1. Introduction

In epidemiology, measurement is the foundation of practice. To allocate resources, identify outbreaks, or evaluate treatments, we must move beyond “many people are sick” to precise mathematical expressions.

This module focuses on Morbidity (the occurrence of disease) and Mortality (the occurrence of death).

2. Fractions in Epidemiology

Before measuring disease, we must distinguish between three types of mathematical structures:

  1. Ratio: \(x / y\). The numerator is NOT part of the denominator (e.g., Male-to-Female ratio).
  2. Proportion: \(x / (x + y)\). The numerator is part of the denominator. Usually expressed as a percentage (0–100%).
  3. Rate: \(x / \text{time}\). Includes a measure of time in the denominator.

3. Measuring Morbidity (Disease Frequency)

There are two primary ways to measure disease frequency: Incidence and Prevalence.

3.1 Prevalence

Prevalence measures the burden of disease in a population at a specific time. It includes both new and existing cases.

Formula: \[Prevalence = \frac{\text{Number of existing cases at a specific time}}{\text{Total population at that time}}\]

  • Point Prevalence: Disease status at a single point in time (e.g., “Do you currently have a cold?”).
  • Period Prevalence: Disease status over a window of time (e.g., “Have you had a cold in the last 12 months?”).

3.2 Incidence

Incidence measures the risk or the speed at which new cases develop.

A. Cumulative Incidence (Risk)

\[CI = \frac{\text{Number of NEW cases during a period}}{\text{Number of people at risk at the start of the period}}\]

B. Incidence Rate (Incidence Density)

This is used when individuals are followed for different lengths of time. \[IR = \frac{\text{Number of NEW cases}}{\sum \text{Person-time at risk}}\]

4. Visualizing the Difference

The “Bathtub Analogy” is the best way to understand this. * Incidence is the water flowing from the faucet (new cases). * Prevalence is the water level in the tub (all cases). * Recovery/Death is the drain (cases leaving the prevalence pool).

5. The Relationship between P and I

If the disease is stable (steady state) and rare, the relationship is: \[Prevalence \approx \text{Incidence} \times \text{Average Duration of Disease}\]

Real-Life Example: * HIV: Before Anti-Retroviral Therapy (ART), duration was short. Prevalence was lower. With ART, people live longer; therefore, even if incidence stays the same, prevalence increases because people stay in the “tub” longer.

6. Measuring Mortality (Death)

6.1 Crude Death Rate

Total deaths from all causes in a population during a specific period. \[CDR = \frac{\text{Total Deaths}}{\text{Total Population}} \times 1,000\]

6.2 Case Fatality Rate (CFR)

Measures the lethality of a disease. \[CFR (\%) = \frac{\text{Deaths from specific disease}}{\text{Total diagnosed cases of that disease}} \times 100\]

Example Comparison: * Rabies: CFR is nearly 100%. * Seasonal Flu: CFR is approx 0.1%.

6.3 Proportionate Mortality

Of all deaths, what percentage was due to a specific cause? \[PM = \frac{\text{Deaths from Cause X}}{\text{Total deaths from all causes}} \times 100\]

7. Real-Life Case Study: COVID-19 Metrics

Imagine a city of 100,000 people. - On October 1st, 500 people are already sick with COVID-19. - During October, 200 new people test positive. - By the end of October, 10 people have died from the virus.

Calculations: 1. Point Prevalence (Oct 1): \(500 / 100,000 = 0.5\%\). 2. Cumulative Incidence (Oct): \(200 / (100,000 - 500) \approx 0.2\%\). (Note: We subtract the 500 already sick because they are no longer ‘at risk’ of getting it). 3. Case Fatality Rate: \(10 / (500 + 200) = 1.4\%\).

8. Summary Table for Review

Measure Numerator Denominator What it tells us
Prevalence All cases (old + new) Total Population The burden on the healthcare system.
Incidence New cases only Population at Risk The risk of contracting the disease.
Case Fatality Deaths from Disease X Cases of Disease X The severity or lethality of the disease.

9. Lab Exercise (Using R)

Try running this code in your console to see how mortality rates change as a population ages.

# Population data
pop_data <- data.frame(
  Age_Group = c("0-19", "20-39", "40-59", "60+"),
  Deaths = c(5, 15, 100, 500),
  Population = c(30000, 25000, 20000, 10000)
)

# Calculate Age-Specific Mortality Rate per 1,000
pop_data <- pop_data %>%
  mutate(Mortality_Rate = (Deaths / Population) * 1000)

print(pop_data)
##   Age_Group Deaths Population Mortality_Rate
## 1      0-19      5      30000      0.1666667
## 2     20-39     15      25000      0.6000000
## 3     40-59    100      20000      5.0000000
## 4       60+    500      10000     50.0000000

End of Module 3 Notes ```