Public Health Economics
Meeting 1: Introduction to summary measures of population health &
the (Sullivan) life table
Part 1: Population Health Measurement
SMPH:
- Allow comparison of
o Different countries
o Different subgroups within countries (e.g. socio-economic status)
o Countries overt time
- With the goal to identify
o Progress
o The impact of interventions (economic evaluations/ HTA/ CEA)
o Disadvantaged populations/ subgroups in need
Measures
- Death rate per country
o More in Russia, South of Africa
o To be able to compare, death rates/ per cent numbers are not enough
- Infant mortality world wide
o Specifically focus on mortality
o Infant mortality in Africa is high
- Death rates comparison in age category across countries (time trends)
o Death rates per age group in time across countries
- Different age groups in 1 country over time
Measuring population health
- Counting the dead says something, but does not tell the whole story
o It does not reflect (life) time
▪ Age composition?
▪ Not able to compare ‘overall’ but only in age groups
- LE is a simple measure to compare mortality over time, across countries etc.
o Translate mortality risk at different ages into time:
▪ Average amount of years lived
• Make life time comparisons over time and across countires
Part 2: The life table
Life table
- A useful tool to summarize mortality probabilities
- At the heart of modelling the impact of public health interventions
- A simple way to create survival curves and calculate life expectancy
- Can be extended to calculate DFLE/ QALE and expected lifetime health care expenditures
o DFLE: disability free life expectancy
o QALE: quality adjusted life expectancy
Life expectancy
The crucial lifetime equation
1
, - Continuous: above
o LE: Area under the curve of the survival
curve
▪ Integral of the survival function
at a specific age until infinity
▪ Age A= death age A>a
- Discrete: below
o More closely related to life table
o Not the integral, but sum up survival function over different ages
The Survival Curve
- age 20: =±0.45.
- Probability that someone at age 0 will still be alive
at age 20 = 0.45
- LE: area under the survival curve
- Age 0: LE is the integral from 0- infinity (purple
area)
- Remaining LE at age 20: part of the survival curve
after age 20.
o Purple area/ probability still alive at 20
o Only interested in people that are still alive
at a specific age
- mortality rate
o is the ratio of people dying within a certain period
and the amount of time lived (A/ B)
▪ line A/ surface B
o For each point in time/ for each age interval. The
people that die in that interval, related to the total
number of life years lived is constant. Relation AB
is the same
o The average number of life years lived between
ages 0 and 20 is B
▪ Someone with age zero has a …% chance
to make it to age 20
o LE= 1/m
▪ B/A= D/C= 1/m: ratio is equal in all points
2
,Survival curve in practice
- We only know the number of deaths
per age
Part 2B: What is a life table?
- A collection of age specific mortality probabilities
- A table which shows
o For each age, what the probability is that a person of that age will die before their
next birthday
o From this starting point, a number of statistics can be derived and thus also included
in the table
▪ The probability of surviving any particular year of age
▪ Remaining life expectancy for people at different ages
▪ The proportion of the original birth cohort still alive
▪ Estimates of a cohorts longevity characteristics
John Graunt (1620- 1674)
- Inventor of the life table
- Left: at age 0, there are 100 newborns, between
age 0-6: 0.36/ 36% died
o 100-36= 64
o 64- (64*37.5%=24)= 40
o Continue this process
- Assumption: all these birth rates/ death rates
are constant
o Does not hold (elderly vs young)
Calculation of the life table
- Age x
- Mortality risk q(x)
o Probability that someone dies between age x and
x+1
- Number of survivors at x (radix) l(x)
- Deceased:
o How many die at each age
- Years lived between x and x+1 L(x)
- Total years lived after x T(x)
- Life expectancy at x e(x)
3
, How to calculate the life table/ life table functions
- You start with a table with x and q(x)
o X: age
o q(x): the probability to die between x and x+1
▪ q(X) is input to the life table
- Calculate l(x), d(x)
o l(x) l(x)= the number of survivors to age x
▪ I(0), the radix is usually set at 1000 or 100000
▪ l(x)= I(x-1)*(1-q(x-1))
▪ for the second year: l(x)= x,t=1 – d(x)
o d(x)= the number of persons dying between x and x+1
▪ l(x)* q(x)
- Calculate L(x): years lived between a and x+1. We assume that those who died between x
and x+1, we assume that they live half a year
o l(x, t+1) + 0.5*d(x, t=1)
o last age interval: l(x)/ m(x)
- T(x)= the number of person=years lived after x
o Start at bottom/ the end
o T(x)= L(X)+ T(x+1)
o Last year: l(x)/ m(x)
- Calculate e(x)= average number of total life years lived per person
o T(x)/ l(x)
o Is decreasing at higher ages (logically)
o And higher above age 1 (infant mortality)
- Make a Curve: l(x)
o LE is the area under the curve
o Example remaining LE at age 3
▪ T(X) / l(x)= e(x)
4
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