L58 - Measures of Disease and Risk in Populations

Why do we Measure Disease in Populations?

• To identify changing disease patterns

• Establish baselines

• Investigate risk factors

What is the Relationship between an Exposure and an Outcome?

• An Exposure is a potential risk factor

• An Outcome is the health event being measured

What are the Two Types of Data?

1. Quantitative Data

   • EX: Age, weight, flock size

2. Qualitative Data

   • Nominative → EX: Live or dead, ill or well (dichotomous), race, breed 

   • Ordinal → EX: Illness score, body condition score

Why must the Numerator and Denominator be Appropriately Matched?

The denominator must include individuals eligible to experience the outcome in the numerator

What is a Ratio?

A comparison of two mutually exclusive frequencies

• Expressed as A:B or A/B

What is the Formula for Disease Odds?

Number diseased

÷

Number nondiseased (cases/noncases)

How can a Ratio be Converted into a Proportion?

For A:B, calculate A/(A+B)

What is a Proportion?

A fraction in which the numerator is included in the denominator

What is the Formula for a Proportion?

Number of events

÷

Total population

How is a Proportion Converted into a Percentage?

Multiply the proportion by 100

QUESTION 1: What are the odds for ‘heads’ to ‘tails’ when you flip a coin?

→ 1:1 

QUESTION 2: What is the probability that you will get ‘heads’ when you flip a coin?

→ 50%

What is a Rate?

A measure of how quickly events occur, incorporating population-time at risk

What is the Formula for an Incidence Rate?

New cases

÷

Total population-time at risk

What is Population-Time at Risk?

The sum of time individuals remain eligible to develop the outcome

How can Population-Time be Estimated?

• Count the population midway through the time period

• Take the average of the population at the beginning and end of the time period

• Take counts at multiple times (e.g. monthly) and average them

QUESTION 3: The number of cats in a shelter was 1000 on Jan 1, 2019, and 1200 on Jan 1, 2020. Which is the most accurate estimate of cat-years at risk?

a.) First day population: 1000 cat yrs

b.) Average: (1000+1200)/2 = 1100 cat yrs

c.) Average of weekly cat counts

d.) Average of monthly cat counts

→ c.) Average of weekly cat counts

What is Crude Mortality?

Deaths from all causes

÷

Total population at risk for death

What is Cause-Specific Mortality?

Deaths from a specific cause

÷

Total population at risk for death

What is Case Fatality?

Deaths from a specific disease

÷

Total cases of that disease

What is Proportionate Mortality?

Deaths from a specific cause

÷

Deaths from all causes

How does Case Fatality differ from Cause-Specific Mortality?

• Case fatality uses disease cases as the denominator

• Cause-specific mortality uses the population at risk

QUESTION 4: Dr. Johnson found that 38% of sea otter deaths were due to parasitic diseases. What measure of risk was used?

a.) Case-fatality

b.) Proportionate mortality

c.) Crude mortality

d.) Cause-specific mortality

→ b.) Proportionate mortality

• Because parasite deaths are divided by all deaths

QUESTION 5: In one year, 30 sea otters die, with 3 of the deaths due to sharkbite, out of a total sea otter population of 3000. What is the crude mortality?

a.) <1%

b.) 1%

c.) 10%

d.) 100%

→ 1%

• 30/3,000 × 100 = 1%

• All causes of death are included.

What is Prevalence?

A snapshot of all existing cases at a particular point in time

What is the Formula for Point Prevalence?

Existing cases at a point in time

÷

Total population at that time

What is Incidence?

The occurrence of new cases during a defined period

What are the Two Main Types of Incidence?

1. Cumulative incidence (CI)

2. Incidence density rate (IDR)

What is the Formula for Cumulative Incidence?

New cases during a period

÷

Population initially at risk

What is the Formula for Incidence Density Rate?

New cases

÷

Total animal-time at risk

How does Prevalence differ from Incidence?

• Prevalence measures existing cases

• Incidence measures new cases over time

What is the Water Glass Analogy for Prevalence and Incidence?

• Water present = Prevalence

• Water entering = Incidence

• Water leaving = recovery or removal

What Factors can Increase or Decrease Prevalence?

• New cases increase it

• Recovery

• Death

• Removal of cases

QUESTION 6: How could we go about measuring only incident (new) cases of diarrheal disease from Salmonella in the gorilla population?

Identify baseline cases, then monitor initially unaffected gorillas for new cases.

What is the Purpose of a 2 × 2 Epidemiological Table?

To classify individuals by exposure and disease status and compare disease risk

What do A, B, C, and D Represent in a 2 × 2 Table?

• A: Exposed/case

• B: Exposed/noncase

• C: Unexposed/case

• D: Unexposed/noncase

What is the Formula for Risk in the Exposed Group?

A/(A+B)

What is the Formula for Risk in the Unexposed Group?

C/(C+D)

What is the Formula for Risk Ratio (RR)?

RR = [A/(A+B)] ÷ [C/(C+D)]

How are Risk Ratio Values Interpreted?

• RR = 1: Equal risk

• RR > 1: Higher exposed risk

• RR < 1: Lower exposed risk

What is the Formula for Attributable Risk (Risk Difference)?

AR = [A/(A+B)] − [C/(C+D)]

What is the Risk Ratio for Young vs. Old Gorillas?

(30/100) ÷ (80/600) ≈ 2.3

QUESTION 7: What does this risk ratio of 2.3 mean?

a.) Old animals were 2.3 times as likely to get respiratory disease compared to old animals

b.) Young animals were 2.3 times as likely to get respiratory disease compared to old animals

→ a.) Old animals were 2.3 times as likely to get respiratory disease compared to old animals

QUESTION 8: What is the attributable risk due to being young?

a.) Inc.(young) - Inc.(old) = 0.3 -0.13 =0.17

b.) Inc.(old) - Inc.(young) = 0.13 -0.3 = -0.17

c.) Inc.(old) / Inc.(young) = 0.13/0.3 = 0.43 = 43%

d.) c.) Inc.(yound) / Inc.(old) = 0.3/0.13 = 2.31 = 231%

→ a.) Inc.(young) - Inc.(old) = 0.3 -0.13 =0.17

Ratio vs. Proportion vs. Rate SUMMARY

Measurement	Definition	Formula	Key Difference
Ratio	Compares two mutually exclusive groups	A/B	Numerator is NOT included in denominator
Proportion	Compares a subset to the total	A/(A+B)	Numerator IS included in denominator
Rate	Measures how quickly events occur over time	Events / Population-time at risk

Examples:

• Ratio: 4 female students : 1 male student = 4:1

• Proportion: 3 diseased animals / 15 total animals = 20%

• Rate: 10 new disease cases / 100 animal-years = 0.10 cases per animal-year

Remember:

• Ratio = Comparison

• Proportion = Part of whole

• Rate = Speed of occurrence

Four Mortality Measurements SUMMARY

Measurement	Numerator	Denominator	What It Tells You
Crude Mortality	All deaths	Total population at risk	Overall mortality
Cause-Specific Mortality	Deaths from disease X	Total population at risk	Mortality due to disease X
Case Fatality	Deaths from disease X	Total cases of disease X	How often disease X is fatal
Proportionate Mortality	Deaths from disease X	All deaths	Percentage of deaths due to disease X

How to Recognize Each Mortality Measurement on an Exam SUMMARY

Question	Measurement
How many animals died from ANY cause?	Crude mortality
How many animals in the population died from disease X?	Cause-specific mortality
Of the animals WITH disease X, how many died?	Case fatality
Of ALL deaths, how many were caused by disease X?	Proportionate

Prevalence vs. Incidence SUMMARY

Feature	Prevalence	Incidence
Measures	Existing cases	New cases
Time	Point in time	Defined time period
Includes	Old + new cases present	Only new cases
Main Question	How much disease exists?	How frequently does new disease occur?
Formula	Existing cases / Total population	New cases / Population at risk or animal-time
Purpose	Measures disease burden	Measures occurrence of new disease
Analogy	Photograph	Video

Remember: 

• Prevalence = Being a case

• Incidence = Becoming a case

Two Types of Incidence SUMMARY

Feature	Cumulative Incidence (CI)	Incidence Density Rate (IDR)
Measures	Risk of becoming a new case	Rate of developing new cases
Numerator	New cases	New cases
Denominator	Population initially at risk	Total animal-time at risk
Formula	New cases / Population at risk	New cases / Animal-time
Units	Proportion or % over a period	Cases per animal-day, month, or year
Interpretation	Probability of developing disease	Speed of new case occurrence

Important: Cumulative incidence uses the number of individuals at risk, while incidence density uses their total time at risk

The 2 × 2 Epidemiological Table

Exposure Status	Disease +	Disease −	Total
Exposed	A	B	A+B
Unexposed	C	D	C+D

Calculation	Formula
Risk in Exposed	A/(A+B)
Risk in Unexposed	C/(C+D)
Risk Ratio (RR)	[A/(A+B)] / [C/(C+D)]
Attributable Risk (AR)	[A/(A+B)] − [C/(C+D)]

Remember: Calculate the risk in each group FIRST, then divide for risk ratio or subtract for attributable risk.

Risk Ratio vs. Attributable Risk SUMMARY

Feature	Risk Ratio (RR)	Attributable Risk / Risk Difference (AR)
Measures	Relative difference in risk	Absolute difference in risk
Operation	Division	Subtraction
Formula	Exposed risk / Unexposed risk	Exposed risk − Unexposed risk
Reference Value	1 = equal risk	0 = no difference
Interpretation	How many times the risk?	How much additional risk?

Risk Ratio Interpretation SUMMARY

RR Value	Meaning
RR = 1	Equal risk in exposed and unexposed
RR > 1	Greater risk in exposed
RR < 1	Lower risk in exposed

Gorilla Respiratory Disease Practice Example SUMMARY

Measurement	Young Gorillas (Exposed)	Old Gorillas (Unexposed)
New cases	30	80
Population at risk	100	600

Measurement	Young Gorillas (Exposed)	Old Gorillas (Unexposed)
New cases	30	80
Population at risk	100	600
Risk	30/100 = 0.30	80/600 ≈ 0.13
Percentage	30%	13%

Risk Ratio:

Interpretation: Young gorillas had approximately 2.3 times the risk of respiratory disease compared with old gorillas.

Attributable Risk:

Interpretation: Young gorillas had approximately 17 additional cases per 100 gorillas at risk compared with old gorillas during the year