1. Introduction

In epidemiology, we don’t just ask “Who is sick?” but “How many are sick relative to the population?” Measuring disease frequency is the foundation of descriptive epidemiology. It allows us to: * Assess the health status of a population. * Identify high-risk groups. * Evaluate the effectiveness of health interventions.

2. Basic Mathematical Tools

Before calculating disease, we must distinguish between three fundamental types of fractions.

2.1 Ratio

A ratio is the relative magnitude of two quantities. The numerator is not necessarily included in the denominator. \[\text{Ratio} = \frac{x}{y}\] Example: The ratio of male to female births in a hospital (e.g., 1.05:1).

2.2 Proportion

A type of ratio where the numerator is included in the denominator. It is often expressed as a percentage. \[\text{Proportion} = \frac{x}{x + y}\] Example: 15 students in a class of 60 have the flu (15/60 = 25%).

2.3 Rate

A measure of the frequency with which an event occurs in a defined population over a specified period of time. Note: In strict epidemiology, a rate includes “Time” in the denominator.

3. Measures of Morbidity

Morbidity refers to the state of being diseased or unhealthy. The two primary measures are Prevalence and Incidence.

3.1 Prevalence

Prevalence measures the existing cases of a disease at a specific time or over a period. It is a “snapshot.”

Point Prevalence

\[\text{Point Prevalence} = \frac{\text{Number of existing cases at a specific point in time}}{\text{Total population at that point in time}} \times 10^n\]

Period Prevalence

\[\text{Period Prevalence} = \frac{\text{Cases existing at any time during a period}}{\text{Average population during that period}}\]

Real-Life Example: On December 29, 2025, there are 5,000 people living with Type 2 Diabetes in a city of 100,000. The point prevalence is 5%.

3.2 Incidence

Incidence measures the new cases of a disease that develop in a population at risk over a period of time.

Cumulative Incidence (Risk)

Used when the entire population is followed for the same amount of time. \[\text{CI} = \frac{\text{Number of new cases during a period}}{\text{Population at risk at start of period}}\]

Incidence Rate (Incidence Density)

Used when people are followed for different lengths of time (utilizes Person-Time). \[\text{IR} = \frac{\text{Number of new cases}}{\text{Total person-time of observation}}\]

4. The Relationship Between Prevalence and Incidence

Think of a bathtub: * Incidence is the water flowing from the faucet (new cases). * Prevalence is the water level in the tub (total existing cases). * Recovery and Death are the water draining out (cases leaving the prevalence pool).

Formula: \[Prevalence \approx \text{Incidence} \times \text{Duration of Disease}\]

Figure 1: Visualizing the Bathtub Analogy

5. Measures of Mortality

Mortality measures the frequency of death in a population.

5.1 Crude Death Rate

The total number of deaths in a year per 1,000 people. \[\text{CDR} = \frac{\text{Total Deaths}}{\text{Total Mid-year Population}} \times 1,000\]

5.2 Case Fatality Rate (CFR)

Measures the severity of a disease (the proportion of people with a disease who die from it). \[\text{CFR} = \frac{\text{Deaths from a specific disease}}{\text{Number of people with that disease}} \times 100\]

Real-Life Case: During the initial outbreak of Ebola in 2014, the CFR was approximately 50%, meaning half of all people who contracted the virus died.

5.3 Proportionate Mortality

The percentage of all deaths attributable to a specific cause. \[\text{PM} = \frac{\text{Deaths from cause X}}{\text{Total deaths from all causes}} \times 100\]

6. Real-World Application: COVID-19 Data

Let’s look at a hypothetical dataset of 10 individuals followed for 1 year to calculate Incidence Density.

# 0 = healthy, 1 = sick, 2 = died/left study
follow_up <- data.frame(
  Patient_ID = 1:5,
  Months_Followed = c(12, 4, 12, 8, 2), # Person-months
  Outcome = c("Healthy", "Sick", "Healthy", "Sick", "Died")
)

print(follow_up)
##   Patient_ID Months_Followed Outcome
## 1          1              12 Healthy
## 2          2               4    Sick
## 3          3              12 Healthy
## 4          4               8    Sick
## 5          5               2    Died
# Calculate Total Person-Months
total_person_months <- sum(follow_up$Months_Followed)
new_cases <- 2 # Patient 2 and 4

incidence_rate <- new_cases / total_person_months

Calculation: * Total Person-Months: 38 * New Cases: 2 * Incidence Rate: 0.0526 cases per person-month (or 0.63 cases per person-year).

7. Summary Table

Measure Numerator Denominator Application
Prevalence Existing cases Total population Resource planning, chronic disease burden.
Incidence New cases Population at risk Finding causes (etiology), acute outbreaks.
CFR Deaths from disease Total cases of disease Measuring disease virulence/severity.

8. Exercises

  1. In a town of 10,000 people, 500 have asthma. During 2024, 50 more people developed asthma. Calculate the point prevalence on Jan 1st, 2025.
  2. Why is the denominator for Incidence “Population at risk” and not the “Total population”? (Hint: Think about calculating uterine cancer rates in a population that includes men).

End of Module 4 Notes. ```