For epidemiology students

1. MEASURES OF MORTALITY
Ankunda Racheal Kabali (BSN,MPH)

2. MORTALITY
• Death is the permanent disappearance of all evidences of life at any time
after birth (WHO)
Mortality is of great interest because;
• Death is the ultimate experience that every human being is destined to
have.
• Therefore, death is of tremendous importance to each person. The
questions of when and how death will occur and whether there is any way
to delay it are very important.
• From the standpoint of studying disease occurrence, expressing mortality
in quantitative terms can pinpoint differences in the risk of dying from a
disease between people in different geographic areas and subgroups in the
population.

3. CONT…
• Mortality rates can serve as measures of disease severity, and thus
help us to determine whether the treatment for a disease has
become more effective over time.
• Given the problem that often arises in identifying new cases of a
disease, mortality rates may serve as substitutes/ alternatives for
incidence rates when the disease being studied is a severe and lethal
one.

4. Determinants of mortality
• Factors of mortality patterns can be endogenetic( biological) or
exogenetic (environmental) and may vary over time and space.
• These are classified into two;
1.Demographic structure:- age, sex composition etc.
2.Social adversements:- age at marriage, adequacy of medical facilities,
general condition of nutrition, housing and sanitation, literacy,
religion, standard of leaving or per capita income, type of economy
etc.

5. Mortality rates :How is mortality expressed in quantitative terms?
• Types of mortality rates;
1.Annual/ crude death rate ( death from all causes) d = 𝐷
𝑃 𝑋 1000
D = number of deaths in a population during a given calendar year
P=number of persons living in a population at mid year/average number of
persons living in a population during the year.
• Crude Death rate =
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑒𝑎𝑡ℎ𝑠
𝑡𝑜𝑡𝑎𝑙 𝑚𝑖𝑑 𝑦𝑒𝑎𝑟 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛
x 1000.
Advantages; requires minimum data on mortality and is easy to interpret
Disadvantages; since risk of death is not uniform among different segments
of a population, crude measure cannot be used directly for comparing levels
of mortality between countries.

6. 2. Specific death rate.
The crude death rates for specific causes of death are calculated in a
similar way by selecting deaths due to specific cause as the numerator
and mid-year population as the denominator. Thus,
• Cause specific death rate =
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑒𝑎𝑡ℎ𝑠 𝑑𝑢𝑒 𝑡𝑜 𝑠𝑜𝑚𝑒 𝑝𝑎𝑟𝑡𝑖𝑐𝑢𝑙𝑎𝑟 𝑐𝑎𝑢𝑠𝑒
𝑡𝑜𝑡𝑎𝑙 𝑚𝑖𝑑− 𝑦𝑒𝑎𝑟 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛
x1000
• The rates could be made specific to sex/age by selecting the
numerator and the denominator for each sex/age of the population.

7. Crude death rate
• Advantages;
Provides an overview of risk of death in a population
Easy to compute as it uses population at mid year as the denominator
and to interprete.
It is part of the population growth equation
Disadvantages
It is not a reliable indicator of comparative mortality levels because it is
does not take into account the effect of age, sex and other confounding
factors on the mortality

8. Crude versus specific rates
• Crude rate is the rate in which the denominator includes the total
population.
• Specific rate stands for the rate that measures morbidity or mortality
for a particular population or disease

9. example
• If we are interested in mortality of children younger than 10 years, we
can calculate the rate specifically for that group as follows;
𝑎𝑛𝑛𝑢𝑎𝑙 𝑚𝑜𝑟𝑡𝑎𝑙𝑖𝑡𝑦𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑖𝑙𝑑𝑟𝑒𝑛 𝑦𝑜𝑢𝑛𝑔𝑒𝑟 𝑡ℎ𝑎𝑛 10 𝑦𝑒𝑎𝑟𝑠
=
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑒𝑎𝑡ℎ𝑠 𝑓𝑟𝑜𝑚 𝑎𝑙𝑙 𝑐𝑎𝑢𝑠𝑒𝑠 𝑜𝑓 𝑐ℎ𝑖𝑙𝑑𝑟𝑒𝑛 𝑦𝑜𝑢𝑛𝑔𝑒𝑟 𝑡ℎ𝑎𝑛 10 𝑦𝑒𝑎𝑟𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐ℎ𝑖𝑙𝑑𝑟𝑒𝑛 𝑦𝑜𝑢𝑛𝑔𝑒𝑟 𝑡ℎ𝑎𝑛 10 𝑦𝑒𝑎𝑟𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑎𝑡 𝑚𝑖𝑑 𝑦𝑒𝑎𝑟
𝑥 1000
Note that on putting a restriction, e.g. age, it should apply to both the
numerator and denominator.

10. Case fatality
Case fatality is the proportion of people who die from a specific disease in a specified period of time.
• Different from mortality rate and calculate
𝑐𝑎𝑠𝑒 𝑓𝑒𝑡𝑎𝑙𝑖𝑡𝑦 𝑟𝑎𝑡𝑒 % =
𝑛𝑜 𝑜𝑓 𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙𝑠 𝑑𝑦𝑖𝑛𝑔 𝑑𝑢𝑟𝑖𝑛𝑔 𝑎 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑒𝑑 𝑝𝑒𝑟𝑖𝑜𝑑 𝑜𝑓 𝑡𝑖𝑚𝑒
𝑎𝑓𝑡𝑒𝑟 𝑑𝑖𝑠𝑒𝑎𝑠𝑒 𝑜𝑛 𝑠𝑒𝑡 𝑜𝑟 𝑑𝑖𝑎𝑔𝑛𝑜𝑠𝑖𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙𝑠 𝑤𝑖𝑡ℎ 𝑡ℎ𝑒 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑒𝑑 𝑑𝑖𝑠𝑒𝑎𝑠𝑒
𝑥100
• Date of disease on set would be the ideal, however, it is hard to standardize as most patients do not
remember it. Date of diagnosis is easily traced from medical records.
• The numerator of case-fatality should ideally be restricted to deaths from that disease. However, it is not
always easy to distinguish between deaths from that disease and deaths from other causes. E.g. a person
with the disease could die in a car accident.
• Case fatality is not a rate but a percentage of those with the disease.

11. Use of Case fatality rate(CFR)
• Represents the ratio of death to cases
• Virulence of organisms and killing power of a disease
• Useful in acute infectious diseases e.g Ebola, covid-19,cholera and
measles
• Mortality rate depends on case fatality rate and incidence.
• Mortality rate =𝐶𝐹𝑅𝑋𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑐𝑒 𝑟𝑎𝑡𝑒.
• If the CFR is high, then the mortality rate will be high for a given
incidence
• If there are lots of cases(high incidence), then the mortality rate will
tend to higher for a given case fatality rate

12. What is the difference incase fatality and
mortality rate ?
• In a mortality rate, the denominator represents the entire population
at risk of dying from the disease, including both those who have the
disease and those who do not have the disease (but who are at risk of
developing the disease).
• In case fatality, however, the denominator is limited to those who
already have the disease. Therefore case fatality is a measure of
severity of disease and can also be used to measure any benefits of a
new therapy.

13. example
• Assume that in a population of 100,000 persons, 20 have disease X. In
one year, 18 people die from that disease. The mortality is very low
(0.018%)because the disease is rare; however, once a person has the
disease, the chances of his or her dying are great (90%).
𝑚𝑜𝑟𝑡𝑎𝑙𝑖𝑡𝑦 𝑟𝑎𝑡𝑒 𝑓𝑟𝑜𝑚 𝑑𝑖𝑠𝑒𝑎𝑠𝑒 𝑋 =
18
100,000
=0.00018 or 0.18%
𝑐𝑎𝑠𝑒 𝑓𝑒𝑡𝑎𝑙𝑖𝑡𝑦 𝑓𝑟𝑜𝑚 𝑑𝑖𝑠𝑒𝑎𝑠𝑒 𝑋 =
18
20
= 0.9 𝑜𝑟 90%

14. Proportionate mortality
• Another measure of mortality which is not a rate.
• It calculates the proportion of death due to a particular disease or
cause.
• For example;
𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛 𝑜𝑓 𝑑𝑒𝑎𝑡ℎ 𝑑𝑢𝑒 𝑡𝑜 𝑐𝑎𝑟𝑑𝑖𝑜𝑣𝑎𝑠𝑐𝑢𝑙𝑎𝑟 𝑑𝑖𝑒𝑎𝑠𝑒 𝑖𝑛 2010
= 𝑛𝑜.𝑜𝑓 𝑑𝑒𝑎𝑡ℎ𝑠 𝑓𝑟𝑜𝑚𝑐𝑎𝑟𝑑𝑖𝑜𝑣𝑎𝑠𝑐𝑢𝑙𝑎𝑟 𝑑𝑖𝑒𝑎𝑠𝑒𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑈.𝑆 𝑖𝑛 2010
𝑇𝑜𝑡𝑎𝑙 𝑛𝑜.𝑜𝑓 𝑑𝑒𝑎𝑡ℎ𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑈.𝑆 𝑖𝑛 2010
𝑥100

15. Years of potential life lost(YPLL)
• Is a measure of premature mortality or early death.
• YPLL recognizes that death occurring in the same person at a younger
age clearly involves a greater loss of future productive years than
death occurring at an older age.
• Calculation involves two steps;
First, age at death from a certain cause is subtracted from a
predetermined age at death (75yrs in the U.S). If a child dies at 2 years
=75-2=73
Second, the YPLL for each individual are then added together to yield
the total YPLL for the specific cause of death.

16. Comparing mortality in different populations
• Mortality data can be used to compare two or more populations or
the same population in different time periods.
• Such characteristics may have differing characteristics that affect
mortality of which age is the most important factor.
• Therefore, methods have been developed for comparing mortality in
such populations while effectively holding constant characteristics
such as age.

17. example,
Crude Mortality Rates by Race,
Baltimore City, 1965
race Mortality per 1000 population
whites 14.3
blacks 10.2

18. Crude birth rate
• Crude birth rate indicates the number of live births occurring the year
per 1000 population estimated at mid year.
• Subtracting crude death rate from crude birth rate provides the rate
of natural increase which is equal to the rate of population change in
the absence of migration
• crude birth rate =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑖𝑟𝑡ℎ𝑠 𝑥1000
𝑒𝑠𝑡𝑖𝑙𝑎𝑡𝑒𝑑 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑎𝑡 𝑚𝑖𝑑 𝑦𝑒𝑎𝑟.
• Crude birth rate can help estimate general fertility and pregnancy
rate.

19. Neonatal and perinatal mortality rate
• Neonatal mortality rate is the total number of neonatal babies in a
year divided by the number of live births occurring in a year
multiplied by 1000.
• Perinatal mortality rate is the sum of the number of still births and
early neonatal deaths(under 7 days) divided by the number of
pregnancies of 7 months(28 weeks) or more months duration
expressed per 1000. or the number of still births and deaths in the
first week of live per 1000 live births

20. Maternal mortality rate
• Is the number of resident maternal deaths within 42 days of
pregnancy termination due to complications of pregnancy, childbirth
and the pueperium in a specified geographic area for a specified
period of time usually a year multiplied x 100000.
• Maternal mortality rate =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑟𝑒𝑠𝑖𝑑𝑒𝑛𝑡 𝑚𝑎𝑡𝑒𝑟𝑛𝑎𝑙 𝑑𝑒𝑎𝑡ℎ𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑟𝑒𝑠𝑖𝑑𝑒𝑛𝑡 𝑙𝑖𝑣𝑒 𝑏𝑖𝑟𝑡ℎ𝑠
x100000
• Example ; 84 maternal deaths in 2008
130,000 live births in 2008
Maternal mortality rate =84
130,000x100000 =64.6 maternal deaths per
100, 000 live births

21. Maternal mortality rate
• Is considered a primary and important indicator of a geographic area’s
overall health status or quality of life.

22. QALY (Quality-Adjusted Life Year)
• A QALY is the arithmetic product of life expectancy combined with a
measure of the quality of life-years remaining. The calculation is relatively
straightforward; the time a person is likely to spend in a particular state of
health is weighted by a utility score from standard valuations.
• In such valuation systems, ‘1’ equates perfect health and ‘0’ equates death.
Since certain health states that are characterised by severe disability and
pain are regarded as worse than death, they are assigned negative values.
• If an intervention provided perfect health for one additional year, it would
produce one QALY. Likewise, an intervention providing an extra two years
of life at a health status of 0.5 would equal one QALY.
• This effect is related to cost; cost per QALY. For example, if a new treatment
gave an additional 0.5 QALYs and the cost of the new treatment per patient
is a5,000 then cost per QALY would be a10,000 (5,000/0.5).2

23. The Calculation
• The QALY can be calculated using the following formula which assumes a utility value (quality of life)
between 1 = perfect health and 0 = dead:
Years of Life x Utility Value = #QALYs
• This means:
• If a person lives in perfect health for one year, that person will have 1 QALY.
(1 Year of Life × 1 Utility Value = 1 QALY)
• If a person lives in perfect health but only for half a year, that person will have 0.5 QALYs.
(0.5 Years of Life x 1 Utility Value = 0.5 QALYs)
• Conversely, if a person lives for 1 year in a situation with 0.5 utility (half of perfect health), that person will
also have 0.5 QALYs.
(1 Year of Life x 0.5 Utility Value = 0.5 QALYs)
• In cost-effectiveness studies (or: health economic evaluations) the QALY is used to quantify the effectiveness
of, for instance, a new medicine versus the current one. In other words, the current standard of care is taken
as the baseline, and the QALYs gained from the new (improved) intervention are counted in addition.

24. Example
• If a person lives for 3 years with a disease and the current standard of care for
that disease means he/she lives with a utility level of 0.7, that person will have
2.1 QALYs.
(3 Years of Life x 0.7 Utility Value = 2.1 QALYs)
• If that person takes a new medicine (Med A) whereby his/her utility level
increases to 0.9, that person will now have 2.7 QALYS. Therefore, the benefit of
the new medicine will be counted as 0.6 QALYs as this is the increase over the
current standard of care.
(3 Years of Life x 0.2 Additional Utility Level = 0.6 QALYs)
• Similarly, if a new medicine (Med B) prolongs the patient’s life by 2 years, at a
utility level of 0.7, the new medicine will provide the person with 1.4 additional
QALYs.
(2 Years of Additional Life x 0.7 Utility Value = 1.4 QALYs)

25. DALY (Disability-Adjusted Life Year)
• DALYs sum years of life lost (YLL) due to premature mortality and years
lived in disability/disease (YLD
• YLL are calculated as the number of deaths at each age multiplied by the
standard life expectancy for each age.
• YLD represent the number of disease/disability cases in a period multiplied
by the average duration of disease/disability and weighted by a
disease/disability factor.
• As an example, a woman with a standard life expectancy of 82.5 years and
dying at age 50 would suffer 32.5 YLL. If she additionally turned blind at
aged 45, this would add 5 years spent in a disability state with a weight
factor of 0.33, resulting in 0.33 x 5 = 1.65 YLD. In total, this would amount
to 34.15 DALYs.

26. DALYs
• For DALYs, the scale used to measure health state is inverted to a
‘severity scale’, whereby ‘0’ equates perfect health and ‘1’ equates
death. The weight factors are age-adjusted to reflect social preference
towards life years of a young adult (over an older adult or young
child). Furthermore, they are discounted with time, thus favouring
immediate over future health benefits.
• It is important to understand the differences between QALYs and
DALYs, they are not interchangeable. The two measures can produce
different results dependent on age at onset and duration of disease,
and whether age and disability are weighted.

27. Limitations of DALYs and QALYs
• Neither measure fully captures the wider effects that stem from interventions:
emotional and mental health, impact on careers and family, or non-health effects
such as economic and social consequences (e.g. loss of work).
• QALYs can lack sensitivity and may be difficult to apply to chronic disease and
preventative treatment. The derivation of ‘health state utilities’, i.e. defining
weighting factors for specific health states, is subjective and controversial.
Disease-specific measures may be used, but must be interpreted with caution.
• Similarly, standard life expectancy figures may overestimate DALYs saved when
actual (local) life expectancy is shorter.
• Social preference weighting and discounting of DALYs present certain ethical
issues: are young adults and non-disabled more productive and valuable to
society? Does the value of health decrease over time?

28. references
• Epidemiology (5th Edition) by Leon Gordis
• https://www.cdc.gov/ principles of epidemiology/ morbidity
frequency measures