EPID 600; Class 3 Measuring disease occurrence University of Michigan School of Public Health
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Epidemiology and measurement Measurement is central to epidemiology Fundamental observations in epidemiology are measures of the occurrence of illness
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Quantification in epidemiology 1.
Prevalence
2.
Risk (incidence proportion)
3.
Incidence rate
4.
Odds
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1. Prevalence (proportion)
Number of cases Prevalence
= Number of persons in population
at a specified time
Specified time interval can be a ‘point’ or ‘period’ of time EXAMPLES 14 adult men per 1,000 were HIV + in Tanzania in June 1995 27 adult men per 1,000 were HIV+ in Tanzania in 1995
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2. Risk (incidence proportion) In epidemiology, risk applies to an individual and refers to the probability that a person will develop a given disease In epidemiology, risk is seldom measured at the individual level but rather at the population level, hence, the risk measurement for agroup is referred to as incidence proportion
Risk =
Number of new cases of disease Number of persons followed
over a time period
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Example, risk Fixed population: 1000 people observed for 5 years When people become ill, assume all become ill on the last day of the time period
0.5 years
3 sick
1.0 years
5 sick
1.5 years
4 sick
2.0 years
3 sick
2.5 years
3 sick
3.0 years
5 sick
3.5 years
1 sick
4.0 years
2 sick
4.5 years
3 sick
5.0 years
4 sick
967 people never became ill Therefore, Risk = # sick/total pop = 33/1000=0.033
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Risk, examples Voluntary risks
Risk of death per person per year
Motorcycling
1 in 50
Smoking a pack a day
1 in 200
Taking contraceptive pills
1 in 5,000
Legal abortion, >12 weeks
1 in 5,900
Drinking 1 bottle of wine/day
1 in 13,300
Playing soccer
1 in 25,500
Canoeing
1 in 100,000
Skiing
1 in 430,000
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Different risk patterns over time Morbidity B
Annual risk of morbidity
Morbidity A
Age
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Two key notions in stating and interpreting risk Risk is meaningless without a time interval e.g., “Risk of death from cardiovascular disease among women 60 years of age is 2%”...means what? Competing risks make it difficult to use risk as the only assessment of disease occurrence in a study although this can be done in studies where follow-up is short and competing risks are low; e.g., Salk vaccine trial in children
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3. Incidence rate One solution to dealing with competing risk problem faced by incidence proportion is to consider incidence rates Incidence rates are concerned with the number of new cases during a particular person time of follow-up In some cases, e.g., national mortality rates, time period is taken as mid-point of a specific interval (i.e., mid-year)
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Incidence rate
Number of new cases Incidence Rate = Total time at risk of persons followed
EXAMPLE 20 new cases of HIV infection during 8,000,000 person years of follow-up, that is, among 8,000,000 persons followed-up for 1 year
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Understanding person-time T1
T2
T3
T4
T5
T6
T7
T8
T9
T10
T11
T12
T13
T14
T15
T16
T17
T18
T19
T20
TT
P1
P2
P3
P4
P5
P6
P7
P8
P9
P10
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A person-time example T1
T2
T3
T4
T5
T6
T7
T8
T9
T10
T11
T12
T13
T14
T15
T16
T17
T18
T19
T20
TT
P1
14
P2
20
P3
11
P4
11
P5
20
P6
20
P7
10
P8
20
P9
2
P10
10
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An example T1
T2
T3
T4
T5
T6
T7
T8
T9
T10
T11
T12
T13
T14
T15
T16
T17
T18
T19
T20
TT
P1
14
P2
20
P3
11
P4
11
P5
20
P6
20
P7
10
P8
20
P9
2
P10
10
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Therefore Assume lightning bolt is disease onset
Pr evalence at T11 =
1 7
3 Risk = new cases over a given time period 10 3 3 new cases Incidence rate = = 14 + 20 + 11 + 11 + 20 + 20 + 10 + 20 + 2 + 10 138 person time
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Example, Incidence Rate Fixed population: 1000 people observed for 5 years When people become ill, assume all become ill on the last day of the time period 0.5 years
3 sick
1.0 years
5 sick
1.5 years
4 sick
2.0 years
3 sick
2.5 years
3 sick
3.0 years
5 sick
3.5 years
1 sick
4.0 years
2 sick
4.5 years
3 sick
5.0 years
4 sick
967 people never became ill Therefore, IR= # sick/PYO = 33/[(967*5)+(3*0.5)+...etc]=33/4,921=6.7/1000 PYOs 16
Another way to think of incidence and prevalence Incidence
Prevalence
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Another way to think of incidence and prevalence Incidence
Prevalence
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Another way to think of incidence and prevalence Incidence
Prevalence factors affecting prevalence include incidence, duration of disease, death rates 19
Factors leading to increased prevalence Increased incidence rate Increased duration of disease, e.g., prolonged survival More case finding, e.g., screening Lower mortality
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HIV Prevalence and Incidence
time
number of new cases per 100,000 population per year
number of cases per 100,000 population
Comparing incidence and prevalence
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Notes about prevalence and incidence Prevalence represents the number of cases among persons of interest at a given point in time Therefore, prevalence is not a rate; the term “prevalence rate” should not exist Incidence (including both incidence proportion and incidence rate) represents number of new cases over a particular person-time of follow-up Therefore risk (incidence proportion) and incidence rate both are not meaningful without a time unit Always be as specific as possible when articulating units of measurement...what are you measuring? among who? over what time period?
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Comparing prevalence, risk (incidence proportion), and incidence rates Risk
and prevalence range from 0 to 1
Incidence
rate ranges from 0 to infinity
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Issues in measurement of incidence and prevalence Think of numerator and denominator How do we know something is a “case”? How do we count population “at risk”? What is a specific “time period”?
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Interrelations among measures (1), incidence proportion and incidence rate
Risk = Incidence rate x time [0-1]
[0-∞]
[0-∞]
This is only applicable where risk is low (<20%?)
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Example, incidence proportions and rates Population of 1,000 persons Mortality rate of 11 deaths per 1000 person years over a 20 year time period Therefore, Risk = [11/1000]*20 year = 0.22 So, risk is that among 1000 people there would be 220 deaths (22%) over the 20 years This ignores population change or possible addition or removal of population from follow-up
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Interrelations among measures (2), prevalence and incidence rate
IR * D =
P 1–P
This applies only in “steady state”, where incidence rates and disease duration are stable over time
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And.... P = IR * D 1− P therefore P = ( IR * D) *(1 − P) P = IR * D − IR * D * P P + IR * D * P = IR * D P(1 + IR * D) = IR * D IR * D P= 1 + IR * D 28
Therefore, prevalence and incidence rate
IR * D =
P 1–P if p <0.10, then 1-P ~1
Therefore, for low prevalence (and steady state), IR * D ≅ P
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4. Odds
p odds = 1− p
probability, risk
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Interpreting odds Odds = p/(1-p) Therefore, if probability is 0.75, odds are 0.75/(1-0.75)=0.75/0.25=3 Note that 3:1 odds means that a horse has a 75% probability of losing a race Good odds, if this is a horse race, are 1:1, that is, probability is 0.50 and odds are 0.50/(1-0.50)=1; this then means that a horse has a 50:50 chance of winning or losing
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Annual mortality rate
Annual mortality = rate
# of deaths in 1 year x 1000
# of persons in population at mid-year
Notes
Multiplication by 1000 is by convention
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Case fatality rate
Case fatality = rate
total # of deaths x 1000
# of persons with a disease
Notes
Multiplication by 1000 is by convention
The time period here is implicit as the time for persons with disease, presumably low
For diseases with low fatality, survival measures are better used
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Attack rate
Attack rate
total # of new persons with disease =
x 100 # of persons at risk of disease
Note: the time period here is implicit as the time for persons with disease, presumably low
For diseases with low fatality, survival measures are better used 34
Some examples Is the prevalence of osteoarthritis in the population low or high? Is the annual mortality rate from osteoarthritis low or high? Is the annual mortality rate from respiratory anthrax low or high? Is the case fatality rate from respiratory anthrax low or high?
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Measuring Tuberculosis Recap...some reasons why accurate measurement is important To define public health needs To assess how well we are doing at addressing those needs
A review of measurement issues in the context of the global TB burden was published in the Lancet in April 2008
36 Dye et al. Lancet. Measuring tuberculosis burden, trends, and the impact of control programmes. 2008; 8: 233-243.
Measuring Tuberculosis trends
37 Dye et al. Lancet. Measuring tuberculosis burden, trends, and the impact of control programmes. 2008; 8: 233-243.
Measuring Tuberculosis trends “incidence” over time by country
38 Dye et al. Lancet. Measuring tuberculosis burden, trends, and the impact of control programmes. 2008; 8: 233-243.
Measuring Tuberculosis trends Prevalence estimates
39 Dye et al. Lancet. Measuring tuberculosis burden, trends, and the impact of control programmes. 2008; 8: 233-243.
Measuring Tuberculosis trends
Problems: Plausibility of measured distribution Cases/suspects Fluctuations in reported cases 40 Dye et al. Lancet. Measuring tuberculosis burden, trends, and the impact of control programmes. 2008; 8: 233-243.
Measuring Tuberculosis trends
Problems: Plausibility of measured distribution Cases/suspects Annual fluctuations in reported cases 41 Dye et al. Lancet. Measuring tuberculosis burden, trends, and the impact of control programmes. 2008; 8: 233-243.
Final notes (1), expressing prevalence and incidence Prevalence often expressed as cases per 100,000 Incidence rate is also sometimes expressed as per 100,000 but this is wrong since needs time dimension (per year?)
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Final notes (2), other terms for measures of disease occurrence Frequently we see “period prevalence” referred to, which refers to prevalence measured during a time period (e.g., one year) Cumulative incidence is sometimes used to measure the incidence of disease during a given time period divided by population at risk; this is the same as incidence proportion Incidence density is sometimes used instead of incidence rate to refer to computations that use person-time; this is identical to incidence rate discussed here
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Summary of measures of disease frequency Prevalence
Risk
Incidence rate
Odds
Number with disease
Number with new disease
Number with new disease
Risk
Denominator
Total number of people
Total number of people at risk at baseline
Person years at risk
1-Risk
Time
At a point in time
Over a time interval
Over a time interval
Over a time interval
Numerator
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