Quantifying Disease Occurrence

Measures of Disease Page 1
Quantifying Disease Occurrence
Prepared by:
Dr. Ronnie D. Domingo
Session objectives:
At the end of this topic, the participants should be able to:
1. Explain the differences of ratios, proportions and rates.
2. Describe the different measures of morbidity, mortality and production;
3. Select the right measure for a given population data;
4. Compute the appropriate measures when provided with the necessary data

General Considerations
Importance of correct counting
• Since epidemiology deals with populations, epidemiologists need to count and
summarize the number of cases of disease.
• Health status of a herd is assessed by the collection, compilation, analysis and
interpretation of data on illness (morbidity), death (mortality), and production
performance.
• If the right measurements are performed, the veterinarian can decide confidently on
issues such as disease prioritization, control program and monitoring of disease
control impact.
• When comparison is being made between two groups or more, the first thing to verify
is that you are comparing apples with apples.
Definitions
 Population- The complete collection of elements, groups, or individuals to be studied.
 Population at risk- The animals that are really susceptible to the disease being studied.
Population at risk in a study of carcinoma of the cervix (WHO)
Source: (Beaglehole, Bonita, & Kjellstrom, 1994)
Counts, rates, proportion and ratio
Count
 A simple enumeration of the absolute number of cases of disease or number of
animals affected with a condition in a given population.
Example
o Simple count: there are 40 sows diagnosed with brucellosis in barangay Rizal
last month.
o (Note: no mention about the total number of pigs in Rizal)

Ratio
Ratio is the result of dividing one quantity by another
Ratio=
𝑎
𝑏
Examples
Sex ratio=
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑒𝑚𝑎𝑙𝑒𝑠
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑎𝑙𝑒𝑠
• If there are 42 cows and 2 bulls in a farm, you could compare the number of
cows to bulls by saying there is a ratio of 42 cows to 2 bulls. You could represent
that comparison in three different ways:
 42 to 2
 42 : 2
 42/2
Remember that a ratio must always be in simplest form but have two numbers.
• The first operation to perform on a ratio is to reduce it to lowest terms
42:2 =
42/2
2/2
=
21
1
= 21:1
Additional applications
• boar to sow ratio
• Feed conversion ratio
• Relative risk
• Odds ratio
Proportion
A proportion is a special type of ratio, in which a is part of the denominator (a + b),
Proportion=
𝑎
𝑎+𝑏
 All proportions are ratios – not all ratios are proportions.
 A proportion can be expressed as a number between 0 and 1 or as a percentage
between 0 and 100%.
• 10ⁿ is a constant that is used to transform the result of the division into a uniform
quantity.
• The size of 10ⁿ may equal 1, 10, 100, 1000 and so on depending on the value of n.
• Examples:
10² = 10 x 10 = 100
10³ = 10 x 10 x 10 = 1000
10⁵ = 10 x 10 x 10 x 10 x 10 = 100,000
Examples:
 The proportion of pigs infected with hog cholera in Sta. Cruz is 1.2%.
 The proportion of pregnancies ending in abortions in a piggery farm is 90/890 or
approximately 10%.
 The proportion of pigs with lungworm is 24 per 100,000 pigs.

Rate
Rate is another type of ratio. Rates have the added dimension of time.
An epidemiologic rate will contain the following: disease frequency (numerator), unit of
population size, and the time period during which the event occurred
Rate =
number of cases occurring during a given time period
population at riskduring the same time period
x 10ⁿ
Example:
 There were 22 new cases of rectal prolapse per 10,000 sows in
Pangasinan in 2011.
Presentation of percentages
Toma, et al., 1999 wrotte the following principles in expressing relative frequencies in the form
of percentages.
Principles
1. In epidemiology, the percentage is
commonly calculated using the formula.
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 =
𝑛
𝑁
∗ 100 where n corresponds to the
number of events while N to the population size
2. If N (or the population size) is less than 10,
the result should not be expressed in
percentage to avoid the false impression of
deriving the result from a large population
and from a precise calculation. It is better to
write “five out of ten animals...” instead of
“50% of animals.”
3. If N is less than 100, the percentages should
be expressed only as whole numbers.
4. If N is between 100 and 1000, the
percentage is given with a single figure after
the decimal point.
5. If N is above 1000, the percentage is given
with two figures after the decimal point.
6. If the percentage is computed from a sample
(n), always include the confidence interval.
Examples
50
100
∗ 100 = 50%
“five out of ten animals...”
33
95
∗ 100 = 35%
(Wrong: 34.74%)
47
680
∗ 100 = 6.9%
(Wrong: 6.91%)
125
3400
∗ 100 = 3.68%
(Toma, 1999)

Measures of Morbidity
Prevalence Incidence
• Period prevalence
• Point prevalence
• TRUE RATE: Incidence density (also called
true incidence rate , hazard rate, force of
morbidity or mortality)
• RISK RATE: Incidence risk or cumulative
incidence
• ATTACK RATE (during a disease outbreak)
Incidence
• Measures the rapidity with which NEW cases are occurring in a population (how quickly
animals are catching the disease)
• Time, (i.e., day, month, year) must be specified
There are three ways of expressing incidence:
• Incidence count
• Incidence risk (cumulative incidence)
• Incidence rate (Incidence density)
Incidence count
• Incidence count is the simple count of the number of cases of disease observed in a
population.
• Because it is merely a count, there are limits to the inferences that can be made from
count data.
• Incidence counts are rarely used in epidemiologic research
• Example:
Hong Kong had 2 cases of bovine spongiform encephalopathy (BSE).
Incidence Risk
Synonym: cumulative incidence (CI)
• An incidence risk is the probability that an animal will contract or develop a disease in a
defined time period.
• It is the ratio between the number of animals that contracted the disease in a certain
period and the number of healthy animals at risk in the population at the start of that
period.
Incidence risk=
# of newcases during a specified period
Number of animals free of the disease inthe population at riskat the beginning ofthe period
x 10 n

Additional notes about CI:
1. The value can be anywhere between O to 1.
2. The time period to which the risk applies must be specified (e.g., “3-year CI”).
3. It assumes that the entire population at risk at the beginning was followed-up for the time
period of observation.
4. The term cumulative incidence is applied because it measures the amount of new cases
of disease that accumulated in time. This means that the longer is the period of
observation, the higher would be the cumulative incidence.
Sample calculation (Baumann, 2009)
• Suppose that 20 out of 100, initially uninfected, pigs develop pseudorabies in a one
week period.
• The cumulative incidence in that week then is: 20/100 = 0.2.
• When in the subsequent week another 15 pigs get pseudorabies, the cumulative
incidence over the 2-week period amounts to 0.35 (see table):
Week Number of new cases CI
1 20 0.20
2 15 0.35
3 10 0.45
4 5 0.50
5 1 0.51
Interpretation:
The cumulative incidence over the entire 5-week period is 0.51.
Incidence Rate
Synonym: Incidence density or ID or incidence density rate (also called true incidence rate,
hazard rate, force of morbidity or mortality)
• An incidence rate is the number of new cases of disease in a population per unit of
animal-time during a given time period.
• A measure of the average speed (velocity) at which the disease is spreading.
ID =
Totalnew cases during stated period
Sum of the length oftime at riskfor eachanimalinthe population(expressed in animaltime)
• Animal time = total time each animal in the population was at risk of getting the
disease
• Interpretation:
o ID addresses the question “How rapidly is the disease occurring in the
population, relative to its size?”
o “What is the intensity with which the disease is occurring?”

Sample calculation from (Pfeiffer, Dirk, 2009)
A study was conducted over a period of 12 months to determinate the mortality of cows
in a village which has a total 100 cows at the beginning of the study.
• 5 cows die after 2 months which means they were 5* 2 = 10 animal months at risk
• 2 cows die after 5 months which means they were 2 * 5 = 10 animal months at risk
• 3 cows die after 8 months which means they were 3 * 8 = 24 animal months at risk
This means a total of 10 cows die, and these experienced 44 animal months at risk
based on the calculation (5* 2 + 2*5 + 3*8)
• 90 cows survive past the study period which means they were 90*12 months
= 1080 animal months at risk
Therefore, the incidence density of cow mortality in this village is calculated as
10 / 1124 = 0.009 deaths per animal month.

Hypothetical Study
Modified from (Stevenson, 2008)
Number present at start 10
Number of withdrawn animals 2
Number present at end of study 8
Number of disease events 4
Prevalence in June AD and F or 3/9 33%
Prevalence in December
ADF and G or
4/8 50%
Cumulative incidence 40% (4 cases in 10 animals)
Incidence density
(exact) 4 cases per 80 cow-months at risk

Attack rate
The term “attack rate” is often used instead of incidence during a disease outbreak in a
narrowly-defined population over a short period of time.
Attack Rate =
Number of newcases among the population during the period
population at riskat the beginning of the period
X 100
The attack rate is not truly a rate but a proportion
The higher the attack rate, the more important the specific factor is in increasing risk of disease.
Usually a percentage: 10ⁿ where n = 2
Sample calculation 1. Source: (Dicker, Coronado, Koo, & Parrish, 2006)
• Of 75 persons who attended a church picnic, 46 subsequently developed a
gastrointestinal illness.
• Cases of GI illness occurring within the incubation period for GI illness among persons
who attended the picnic = 46
• Number of persons at the picnic = 75
• Then, the attack rate for GI illness is
46
75
x 100 = 61%
• Interpretation:
Among persons who attended the picnic, the probability of developing GI illness was
61%, or the risk of developing GI illness was 61%.

Measures of Disease Page
10
Prevalence
1. It describes the proportion of the population that is in the disease state at a specific time.
2. A snapshot of the situation at a single point in time.
3. Prevalence can be expressed per 100 people (per cent, %) or per 1,000 (10 3
), 10,000 (10
4
) or 100,000 (10 5
)
4. The term ‘prevalence rate’ is not a true rate because a rate should include units of time.
Point Prevalence
 It is the probability that a randomly selected animal suffers from that disease at a certain
moment.
 Point Prevalence =
Number of animals with disease at a given point in time
Totalnumber of animals in the population at a given point intime
x 100
Example
 A population of 10,500 pigs held at a quarantined farm was investigated on April 04,
2015. A total of 140 cases of FMD were identified.
 The point prevalence of FMD at that farm on April 04 was:
 Point Prevalence=
140
10500
x 100 = .013 x100 = 1.3 % or 13 cases per 1000 pigs
Period Prevalence
 Period prevalence refers to the proportion of the population that had the disease during
a specified PERIOD of time.
 It combines the point prevalence at the beginning of the period and the incidence
(number of new cases that occur during the period).
 Period prevalence can be calculated for a week, month, year, decade, or any other
specified length of time.
 Period Prevalence =
Number of animals with disease at a given period oftime
Totalnumber of animals in the population at a given period of time
x 100

11
Prevalence Illustrated
* Point prevalence
- 01/01/2009: case No. 2, 4, 5. Point prevalence in 01/01/2009 is 3/10 or 0.3 or 30 %
- 31/12/2009: case No. 6, 7, 10. Point prevalence in 31/12/2009 is also 3/10 or 30%
* Period prevalence between 01/01-31/12/2009:
Case No. 2, 3, 4, 5, 6, 7, 9, 10
Period prevalence between 01/01-31/12/2009= 8/10 or 0.8 or 80%
Relationship between prevalence, incidence and duration of disease state
1. Prevalence differs from incidence in that prevalence includes all cases, both new and
preexisting, in the population at the specified time, whereas incidence is limited to new
cases only.
2. Prevalence refers to proportion of animals which have a condition at or during a
particular time period, whereas incidence refers to the proportion or rate of animals
which develop a condition during a particular time period.
3. A disease with a long duration has a higher chance of being counted during a cross-
sectional survey than a disease with short duration. Given the assumption that
population is stable and incidence and duration are unchanging, the relation between
incidence and prevalence can be expressed as
P ≈ IR × D
Where:
≈ means approximately equal to.
P = prevalence
IR= incidence rate
D = average duration of disease
4. High prevalence of a disease within a population might reflect high incidence or
prolonged survival without cure or both. Conversely, low prevalence might indicate low
incidence, a rapidly fatal process, or rapid recovery.

12
Wash basin Analogy.
 Incidence is depicted by water flowing from a faucet into a basin, and prevalence is
represented by the volume water in the basin. When the inflow is copious, the basin
readily fills.
 The process, however, is influenced by another factor, which is represented by the basin
drain.
 This factor is disease resolution or duration. If the disease resolves fast by recovery or
death, this will have the effect of decreasing the prevalence unless the inflow is heavy
enough to sustain the water level in the basin.

13
A comparison of the main features of prevalence, incidence risk, and incidence rate
Point prevalence Period
prevalence
Incidence risk Incidence rate
Numerator All cases
counted on a
single occasion
Cases present at
period start +
new cases
during follow-up
period
New cases
during follow-up
period
New cases
during follow-up
period
Denominator All individuals
examined
All individuals
examined
All susceptible
individuals
present at the
start of the study
Sum of time
period at risk for
susceptible
individuals
present at the
start of the study
Time Single point or
period
Defined follow-
up period
Defined follow-
up period
Measured for
each individual
from beginning of
study until
disease event,
exit from the
population, or
end of the follow-
up period
Study type Cross-sectional Cohort Cohort Cohort
Interpretation Probability of
having disease
at a given point
in time
Probability of
having disease
over a defined
follow-up period
Probability of
developing
disease over a
defined follow-up
period
How quickly new
cases develop
over a defined
follow-up period
Source: (Stevenson, 2005)

14
Measures of Mortality
Crude death rate (Death rate or Crude mortality rate)
The crude mortality rate is the mortality rate from all causes of death for a population.
• The denominator is the population at the mid-point of the time period.
Crude mortality rate =
Number of deaths reported within a given period
Population size at the middle of that period
• Example
The crude mortality rate for Quezon City in 2009 was 896 deaths per 100,000 people.
Case-fatality rate
 Case fatality risk (or rate) refers to the incidence of death (proportion) among individuals
who develop a specific disease (within a specified time period).
 Its denominator is limited to those who possess the disease.
Case fatality rate =
Totalnumber of animals dying from the disease during (specified period)
Totalnumber of animals whohadthe disease during (specified period)
Example:
The case-fatality rate of PED last April 2015 in Masagana Swine Farm was 6,000 deaths
due to PED/10,000 piglets diagnosed with PED disease or 60%.
Cause-specific mortality rate
 The cause-specific mortality rate is the mortality rate concerning a specified cause for a
population during a specified time period.
 The numerator is the number of fatalities attributed to a specific cause while the
denominator consists of the population at the midpoint of the time period.
Example:
In the United States in 2003, a total of 108,256 deaths were attributed to accidents
(unintentional injuries), yielding a cause-specific mortality rate of 37.2 per 100,000
population.
= 8.18 / 100,000
Proportional mortality/morbidity
 Calculated by dividing the number of cases (or deaths) due to a specific disease by
the number of cases (or deaths) from all disease s diagnosed.
Proportional mortality =
Number of deaths from the disease
Number of deaths from all causes

15
Summary of common measures of mortality
Crude death rate =
C
D
Where D represents the total number of animals in the study population, both sick and
healthy.
Cause specific mortality rate =
Bm
D
Bm
Am
(note that Am includes Bm in the drawing above)
Proportional mortality rate =
Bm
C
Source: (Dicker, 2006)

16
Adjusted Measures of Disease
Crude measures give a snap shot of the disease situation in a given population. For a
homogenous population, crude measures may be sufficient.
However, for a heterogeneous population, crude measures must be adjusted in order to
determine the true distribution of the disease problem.
Source: (Baumann, 2009)
Example
Point prevalence (crude) of porcine circovirus type 2 in Bulacan Piggery Farm
Crude Stratified
Age
(months)
Herd
Size
PCV2
+
Point
Prevalence
Total 1012 439 0.43
Age
(months)
Herd
Size
PCV2
+
Point
Prevalence
Below 6 680 354 0.52
6-12 220 67 0.30
Above 12 112 18 0.16
Total 1012 439 0.43

17
References
Baumann, M. P. O. (2009). Quantification of animal health and disease.
Beaglehole, Bonita, & Kjellstrom, R. &. (1994). Basic Epidemiology. Orient BlackSwan.
Dicker, R., Coronado, F., Koo, D., & Parrish, R. G. (2006). Principles of Epidemiology in Public
Health Practice, 3rd Edition (3rd edition). CDC.
Pfeiffer, Dirk. (2009). Veterinary Epidemiology: An Introduction.
Stevenson, M. (2008). An Introduction to Veterinary Epidemiology. Massey University,
Palmerston North, New Zealand. Retrieved from
http://www.sciencedirect.com/science/article/pii/0197245686900462
Toma, B. (1999). Applied Veterinary Epidemiology and the Control of Disease in Populations.
AEEMA.

18
WORKSHOP 3: Measuring morbidities
and mortalities
Bacolod Sheep Importation
The City of Bacolod imported 5000 sheep from New Zealand in 2010. After five months, 2800
animals showed signs of anemia and diarrhea due to blood-sucking roundworms identified by
fecalysis as Haemonchus sp. Overall, 1100 animals died. However, during necropsy, the
roundworm was recovered only in 730 sheep.
Calculate the following:
Crude death rate =
Cause specific mortality rate =
Proportional mortality rate =

19
Fasciolosis in Kabacan, North Cotabato
Fecal samples were collected rectally from carabaos and cattle from five selected
barangays, namely Colambog and Takepan in Pikit, Malanduage, Pisan, and Bannawag in
Kabacan. The age, sex, and condition of female animals (whether pregnant or lactating) were
noted. Groupings according to age were as follows: 0-2.9 years; 3-5.9 years; 6-8.9 years; and,
9 years and above. The feces were examined for the presence of fasciola eggs using the
sedimentation technique adapted from Suhardono (1998). The results are shown below (note
that for this exercise, the values fromthe original document were modified).
Table M1 summarizes the results of examination of fecal samples from cattle while
Table M2 summarizes the results from carabao samples. For each table, write an appropriate
table title and supply the missing figures.
Table M1. Prevalence of . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Age Group Fecalysis (+) Fecalysis (-) Total Prevalence (%)
0-2.9 51 170
3-5.9 51 59
6-8.9 33 29
9 and above 17 14
Total 152 272
Table M2. Prevalence of . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Age Group Fecalysis (+) Fecalysis (-) Total Prevalence
(%)
0-2.9 48 78
3-5.9 58 41
6-8.9 45 30
9 and above 24 17
TOTAL 175 166

20
Cattle Anaplasmosis
Hypothetical study. A total of 80 beef cattle imported from Australia were delivered in
Busuanga Animal Quarantine Station in 2011. The field epidemiologist monitored the health
condition of the animals for six months. Several animals became infected with a protozoan tick-
borne disease, Anaplasmosis. Some animals recovered while others died. A timeline was
shown to you to visualize what happened to the 12 animals:
Note: S= onset of illness; R= date of recovery; D= date of death
Calculate the following:
1. Point prevalence of Anaplasmosis on July 01, 2011.
Answer:
2. Point prevalence of Anaplasmosis on September 03, 2011.
Answer:
3. Period prevalence of Anaplasmosis from June 1 to August 01, 2011
Answer:

Quantifying Disease Occurrence

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