = d(x) / L(x,x+1). Note that m(x) is always larger than q(x) since
L(x,x+1) is always smaller than l(x). Finally, keep in mind that rates can be added but probabilities not.
Video Lecture 1.4 – Cohort Life Expectancy
A life table represents the experience of a cohort. But which cohort? A hypothetical cohort, exposed to
current mortality rates. Hence, we refer to these life tables as ‘current’ or ‘period’ life tables, as they give
a summary of current mortality conditions. But this differs from the experience of a real cohort that is
followed longitudinally over time. If we would look at an actual birth cohort and their actual mortality
probabilities at different stages of their life, then we use ‘cohort’ or ‘generation’ life tables.
To explain the difference between a period life table and a cohort life table, let us consider the current
(2019) period life expectancy at an age of 65 for Dutch women. The current life expectancy for Dutch
women aged 65 is 21.7 years. Is this a good prediction of the number of life years a 65-year-old women
can expect to live? No, because the predicted cohort life expectancy of current 65-year-olds is 23.6 years.
, This example can be further
illustrated by means of the
figure on the right, in which you
see the actual mortality
probabilities of different
cohorts over time. For
instance, the green line
represents the mortality
probabilities of the cohort that
was born in 1955, which are
comprises those people who
are 65 years old in 2020. The
blue and red line represent the
mortality probabilities of the cohorts born in 1930 and 1940, respectively. To get the period life
expectancy for 90-year-olds, we would use the current mortality probabilities of people born in 1930.
Similarly, we would use the current mortality probabilities of people born in 1940 for 80-year-olds. The
question is whether these probabilities are informative for the actual probabilities that the cohort born in
1955 (the current 65-year-olds) will face during the rest of their lives. As you can see in the figure, the
answer is no. This is because the blue line is always higher than the red line (and the red line is always
higher than the green line); across cohorts, survival probabilities are increasing (or mortality probabilities
decreases). So, if we would use the mortality probability at an age of 80 from the current 80-year-olds,
then we overestimate the probability of dying at an age of 80 for the current 65-year-olds. In this case,
the period life expectancy is not a good forecast for the actual life expectancy of the cohort born in 1955.
If we want to make a prediction of the actual life expectancy for the cohort born in 1955, we need to
predict their own future mortality rates. Predicted mortality probabilities are generally below the actual
mortality probabilities of the past.
If there are declining trends in mortality over time, then the period life expectancy generally
underestimates the cohort life expectancy for new cohorts. That is because, for the period life expectancy,
at each point in time you use older survival probabilities while we know that younger cohorts are generally
healthier and therefore have lower mortality probabilities (or higher survival probabilities).
How to make cohort life tables? One way to look
at this is by using a Lexis diagram, as shown on
the right. A Lexis diagram basically uses the same
inputs for period life expectancy (one of the
columns), but then extended over multiple years.
The figure presents mortality probabilities at a
particular year by age for the base year (y) and
the years thereafter. So, we have mortality
probabilities across age and across time. If we
want to follow a particular cohort, we have to go
diagonally through the Lexis diagram. For
instance, if we want to know the mortality probabilities at different ages for people who were aged X in
year y, then we need to look at the mortality probabilities of X+1 in year y+1, X+2 in year y+2, et cetera.
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