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Measures of Disease: Learning Objectives
1. Understand different types of populations as conceptualized in epidemiology and the relevance
of population types to measures of disease
2. Understand concept of disease occurrence in time
a. Understand and be able to define concepts of disease occurrence in time at a population level
(age, period, cohort effects)
b. Understand and be able to define concepts of disease occurrence in time at an individual level
(i.e., latent period, lead time), and their implications for measuring disease at the population level
3. Understand and be able to define and contrast prevalence and incidence
4. Understand and be able to define and contrast risks and rates
5. Calculate and interpret prevalence (this includes knowing the formula)
6. Understand, define, calculate, and interpret cumulative incidence (this includes knowing the
formulae)
a. Know different methods for calculating cumulative incidence and the assumptions and purposes
of each
7. Understand, define, calculate, and interpret incidence density (knowing the formulae)
a. Understand and calculate person-time
8. Define and interpret a hazard rate
9. Understand and be able to convert between prevalence, cumulative incidence and incidence
density (this includes knowing the formulas)
10. Direct and indirect standardization
` a. Perform both and understand when each is appropriate (know the formulae)
b. Know what data are required for each
Measures – cumulative incidence
• Different methods for calculating
– Simple cumulative
– Actuarial
– Kaplan-Meier
– Density
Measures – cumulative incidence
• Subscript notation
– R(t0,tj)
– risk of disease over the time interval t0
(baseline) to tj (time j)
– R(tj-1,tj)
– risk of disease over the time interval tj-1
(time before time j) to tj (time j)
Measures – cumulative incidence
• Subscript notation
– N’0
– number at risk of disease at t0 (baseline)
– N’0j
– number at risk of disease at the beginning of
interval j
Measures – cumulative incidence
• Subscript notation
– Ij
– incident cases during the interval j
– Wj
– withdrawals during the interval j
Measures – cumulative incidence
Simple cumulative method:
R(t0,tj)
= CI(t0,tj)
= I
N'0
• Risk calculated across entire study period assuming all
study participants followed for the entire study period, or
until disease onset
– Assumes no death from competing causes, no withdrawals
• Only appropriate for short time frame
Measures – cumulative incidence
Simple cumulative method:
• Example: incidence of a foodborne illness if all those
potentially exposed are identified
Measures – cumulative incidence
Actuarial method:
R(tj-1, tj)
= CI(tj-1, tj)
=____Ij
____
N'0j
- Wj
/2
• Risk calculated accounting for fact that some
observations will be censored or will withdraw
• Assume withdrawals occur halfway through each
observation period on average
• Can be calculated over an entire study period
– R(t0,tj)
= CI(t0, tj)
= I/(N’0
-W/2)
• Typically calculated over shorter time frames and risks
accumulated
Measures – cumulative incidence
Modification of Szklo Fig. 2-2 – participants observed every 2 months (vs 1)
• Where to start – set up table with time intervals
• Fill incident disease cases and withdrawals into appropriate
intervals
• Fill in population at risk
Measures – cumulative incidence
Actuarial Method
• Calculate interval risk
• R(tj-1, tj)
= Ij
/(N’0j
-(Wj
/2))
• R(0,2)
=1/(10-(1/2)) = 0.11
Measures – cumulative incidence
Actuarial Method
• Calculate interval survival
• next step: S(tj-1,tj)
= 1-R(tj-1,tj)
Measures – cumulative incidence
Actuarial Method
• Calculate cumulative risk – example of time 0 to 10
• R(t0, tj)
= 1 - Π (1 – R(tj-1,tj)
) = 1 - Π (S(tj-1,tj)
)
• R(0, 10)
= 1 – (0.89 x 0.88 x 1.0 x 1.0 x 0.85) = 0.34
Measures – cumulative incidence
Actuarial Method
• Calculate cumulative survival
• S(t0,tj)
= 1-R(t0,tj)
Measures – cumulative incidence
Actuarial Method
• Intuition for why R(t0, tj)
= 1 - Π (Sj
) using
conditional probabilities
• Example of 5 time intervals:
– Π (Sj
) = P(S1)*P(S2|S1)*P(S3|S2)*P(S4|S3)*P(S5|S4)
= P(S5)
– Multiply first two terms: P(S2|S1)*P(S1) = P(S2)
– Multiplying conditional probabilities gives you
unconditional probability of surviving up to any given
time point
– the value (1 - survival) up to (or at) a given time point
is then the probability of not surviving up to that time
point
Measures – cumulative incidence
Measures – cumulative incidence
• Exercise for home (discuss in lab)
– Study population observed monthly for 6 months
– Calculate the cumulative incidence of disease from
month 0 to 6
Measures – cumulative incidence
Kaplan-Meier method:
Rj
= CIj
=____Ij
____
Nj
• Risk calculated at the time each disease event occurs
– Accounts for withdrawals in that Nj
only includes those at risk at
each time j point
– Result differs from actuarial approach in that the time of a
withdrawal (in Kaplan-Meier analysis) coincides with time of an
incident disease
• Risks at each onset time j accumulated
• Where to start – set up table with times of incident cases
• Fill in population at risk – anyone who has withdrawn by a time j is
no longer at risk at that time
Measures – cumulative incidence
Kaplan-Meier Method
JC: discuss withdrawals
• Calculate risk at time j
• Rj
= Ij
/Nj
• R2
=1/10 = 0.10
• R4
=1/8 = 0.125
Measures – cumulative incidence
Kaplan-Meier Method
• Survival calculated as in actuarial method
• Cumulative risk calculated as in actuarial method
– R(t0, tj)
= 1 - Π (1 – Rj
) = 1 - Π (Sj
)
• Cumulative survival calculated as in actuarial method
Measures – cumulative incidence
Kaplan-Meier Method
JC: mention product-limit
Measures – cumulative incidence
Density method:
R(t0,t)
= 1 – S(t0,t)
= 1- e(-ID*Δt)
• Depends on functional relationship between a risk and a
rate
• Can be calculated over an entire study period if the rate
is constant
• Can also be calculated over shorter time frames and
risks accumulated
JC: Mention Elandt-Johnson article
Where to start – set up table with time intervals
• Fill incident disease cases, withdrawals and population at risk by
interval
• Calculate person time (for example used formula PTj
=(N’0j
-(Wj
/2))
Δtj
)
• Calculate IDj
= Ij
/PTj
Measures – cumulative incidence
Density Method
• Calculate interval risk
• R(t0,t)
= 1 – S(t0,t)
= 1- e(-ID*Δt)
• R(0,2)
= 1-e(-0.05*2)
= 0.10
Measures – cumulative incidence
Density Method
• Calculate cumulative risk – example of time 0 to 10
• Accumulate interval risks as in actuarial method
• Or calculate cumulative risk directly
• R(t0,t)
= 1- e(-∑ID*Δt)
• R(0,10)
= 1-e(-(0.05*2+0.06*2+0*2+0*2+0.08*2)
= 0.32
Measures – cumulative incidence
Density Method
• Cumulative survival calculated as in actuarial method
Measures – cumulative incidence
Density Method
Measures – cumulative incidence
Cumulative incidence
• Summary of methods for calculating and basis of
choosing
– Simple cumulative – complete follow-up
– Actuarial – incomplete follow-up
– Kaplan-Meier – incomplete follow-up
– Density – converting incidence density to cumulative incidence
Choosing among the CI methods
• Do you only have rate data? Generally you will choose incidence density.
•
• Do you have zero withdrawals and a short time period of interest? If so,
simple CI usually OK.
•
• Do you have fairly exact data on time of incidence and time of withdrawal?
If so, density preferable.
•
• Do you have fairly exact data on time of incidence but only interval data on
withdrawals? If so, KM most common choice; actuarial or density may not
be too different depending on withdrawal timing.
•
• Do you have interval data for incidence and withdrawal? If so, actuarial
most common choice, KM and density may not be too different depending
on withdrawal timing.
• Assumptions
– Uniformity of events and losses within each interval
(the W/2)
– Independence between censoring and survival –
otherwise biased/not accurate (also true for ID)
– Lack of secular trends
Measures – cumulative incidence
Epidemiologic measures
Szklo Exhibit 2-1
Measures of disease outline
– Big picture
– Illustration/discussion of measuring disease in time
– Populations
– Time scales affecting disease in populations
– Epidemiologic measures
• Basic concepts
• Measuring diseases
• Prevalence
• Incidence density (incidence rate)
• Cumulative incidence (risk)
• Relations among measures
– Standardization
– Summary
– Appendix: specific measures of disease
• Relations among measures
– Incidence and incidence odds
– Prevalence and incidence
– Risk and rate
Epidemiologic measures
Incidence and incidence odds
• CI ~ CI/ (1-CI)
– If disease is rare (<0.10)
• Why?
– Because CI odds = CI/(1-CI)
– if CI is small then 1-CI is close to 1 and CI/(close to
1) = CI
• Relevant because CI often modeled with logistic
regression which models the relative odds
instead of the relative risk (more in the
analyzing epidemiologic data section)
Measures - relations
Prevalence and incidence
• What is incidence density of disease in interval 1,2?
• (1/9 = 0.11/year)
Measures - relations
Prevalence and incidence
• What is this prevalence of disease if the population is
examined at one point in time?
Measures - relations
Prevalence and incidence
• What is incidence density of disease in interval 1,2?
Measures - relations
Prevalence and incidence
• What is this prevalence of disease if the population is
examined at one point in time?
Measures - relations
Prevalence and incidence
• P/(1-P) = ID x D
• Prevalence odds approximates the incidence density
(ID) times duration of disease (D), if population is
steady-state
• Under steady-state, for any given time period (Δt), inflow
(incident cases) = outflow (recovered cases)
– Inflow = incidence rate (i) * susceptible population (NS
)
– Outflow = recovery rate (r) * diseased, not at-risk pop (ND
)
• Under steady state,
• i * NS
= r * ND
• ND
/NS
= i * (1/r)
• Prevalence odds = incidence * avg duration
Measures - relations
JC: mention reciprocal of recovery rate
• P ~ ID x D
• Prevalence also approximates the incidence density
times duration under steady-state if disease is rare
(P<0.1)
• If disease is rare P/(1-P) ~ P
• P ~ P/(1-P) = ID x D
• If disease is not rare, P = (ID x D)/[(ID x D) + 1)]
• see Kleinbaum 7.1.3 for further treatment
• Relevant because studying prevalence odds instead of
prevalence may be less biased if interest is in
estimating measures related to incidence density since
P/(1-P) = ID x D
• Relations between prevalence odds can be modeled
with logistic regression which models the relative odds
(more in the analyzing epidemiologic data section)
Measures - relations
Risk and Rate
• R(t0,t)
= 1 – S(t0,t)
= 1- e(-ID*Δt)
• see Kleinbaum 6.4.3
• mention: N’t
= N’0
exp[-(ID) Δt ]
• Relation used earlier in calculation of risk based on rate
• Rate is the fundamental measure of disease occurrence
• Explanation by analogy: road trip
Measures - relations
Risk and Rate – road trip analogy
• On a road trip, the speed you travel (miles/hr, your rate
of travel) determines how far you have travelled (miles
travelled) at any given time since departure
– Could imagine measuring as cumulative miles/total miles to
destination (what measure of disease is this analogous to?)
• The distance you have travelled at any given time does
not determine your speed (although it is informative
about your speed)
Measures - relations
Measures - relations
Relation between risk and rate
• Recall: N’t
= N’0
exp[-(ID) Δt ]
• Slope = ΔN/Δt
• Slope/N’t
= ΔN/Δt(N’t
)
= -(new cases)/(change in time*population at risk)
= -(new cases)/person-time
= -ID
(new cases will be negative because ΔN is disease free people lost from the
surviving population)
Risk(t0,t)
= (N’0
-N’t
)/N’0
Summary – Rate, Risk and Prevalence
• Rate is the fundamental measure of disease
• Risk reflects the rate over a given time frame of interest
• Prevalence reflects both the rate of disease and the rate
of recovery (duration of disease)
Measures - relations
Measures of disease outline
– Big picture
– Illustration/discussion of measuring disease in time
– Populations
– Time scales affecting disease in populations
– Epidemiologic measures
• Basic concepts
• Measuring diseases
• Prevalence
• Incidence density (incidence rate)
• Cumulative incidence (risk)
• Relations among measures
– Standardization
– Summary
– Appendix: specific measures of disease
Types of rates
• Crude rate: number of events in a total population /
person-time for which the population at risk has been
observed
• Specific rates: number of events in a subpopulation /
person-time for which the subpopulation at risk has
been observed (e.g. for age groups)
• Standardized or adjusted rates: have undergone
statistical transformation to permit comparison of rates
across populations or among groups differing in the
distribution of some characteristic (e.g., age) that may
affect the risk of disease
Standardization
Comparing crude rates
• A crude rate represents the actual experience of the
population and is thus a valuable way to describe the
disease experience
• Comparing crude rates between two or more
populations can be misleading because populations
may differ with respect to characteristics that affect
morbidity and mortality
• What are some of the principal factors that influence
morbidity and mortality?
Standardization
• Consider age-specific rates…
• The crude rate can be thought of as a weighted average
of the age-specific rates
– the weights are the proportion of the population in
each age category
• Crude rate = ∑(age-specific rate x proportion of pop in
that age category)
• Even if two populations had identical age-specific rates,
the crude rates for the two populations would differ if the
age structure of the two populations were different
Standardization
• Population 1:
– 500,000 people aged 20-24
– 500,000 people aged 25-29
• Population 2:
– 200,000 people aged 20-24
– 800,000 people aged 25-29
• In both populations
– CI among 20-24 = 0.002
– CI among 25-29 = 0.009
• What are the crude “rates” in populations 1 & 2?
Standardization
• Crude rate = ∑(age-specific rate x proportion of pop in that age
category)
• Population 1, crude CI = 0.002*0.5 + 0.009*0.5 = 0.0055
• Population 2, crude CI = 0.002*0.2 + 0.009*0.8 = 0.0076
• What do you think about comparing the health experience of these
two populations using their CI values?
Population 1 Population 2
Age rate proportion rate proportion
20-24 0.002 0.5 0.002 0.2
25-29 0.009 0.5 0.009 0.8
Standardization
• Standardization of rates allows direct
comparison of rates between populations
– A standardized rate is a summary rate that has been
adjusted to account for the differences in the
distribution of characteristics that affect disease (e.g.,
age) between populations
– Standardized rates allow fair comparisons to be
made between populations
– Answers the question: what would the death rate be
in each population, if they had identical distributions
of {X}? e.g. age
– Counterfactual idea
Standardization
• Compare the death rates in these two states
• Concerns about direct comparison of these crude rates?
– Age structures of the populations of these two states are quite
different
Standardization
Direct standardization
• Choose a standard population (e.g., 1990 or 2000 US
population from US Census)
• Use the actual age-specific rates from each study
population (e.g., state)
• Apply these rates to the standard population in each
age category
• Calculate the number of outcomes that would have
been observed in the study population if it had the age
distribution of the standard population – a counterfactual
idea
• Calculate the adjusted rate of the outcome
Standardization
• Age adjusted rate = total expected outcomes
total standard population
Standardization
Key for direct adjustment:
Age specific rates come from your study population
Age specific population sizes (i.e, the weights) come from
the standard population
• Where to start – set up table with age intervals
• Fill in age specific rates from study population(s)
• Fill in age specific population sizes from standard population (from
outside source, e.g., US Census)
Standardization
Direct Standardization
• Calculate expected number of deaths for study population(s) within
age strata
• E = RateStudy
*PopulationStandard
• EFL<5
= (179.26/100,000)*18,900,000 = 33,880
Standardization
Direct Standardization
• Sum expected deaths for study population(s) and calculate age
adjusted rates
• Rateadj
= EStudy
/PopulationStandard
• RateadjFL
=1,912,628/248,800,000 = 0.007686 = 768.6/100,000
Standardization
Direct Standardization
Standardization
• Compare the death rates in these two states again
Direct Standardization
• Choice of standard population
– Distribution of one of the two populations you want to
compare
– Distribution of the two populations combined
– Some outside standard (e.g., US population from
census)
– Choice should be driven by the counterfactual
question you want to ask
• What would the rates be if my two study populations had the
same age structure as population X?
Standardization
• Beware: the values you calculate will depend on
the standard population chosen
– Can get different results from different standards if
the standards have notably different age structures
• Note that the actual value of the new adjusted
rate is a product of the choice of a standard
population – it is not a “real” rate
Standardization
Pros:
• Directly standardized rates can be used to compare
disease rates across areas and time
Cons:
• Requires age-specific rates that are not often available
at a local level or in certain populations
• Rates may not be stable for small number of events
(approximately <100 events)
Standardization
Standardization
• At home exercise (for lab)
– Prostate cancer mortality by race
– White men: 1359 deaths / 4,738,246 men
– 28.7 deaths per 100,000 men
– Black men: 121 deaths / 418,992 men
– 28.9 deaths per 100,000 men
Standardization
• At home exercise (for lab)
• Calculate age adjusted rates of prostate cancer
mortality by race
• There may be situations in which age-specific rates are
not available for your study population
– Common in occupational studies – number of cases available
from records but unable to reconstruct rates
• You still want to be able to make a comparison between
the disease experience of your study population and
another population accounting for differences in the
distribution of characteristics (e.g., age)
• If you know the age structure of your study population,
indirect standardization is an option
Standardization
• Choose a standard population for which rates of your
outcome are available
• Use the age-specific rates from the standard population
• Apply these rates to the study population in each age
category
• Calculate expected number of deaths that would have
occurred in the study population
• This expected number of deaths is counterfactual
– It’s the number of deaths that would have occurred in the study
population if it had the same age-specific rates as the standard
population
• Compare the observed number of deaths in the study
population to the expected number of deaths if the
standard rates applied
Standardization
Standardization
• SMR = total observed outcomes x 100
total expected outcomes
• Standardized morbidity/mortality ratio (SMR):
– Ratio of the observed number of outcomes in the study
population to the expected number of outcomes if the study
population had the same age-specific rates as the standard
population
– Answers question: is the morbidity/mortality experience greater
than, less than, or similar to that which is expected in the
standard population? (if equal, SMR = 100)
• Direct vs. indirect standardization
summary
Population used
(weight)
Rate applied
Direct Standard Study
(observed)
Indirect Study
(observed)
Standard
Standardization
Key for indirect adjustment:
Age-specific rates come from your standard population
Age-specific population sizes (also called weights) come
from the study population
Standardization
• Example: we have data from two health care
organizations on the numbers of occupational injuries
reported
– Health care organization 1: 95
– Health care organization 2: 64
• We are wondering how these health care organizations
compare to the US average for those working in health
care regarding injuries
Standardization
• Where to start – set up table with age intervals
• Fill in age-specific rates from standard population
• Fill in age-specific population sizes from study population(s)
Standardization
Indirect Standardization
• Calculate expected number of injuries for study population(s) within
age strata
• E = RateStandard
*PopulationStudy
• EOrg1,15-30
= (60/10,000)*5700 = 34.2
Standardization
Indirect Standardization
• Sum expected injuries for study population(s) and calculate SMR(s)
• SMR = O/E
• SMROrg1
= (95/66.7)*100 = 142
Standardization
Indirect Standardization
• Interpret each SMR as a comparison of that study population to the
standard
– Health care organization 1 had a 42% higher rate of injury than the
health care workers in the US population
– Health care organization 2 had a 9% lower rate of injury than the health
care workers in the US population
• You cannot compare SMRs to each other
Standardization
Indirect Standardization
Pros:
• Indirect standardization does not require age-specific rates, only
total number of events in the study population and age structure of
the study population
Cons:
• SMRs cannot be directly compared
– Each SMR captures a counterfactual comparison within that
specific population
• E.g, Observed deaths from pop A/Expected deaths from pop A (if
standard rates applied)
– The two study populations may have different age structures
and the expected deaths depends on the age structure of each
study population
• Unlike directly standardized rates, SMRs give no idea of the actual
burden of disease
Standardization
Standardization
• Examining the lack of comparability of SMRs by uncovering the
true age-specific injury rates in our two health care organizations
Standardization
• Age-specific injury rates are IDENTICAL in the two health care
organizations
Standardization
• Why are the SMRs so different?
• Org 1 has a younger population and the age-specific rates in that
younger population are higher than in the standard
• Org 2 has an older population and the age-specific rates in that older pop
are lower than in the standard
• Each SMR is a comparison of one study population to the standard – not
a comparison of one study population to another
• Direct vs. indirect standardization
summary
Population used
(weight)
Rate applied
Direct Standard Study
(observed)
Indirect Study
(observed)
Standard
Standardization
Measures of disease outline
– Big picture
– Illustration/discussion of measuring disease in time
– Populations
– Time scales affecting disease in populations
– Epidemiologic measures
• Basic concepts
• Measuring diseases
• Prevalence
• Incidence density (incidence rate)
• Cumulative incidence (risk)
• Relations among measures
– Standardization
– Summary
– Appendix: specific measures of disease
Summary
• Measures of disease are a fundamental tool in
epidemiology
• Measure for any given study should be selected
keeping in mind:
– The type of population from which it will arise
• Example: study capturing an open population should
measure incidence density
Summary
– The disease and how the disease process and
potential exposure disease relation can best be
captured
• Example: study of smoking and heart disease has to follow
participants for long enough that smoking could cause heart
disease
• Example: study of incident Hep C should screen participants
regularly since participants will be unlikely seek care related
to symptoms until disease is well advanced, and those
detected by screening will be those with better access to
health care, different health behaviors etc
Summary
• Measure should be interpreted keeping in mind
and potentially accounting for
– Time scales that can affect disease - age, period and
cohort effects always underlie measures of disease
and can be challenging to disentangle
• Example: at a given time people at older ages have higher
rates of most diseases, which is partly an effect of aging, but
also an effect of cohort of birth (i.e., life expectancy
increasing over time)
Summary
• Accounting for characteristics (e.g., age) that
differ between populations you want to compare
and that affect rates of disease is a fundamental
issue in epidemiology (more in bias –
confounding) – again relates to counterfactual
concept
Measures of disease outline
– Big picture
– Illustration/discussion of measuring disease in time
– Populations
– Time scales affecting disease in populations
– Epidemiologic measures
• Basic concepts
• Measuring diseases
• Prevalence
• Incidence density (incidence rate)
• Cumulative incidence (risk)
• Relations among measures
– Standardization
– Summary
– Appendix: specific measures of disease
Specific measures of disease
• There are a variety of specific measures of
disease used in epidemiology that are important
to know
• Note: many of these measures are called “rates”
but not all of these are true rates
– See if you can determine which are rates and which
are proportions or ratios
Specific measures of disease
• Neonatal mortality rate
• Index of the risk of death in the first 28 days of
life
– Numerator: the number of deaths during one calendar
year of children <28 days old
– Denominator: the number of live births during the
same calendar year
– Usually expressed per 1,000
– Example: in the US in 2007 the neonatal mortality rate
was 4.4 deaths / 1,000 live births
Specific measures of disease
• Postneonatal mortality rate
• Index of the risk of deaths in infants aged 28
days – 1 year
– Numerator: the number of deaths in children aged 28
days – 1 year in a calendar year
– Denominator: the number of live births during that
calendar year
– Usually expressed per 1,000
– NOTE: will all infants who die in a calendar year have
been born in that same calendar year?
– Example: in the US in 2007 the postneonatal mortality
rate was 2.3 deaths / 1,000 live births
Specific measures of disease
• Infant mortality rate
• Index of the risk of deaths in infants up to 1 year
• Sum of neonatal and postneonatal mortality
rates
– Numerator: the number of deaths in children up to 1
year of age in a calendar year
– Denominator: the number of live births during that
calendar year
– Usually expressed per 1,000
– Example: in the US in 2007 the infant mortality rate
was 6.75 deaths / 1,000 live births
Specific measures of disease
• Infant mortality rate in the US in 2007 by cause
– Congenital anomalies 1.3/1,000
– Short gestation, low birth weight 1.1/1,000
– SIDS 0.5/1,000
– Maternal complications of pregnancy 0.4/1,000
– Note: cause specific often presented per 100,000 live
births
Specific measures of disease
• Maternal mortality rate
– Numerator: the number of deaths in a year from
puerperal causes (pregnancy complications,
childbirth, puerperium (time after the birth))
– Denominator: the number of live births during that
same year
– NOTE: denominator is all live births and not all
pregnancies because there is no surveillance system
for pregnancies
– Usually expressed as per 100,000
• Example:
– US 1960: 37.1 maternal deaths / 100,000 live births
– US 1990: 8.3 maternal deaths / 100,000 live births
Specific measures of disease
• Crude birth rate
– Numerator: the number of live births during a given
time interval
– Denominator: estimated total population at mid-
interval
– Usually expressed per 1,000
– Example: (next slide)
Specific measures of disease
Specific measures of disease
• General fertility rate
– Numerator: the number of live births during a given
time interval
– Denominator: estimated number of women aged 15-
44 years (sometimes 15-49) at mid-interval
– Usually expressed per 1,000
– Example: In Germany, the general fertility rate was
2.12 births per 1,000 women per month in April 2006
Specific measures of disease
• Attack rate
– Numerator: number of incident cases of a disease
– Denominator: total population at risk over a restricted
period of observation
– Used frequently in outbreak investigations
– What measure of disease is this?
– Example: respiratory illness attack rate among
members of households in which someone had a
H1N1 diagnosis was 19%
Specific measures of disease
• Case-fatality rate
– Denominator: the number of incident cases of a
disease
– Numerator: the number of deaths (due to the disease)
– This is a true proportion (the subjects in the
numerator must be in the denominator)
– Example: the Spanish flu of 1918 is reported to have
caused 50 million deaths among 500 million people
infected (10% case-fatality rate)
Specific measures of disease
• Death to case ratio
– Numerator: number of deaths attributed to a particular
disease over a specified time period
– Denominator: number of new cases of that disease
during the same time period
– Is this a ratio or a proportion?
– Example: In Finland the 28 day death to case ratio for
nosocomial Staphylococcus aureus bloodstream
infection was 22/100 between 1995 and 2001
Specific measures of disease
• Proportionate mortality
– Numerator: the number of deaths due to a particular
cause
– Denominator: the number of deaths due to all causes
– Each cause must be expressed as a percentage of all
deaths and the sum of all the causes must add to
100%
– Although the term “proportionate mortality” is
infrequently used, the actual concept is frequently
used to present data in newspaper stories (e.g. “the
leading cause of death is…”)
– Example: (next slide)
Specific measures of disease
• Of the estimated 8.795 million deaths in children younger than 5
years worldwide in 2008, infectious diseases caused 68% (5.970
million), with the largest percentages due to pneumonia (18%, 1.575
million), diarrhoea (15%, 1.336 million), and malaria (8%, 0.732
million)
• 41% (3.575 million) of deaths occurred in neonates, and the most
important single causes were preterm birth complications (12%,
1.033 million), birth asphyxia (9%, 0.814 million), sepsis (6%, 0.521
million), and pneumonia (4%, 0.386 million)
Specific measures of disease
• Proportionate mortality ratio (PMR)
– Numerator: the proportional mortality for a specific
cause in one population or subgroup
– Denominator: the proportional mortality for the same
cause in another population or subgroup
Specific measures of disease
• Proportionate mortality ratio for AIDS among children
comparing Africa to the Americas is 4 (4%/1%)
• In Africa the proportion of deaths among children due to
AIDS is 4 times larger than in the Americas
Specific measures of disease
• Example: there were 33,199 YPLL in British
Columbia 2001-2005 due to overdose (OD)
mortality (36.5 YPLL/OD)
Specific measures of disease
• Years of potential life lost (YPLL)
– Sum of the differences between a predetermined
endpoint and the actual ages of death for those dying
before the predetermined endpoint
– The predetermined endpoint chosen is frequently
either age 65 or the average life expectancy or some
other biologically relevant point
– Measures the impact of premature mortality on a
population
Specific measures of disease
• Years of potential life lost (YPLL) rate
– Years of potential life lost per 1,000 population below
age 65
– Allows comparison of premature mortality between
populations
Specific measures of disease
• Example: In British Columbia 2001-2005, among
non-First Nations people there were 158.2
YPLL/100,000 due to OD mortality while among
First Nations people there were 464.5 YPLL/100,
000 due to OD mortality

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Ph250b.14 measures of disease part 2 fri sep 5 2014

  • 1. Measures of Disease: Learning Objectives 1. Understand different types of populations as conceptualized in epidemiology and the relevance of population types to measures of disease 2. Understand concept of disease occurrence in time a. Understand and be able to define concepts of disease occurrence in time at a population level (age, period, cohort effects) b. Understand and be able to define concepts of disease occurrence in time at an individual level (i.e., latent period, lead time), and their implications for measuring disease at the population level 3. Understand and be able to define and contrast prevalence and incidence 4. Understand and be able to define and contrast risks and rates 5. Calculate and interpret prevalence (this includes knowing the formula) 6. Understand, define, calculate, and interpret cumulative incidence (this includes knowing the formulae) a. Know different methods for calculating cumulative incidence and the assumptions and purposes of each 7. Understand, define, calculate, and interpret incidence density (knowing the formulae) a. Understand and calculate person-time 8. Define and interpret a hazard rate 9. Understand and be able to convert between prevalence, cumulative incidence and incidence density (this includes knowing the formulas) 10. Direct and indirect standardization ` a. Perform both and understand when each is appropriate (know the formulae) b. Know what data are required for each
  • 2. Measures – cumulative incidence • Different methods for calculating – Simple cumulative – Actuarial – Kaplan-Meier – Density
  • 3. Measures – cumulative incidence • Subscript notation – R(t0,tj) – risk of disease over the time interval t0 (baseline) to tj (time j) – R(tj-1,tj) – risk of disease over the time interval tj-1 (time before time j) to tj (time j)
  • 4. Measures – cumulative incidence • Subscript notation – N’0 – number at risk of disease at t0 (baseline) – N’0j – number at risk of disease at the beginning of interval j
  • 5. Measures – cumulative incidence • Subscript notation – Ij – incident cases during the interval j – Wj – withdrawals during the interval j
  • 6. Measures – cumulative incidence Simple cumulative method: R(t0,tj) = CI(t0,tj) = I N'0 • Risk calculated across entire study period assuming all study participants followed for the entire study period, or until disease onset – Assumes no death from competing causes, no withdrawals • Only appropriate for short time frame
  • 7. Measures – cumulative incidence Simple cumulative method: • Example: incidence of a foodborne illness if all those potentially exposed are identified
  • 8. Measures – cumulative incidence Actuarial method: R(tj-1, tj) = CI(tj-1, tj) =____Ij ____ N'0j - Wj /2 • Risk calculated accounting for fact that some observations will be censored or will withdraw • Assume withdrawals occur halfway through each observation period on average • Can be calculated over an entire study period – R(t0,tj) = CI(t0, tj) = I/(N’0 -W/2) • Typically calculated over shorter time frames and risks accumulated
  • 9. Measures – cumulative incidence Modification of Szklo Fig. 2-2 – participants observed every 2 months (vs 1)
  • 10. • Where to start – set up table with time intervals • Fill incident disease cases and withdrawals into appropriate intervals • Fill in population at risk Measures – cumulative incidence Actuarial Method
  • 11. • Calculate interval risk • R(tj-1, tj) = Ij /(N’0j -(Wj /2)) • R(0,2) =1/(10-(1/2)) = 0.11 Measures – cumulative incidence Actuarial Method
  • 12. • Calculate interval survival • next step: S(tj-1,tj) = 1-R(tj-1,tj) Measures – cumulative incidence Actuarial Method
  • 13. • Calculate cumulative risk – example of time 0 to 10 • R(t0, tj) = 1 - Π (1 – R(tj-1,tj) ) = 1 - Π (S(tj-1,tj) ) • R(0, 10) = 1 – (0.89 x 0.88 x 1.0 x 1.0 x 0.85) = 0.34 Measures – cumulative incidence Actuarial Method
  • 14. • Calculate cumulative survival • S(t0,tj) = 1-R(t0,tj) Measures – cumulative incidence Actuarial Method
  • 15. • Intuition for why R(t0, tj) = 1 - Π (Sj ) using conditional probabilities • Example of 5 time intervals: – Π (Sj ) = P(S1)*P(S2|S1)*P(S3|S2)*P(S4|S3)*P(S5|S4) = P(S5) – Multiply first two terms: P(S2|S1)*P(S1) = P(S2) – Multiplying conditional probabilities gives you unconditional probability of surviving up to any given time point – the value (1 - survival) up to (or at) a given time point is then the probability of not surviving up to that time point Measures – cumulative incidence
  • 16. Measures – cumulative incidence • Exercise for home (discuss in lab) – Study population observed monthly for 6 months – Calculate the cumulative incidence of disease from month 0 to 6
  • 17. Measures – cumulative incidence Kaplan-Meier method: Rj = CIj =____Ij ____ Nj • Risk calculated at the time each disease event occurs – Accounts for withdrawals in that Nj only includes those at risk at each time j point – Result differs from actuarial approach in that the time of a withdrawal (in Kaplan-Meier analysis) coincides with time of an incident disease • Risks at each onset time j accumulated
  • 18. • Where to start – set up table with times of incident cases • Fill in population at risk – anyone who has withdrawn by a time j is no longer at risk at that time Measures – cumulative incidence Kaplan-Meier Method JC: discuss withdrawals
  • 19. • Calculate risk at time j • Rj = Ij /Nj • R2 =1/10 = 0.10 • R4 =1/8 = 0.125 Measures – cumulative incidence Kaplan-Meier Method
  • 20. • Survival calculated as in actuarial method • Cumulative risk calculated as in actuarial method – R(t0, tj) = 1 - Π (1 – Rj ) = 1 - Π (Sj ) • Cumulative survival calculated as in actuarial method Measures – cumulative incidence Kaplan-Meier Method JC: mention product-limit
  • 21. Measures – cumulative incidence Density method: R(t0,t) = 1 – S(t0,t) = 1- e(-ID*Δt) • Depends on functional relationship between a risk and a rate • Can be calculated over an entire study period if the rate is constant • Can also be calculated over shorter time frames and risks accumulated JC: Mention Elandt-Johnson article
  • 22. Where to start – set up table with time intervals • Fill incident disease cases, withdrawals and population at risk by interval • Calculate person time (for example used formula PTj =(N’0j -(Wj /2)) Δtj ) • Calculate IDj = Ij /PTj Measures – cumulative incidence Density Method
  • 23. • Calculate interval risk • R(t0,t) = 1 – S(t0,t) = 1- e(-ID*Δt) • R(0,2) = 1-e(-0.05*2) = 0.10 Measures – cumulative incidence Density Method
  • 24. • Calculate cumulative risk – example of time 0 to 10 • Accumulate interval risks as in actuarial method • Or calculate cumulative risk directly • R(t0,t) = 1- e(-∑ID*Δt) • R(0,10) = 1-e(-(0.05*2+0.06*2+0*2+0*2+0.08*2) = 0.32 Measures – cumulative incidence Density Method
  • 25. • Cumulative survival calculated as in actuarial method Measures – cumulative incidence Density Method
  • 26. Measures – cumulative incidence Cumulative incidence • Summary of methods for calculating and basis of choosing – Simple cumulative – complete follow-up – Actuarial – incomplete follow-up – Kaplan-Meier – incomplete follow-up – Density – converting incidence density to cumulative incidence
  • 27. Choosing among the CI methods • Do you only have rate data? Generally you will choose incidence density. • • Do you have zero withdrawals and a short time period of interest? If so, simple CI usually OK. • • Do you have fairly exact data on time of incidence and time of withdrawal? If so, density preferable. • • Do you have fairly exact data on time of incidence but only interval data on withdrawals? If so, KM most common choice; actuarial or density may not be too different depending on withdrawal timing. • • Do you have interval data for incidence and withdrawal? If so, actuarial most common choice, KM and density may not be too different depending on withdrawal timing.
  • 28. • Assumptions – Uniformity of events and losses within each interval (the W/2) – Independence between censoring and survival – otherwise biased/not accurate (also true for ID) – Lack of secular trends Measures – cumulative incidence
  • 30. Measures of disease outline – Big picture – Illustration/discussion of measuring disease in time – Populations – Time scales affecting disease in populations – Epidemiologic measures • Basic concepts • Measuring diseases • Prevalence • Incidence density (incidence rate) • Cumulative incidence (risk) • Relations among measures – Standardization – Summary – Appendix: specific measures of disease
  • 31. • Relations among measures – Incidence and incidence odds – Prevalence and incidence – Risk and rate Epidemiologic measures
  • 32. Incidence and incidence odds • CI ~ CI/ (1-CI) – If disease is rare (<0.10) • Why? – Because CI odds = CI/(1-CI) – if CI is small then 1-CI is close to 1 and CI/(close to 1) = CI • Relevant because CI often modeled with logistic regression which models the relative odds instead of the relative risk (more in the analyzing epidemiologic data section) Measures - relations
  • 33. Prevalence and incidence • What is incidence density of disease in interval 1,2? • (1/9 = 0.11/year) Measures - relations
  • 34. Prevalence and incidence • What is this prevalence of disease if the population is examined at one point in time? Measures - relations
  • 35. Prevalence and incidence • What is incidence density of disease in interval 1,2? Measures - relations
  • 36. Prevalence and incidence • What is this prevalence of disease if the population is examined at one point in time? Measures - relations
  • 37. Prevalence and incidence • P/(1-P) = ID x D • Prevalence odds approximates the incidence density (ID) times duration of disease (D), if population is steady-state • Under steady-state, for any given time period (Δt), inflow (incident cases) = outflow (recovered cases) – Inflow = incidence rate (i) * susceptible population (NS ) – Outflow = recovery rate (r) * diseased, not at-risk pop (ND ) • Under steady state, • i * NS = r * ND • ND /NS = i * (1/r) • Prevalence odds = incidence * avg duration Measures - relations JC: mention reciprocal of recovery rate
  • 38. • P ~ ID x D • Prevalence also approximates the incidence density times duration under steady-state if disease is rare (P<0.1) • If disease is rare P/(1-P) ~ P • P ~ P/(1-P) = ID x D • If disease is not rare, P = (ID x D)/[(ID x D) + 1)] • see Kleinbaum 7.1.3 for further treatment • Relevant because studying prevalence odds instead of prevalence may be less biased if interest is in estimating measures related to incidence density since P/(1-P) = ID x D • Relations between prevalence odds can be modeled with logistic regression which models the relative odds (more in the analyzing epidemiologic data section) Measures - relations
  • 39. Risk and Rate • R(t0,t) = 1 – S(t0,t) = 1- e(-ID*Δt) • see Kleinbaum 6.4.3 • mention: N’t = N’0 exp[-(ID) Δt ] • Relation used earlier in calculation of risk based on rate • Rate is the fundamental measure of disease occurrence • Explanation by analogy: road trip Measures - relations
  • 40. Risk and Rate – road trip analogy • On a road trip, the speed you travel (miles/hr, your rate of travel) determines how far you have travelled (miles travelled) at any given time since departure – Could imagine measuring as cumulative miles/total miles to destination (what measure of disease is this analogous to?) • The distance you have travelled at any given time does not determine your speed (although it is informative about your speed) Measures - relations
  • 41. Measures - relations Relation between risk and rate • Recall: N’t = N’0 exp[-(ID) Δt ] • Slope = ΔN/Δt • Slope/N’t = ΔN/Δt(N’t ) = -(new cases)/(change in time*population at risk) = -(new cases)/person-time = -ID (new cases will be negative because ΔN is disease free people lost from the surviving population) Risk(t0,t) = (N’0 -N’t )/N’0
  • 42. Summary – Rate, Risk and Prevalence • Rate is the fundamental measure of disease • Risk reflects the rate over a given time frame of interest • Prevalence reflects both the rate of disease and the rate of recovery (duration of disease) Measures - relations
  • 43. Measures of disease outline – Big picture – Illustration/discussion of measuring disease in time – Populations – Time scales affecting disease in populations – Epidemiologic measures • Basic concepts • Measuring diseases • Prevalence • Incidence density (incidence rate) • Cumulative incidence (risk) • Relations among measures – Standardization – Summary – Appendix: specific measures of disease
  • 44. Types of rates • Crude rate: number of events in a total population / person-time for which the population at risk has been observed • Specific rates: number of events in a subpopulation / person-time for which the subpopulation at risk has been observed (e.g. for age groups) • Standardized or adjusted rates: have undergone statistical transformation to permit comparison of rates across populations or among groups differing in the distribution of some characteristic (e.g., age) that may affect the risk of disease Standardization
  • 45. Comparing crude rates • A crude rate represents the actual experience of the population and is thus a valuable way to describe the disease experience • Comparing crude rates between two or more populations can be misleading because populations may differ with respect to characteristics that affect morbidity and mortality • What are some of the principal factors that influence morbidity and mortality? Standardization
  • 46. • Consider age-specific rates… • The crude rate can be thought of as a weighted average of the age-specific rates – the weights are the proportion of the population in each age category • Crude rate = ∑(age-specific rate x proportion of pop in that age category) • Even if two populations had identical age-specific rates, the crude rates for the two populations would differ if the age structure of the two populations were different Standardization
  • 47. • Population 1: – 500,000 people aged 20-24 – 500,000 people aged 25-29 • Population 2: – 200,000 people aged 20-24 – 800,000 people aged 25-29 • In both populations – CI among 20-24 = 0.002 – CI among 25-29 = 0.009 • What are the crude “rates” in populations 1 & 2? Standardization
  • 48. • Crude rate = ∑(age-specific rate x proportion of pop in that age category) • Population 1, crude CI = 0.002*0.5 + 0.009*0.5 = 0.0055 • Population 2, crude CI = 0.002*0.2 + 0.009*0.8 = 0.0076 • What do you think about comparing the health experience of these two populations using their CI values? Population 1 Population 2 Age rate proportion rate proportion 20-24 0.002 0.5 0.002 0.2 25-29 0.009 0.5 0.009 0.8 Standardization
  • 49. • Standardization of rates allows direct comparison of rates between populations – A standardized rate is a summary rate that has been adjusted to account for the differences in the distribution of characteristics that affect disease (e.g., age) between populations – Standardized rates allow fair comparisons to be made between populations – Answers the question: what would the death rate be in each population, if they had identical distributions of {X}? e.g. age – Counterfactual idea Standardization
  • 50. • Compare the death rates in these two states • Concerns about direct comparison of these crude rates? – Age structures of the populations of these two states are quite different Standardization
  • 51. Direct standardization • Choose a standard population (e.g., 1990 or 2000 US population from US Census) • Use the actual age-specific rates from each study population (e.g., state) • Apply these rates to the standard population in each age category • Calculate the number of outcomes that would have been observed in the study population if it had the age distribution of the standard population – a counterfactual idea • Calculate the adjusted rate of the outcome Standardization
  • 52. • Age adjusted rate = total expected outcomes total standard population Standardization Key for direct adjustment: Age specific rates come from your study population Age specific population sizes (i.e, the weights) come from the standard population
  • 53. • Where to start – set up table with age intervals • Fill in age specific rates from study population(s) • Fill in age specific population sizes from standard population (from outside source, e.g., US Census) Standardization Direct Standardization
  • 54. • Calculate expected number of deaths for study population(s) within age strata • E = RateStudy *PopulationStandard • EFL<5 = (179.26/100,000)*18,900,000 = 33,880 Standardization Direct Standardization
  • 55. • Sum expected deaths for study population(s) and calculate age adjusted rates • Rateadj = EStudy /PopulationStandard • RateadjFL =1,912,628/248,800,000 = 0.007686 = 768.6/100,000 Standardization Direct Standardization
  • 56. Standardization • Compare the death rates in these two states again Direct Standardization
  • 57. • Choice of standard population – Distribution of one of the two populations you want to compare – Distribution of the two populations combined – Some outside standard (e.g., US population from census) – Choice should be driven by the counterfactual question you want to ask • What would the rates be if my two study populations had the same age structure as population X? Standardization
  • 58. • Beware: the values you calculate will depend on the standard population chosen – Can get different results from different standards if the standards have notably different age structures • Note that the actual value of the new adjusted rate is a product of the choice of a standard population – it is not a “real” rate Standardization
  • 59. Pros: • Directly standardized rates can be used to compare disease rates across areas and time Cons: • Requires age-specific rates that are not often available at a local level or in certain populations • Rates may not be stable for small number of events (approximately <100 events) Standardization
  • 60. Standardization • At home exercise (for lab) – Prostate cancer mortality by race – White men: 1359 deaths / 4,738,246 men – 28.7 deaths per 100,000 men – Black men: 121 deaths / 418,992 men – 28.9 deaths per 100,000 men
  • 61. Standardization • At home exercise (for lab) • Calculate age adjusted rates of prostate cancer mortality by race
  • 62. • There may be situations in which age-specific rates are not available for your study population – Common in occupational studies – number of cases available from records but unable to reconstruct rates • You still want to be able to make a comparison between the disease experience of your study population and another population accounting for differences in the distribution of characteristics (e.g., age) • If you know the age structure of your study population, indirect standardization is an option Standardization
  • 63. • Choose a standard population for which rates of your outcome are available • Use the age-specific rates from the standard population • Apply these rates to the study population in each age category • Calculate expected number of deaths that would have occurred in the study population • This expected number of deaths is counterfactual – It’s the number of deaths that would have occurred in the study population if it had the same age-specific rates as the standard population • Compare the observed number of deaths in the study population to the expected number of deaths if the standard rates applied Standardization
  • 64. Standardization • SMR = total observed outcomes x 100 total expected outcomes • Standardized morbidity/mortality ratio (SMR): – Ratio of the observed number of outcomes in the study population to the expected number of outcomes if the study population had the same age-specific rates as the standard population – Answers question: is the morbidity/mortality experience greater than, less than, or similar to that which is expected in the standard population? (if equal, SMR = 100)
  • 65. • Direct vs. indirect standardization summary Population used (weight) Rate applied Direct Standard Study (observed) Indirect Study (observed) Standard Standardization
  • 66. Key for indirect adjustment: Age-specific rates come from your standard population Age-specific population sizes (also called weights) come from the study population Standardization
  • 67. • Example: we have data from two health care organizations on the numbers of occupational injuries reported – Health care organization 1: 95 – Health care organization 2: 64 • We are wondering how these health care organizations compare to the US average for those working in health care regarding injuries Standardization
  • 68. • Where to start – set up table with age intervals • Fill in age-specific rates from standard population • Fill in age-specific population sizes from study population(s) Standardization Indirect Standardization
  • 69. • Calculate expected number of injuries for study population(s) within age strata • E = RateStandard *PopulationStudy • EOrg1,15-30 = (60/10,000)*5700 = 34.2 Standardization Indirect Standardization
  • 70. • Sum expected injuries for study population(s) and calculate SMR(s) • SMR = O/E • SMROrg1 = (95/66.7)*100 = 142 Standardization Indirect Standardization
  • 71. • Interpret each SMR as a comparison of that study population to the standard – Health care organization 1 had a 42% higher rate of injury than the health care workers in the US population – Health care organization 2 had a 9% lower rate of injury than the health care workers in the US population • You cannot compare SMRs to each other Standardization Indirect Standardization
  • 72. Pros: • Indirect standardization does not require age-specific rates, only total number of events in the study population and age structure of the study population Cons: • SMRs cannot be directly compared – Each SMR captures a counterfactual comparison within that specific population • E.g, Observed deaths from pop A/Expected deaths from pop A (if standard rates applied) – The two study populations may have different age structures and the expected deaths depends on the age structure of each study population • Unlike directly standardized rates, SMRs give no idea of the actual burden of disease Standardization
  • 73. Standardization • Examining the lack of comparability of SMRs by uncovering the true age-specific injury rates in our two health care organizations
  • 74. Standardization • Age-specific injury rates are IDENTICAL in the two health care organizations
  • 75. Standardization • Why are the SMRs so different? • Org 1 has a younger population and the age-specific rates in that younger population are higher than in the standard • Org 2 has an older population and the age-specific rates in that older pop are lower than in the standard • Each SMR is a comparison of one study population to the standard – not a comparison of one study population to another
  • 76. • Direct vs. indirect standardization summary Population used (weight) Rate applied Direct Standard Study (observed) Indirect Study (observed) Standard Standardization
  • 77. Measures of disease outline – Big picture – Illustration/discussion of measuring disease in time – Populations – Time scales affecting disease in populations – Epidemiologic measures • Basic concepts • Measuring diseases • Prevalence • Incidence density (incidence rate) • Cumulative incidence (risk) • Relations among measures – Standardization – Summary – Appendix: specific measures of disease
  • 78. Summary • Measures of disease are a fundamental tool in epidemiology • Measure for any given study should be selected keeping in mind: – The type of population from which it will arise • Example: study capturing an open population should measure incidence density
  • 79. Summary – The disease and how the disease process and potential exposure disease relation can best be captured • Example: study of smoking and heart disease has to follow participants for long enough that smoking could cause heart disease • Example: study of incident Hep C should screen participants regularly since participants will be unlikely seek care related to symptoms until disease is well advanced, and those detected by screening will be those with better access to health care, different health behaviors etc
  • 80. Summary • Measure should be interpreted keeping in mind and potentially accounting for – Time scales that can affect disease - age, period and cohort effects always underlie measures of disease and can be challenging to disentangle • Example: at a given time people at older ages have higher rates of most diseases, which is partly an effect of aging, but also an effect of cohort of birth (i.e., life expectancy increasing over time)
  • 81. Summary • Accounting for characteristics (e.g., age) that differ between populations you want to compare and that affect rates of disease is a fundamental issue in epidemiology (more in bias – confounding) – again relates to counterfactual concept
  • 82. Measures of disease outline – Big picture – Illustration/discussion of measuring disease in time – Populations – Time scales affecting disease in populations – Epidemiologic measures • Basic concepts • Measuring diseases • Prevalence • Incidence density (incidence rate) • Cumulative incidence (risk) • Relations among measures – Standardization – Summary – Appendix: specific measures of disease
  • 83. Specific measures of disease • There are a variety of specific measures of disease used in epidemiology that are important to know • Note: many of these measures are called “rates” but not all of these are true rates – See if you can determine which are rates and which are proportions or ratios
  • 84. Specific measures of disease • Neonatal mortality rate • Index of the risk of death in the first 28 days of life – Numerator: the number of deaths during one calendar year of children <28 days old – Denominator: the number of live births during the same calendar year – Usually expressed per 1,000 – Example: in the US in 2007 the neonatal mortality rate was 4.4 deaths / 1,000 live births
  • 85. Specific measures of disease • Postneonatal mortality rate • Index of the risk of deaths in infants aged 28 days – 1 year – Numerator: the number of deaths in children aged 28 days – 1 year in a calendar year – Denominator: the number of live births during that calendar year – Usually expressed per 1,000 – NOTE: will all infants who die in a calendar year have been born in that same calendar year? – Example: in the US in 2007 the postneonatal mortality rate was 2.3 deaths / 1,000 live births
  • 86. Specific measures of disease • Infant mortality rate • Index of the risk of deaths in infants up to 1 year • Sum of neonatal and postneonatal mortality rates – Numerator: the number of deaths in children up to 1 year of age in a calendar year – Denominator: the number of live births during that calendar year – Usually expressed per 1,000 – Example: in the US in 2007 the infant mortality rate was 6.75 deaths / 1,000 live births
  • 87. Specific measures of disease • Infant mortality rate in the US in 2007 by cause – Congenital anomalies 1.3/1,000 – Short gestation, low birth weight 1.1/1,000 – SIDS 0.5/1,000 – Maternal complications of pregnancy 0.4/1,000 – Note: cause specific often presented per 100,000 live births
  • 88. Specific measures of disease • Maternal mortality rate – Numerator: the number of deaths in a year from puerperal causes (pregnancy complications, childbirth, puerperium (time after the birth)) – Denominator: the number of live births during that same year – NOTE: denominator is all live births and not all pregnancies because there is no surveillance system for pregnancies – Usually expressed as per 100,000 • Example: – US 1960: 37.1 maternal deaths / 100,000 live births – US 1990: 8.3 maternal deaths / 100,000 live births
  • 89. Specific measures of disease • Crude birth rate – Numerator: the number of live births during a given time interval – Denominator: estimated total population at mid- interval – Usually expressed per 1,000 – Example: (next slide)
  • 91. Specific measures of disease • General fertility rate – Numerator: the number of live births during a given time interval – Denominator: estimated number of women aged 15- 44 years (sometimes 15-49) at mid-interval – Usually expressed per 1,000 – Example: In Germany, the general fertility rate was 2.12 births per 1,000 women per month in April 2006
  • 92. Specific measures of disease • Attack rate – Numerator: number of incident cases of a disease – Denominator: total population at risk over a restricted period of observation – Used frequently in outbreak investigations – What measure of disease is this? – Example: respiratory illness attack rate among members of households in which someone had a H1N1 diagnosis was 19%
  • 93. Specific measures of disease • Case-fatality rate – Denominator: the number of incident cases of a disease – Numerator: the number of deaths (due to the disease) – This is a true proportion (the subjects in the numerator must be in the denominator) – Example: the Spanish flu of 1918 is reported to have caused 50 million deaths among 500 million people infected (10% case-fatality rate)
  • 94. Specific measures of disease • Death to case ratio – Numerator: number of deaths attributed to a particular disease over a specified time period – Denominator: number of new cases of that disease during the same time period – Is this a ratio or a proportion? – Example: In Finland the 28 day death to case ratio for nosocomial Staphylococcus aureus bloodstream infection was 22/100 between 1995 and 2001
  • 95. Specific measures of disease • Proportionate mortality – Numerator: the number of deaths due to a particular cause – Denominator: the number of deaths due to all causes – Each cause must be expressed as a percentage of all deaths and the sum of all the causes must add to 100% – Although the term “proportionate mortality” is infrequently used, the actual concept is frequently used to present data in newspaper stories (e.g. “the leading cause of death is…”) – Example: (next slide)
  • 96. Specific measures of disease • Of the estimated 8.795 million deaths in children younger than 5 years worldwide in 2008, infectious diseases caused 68% (5.970 million), with the largest percentages due to pneumonia (18%, 1.575 million), diarrhoea (15%, 1.336 million), and malaria (8%, 0.732 million) • 41% (3.575 million) of deaths occurred in neonates, and the most important single causes were preterm birth complications (12%, 1.033 million), birth asphyxia (9%, 0.814 million), sepsis (6%, 0.521 million), and pneumonia (4%, 0.386 million)
  • 97. Specific measures of disease • Proportionate mortality ratio (PMR) – Numerator: the proportional mortality for a specific cause in one population or subgroup – Denominator: the proportional mortality for the same cause in another population or subgroup
  • 98. Specific measures of disease • Proportionate mortality ratio for AIDS among children comparing Africa to the Americas is 4 (4%/1%) • In Africa the proportion of deaths among children due to AIDS is 4 times larger than in the Americas
  • 99. Specific measures of disease • Example: there were 33,199 YPLL in British Columbia 2001-2005 due to overdose (OD) mortality (36.5 YPLL/OD)
  • 100. Specific measures of disease • Years of potential life lost (YPLL) – Sum of the differences between a predetermined endpoint and the actual ages of death for those dying before the predetermined endpoint – The predetermined endpoint chosen is frequently either age 65 or the average life expectancy or some other biologically relevant point – Measures the impact of premature mortality on a population
  • 101. Specific measures of disease • Years of potential life lost (YPLL) rate – Years of potential life lost per 1,000 population below age 65 – Allows comparison of premature mortality between populations
  • 102. Specific measures of disease • Example: In British Columbia 2001-2005, among non-First Nations people there were 158.2 YPLL/100,000 due to OD mortality while among First Nations people there were 464.5 YPLL/100, 000 due to OD mortality