1. Introduction

In epidemiology, measuring disease frequency is the first step in the “Epidemiologic Cycle.” We move from anecdotal evidence (e.g., “there seems to be a lot of flu”) to quantitative data (e.g., “the incidence is 5 per 1,000 person-years”).

2. Fractions in Epidemiology

There are three fundamental ways to express the relationship between a numerator ($x$) and a denominator ($y$).

Type	Definition	Example
Ratio	$x$ is not part of $y$	5 males : 10 females
Proportion	$x$ is a part of $y$	5 cases / 100 people (5%)
Rate	Proportion + Time element	5 cases per 1,000 people per year

3. Prevalence (The “Snap-shot”)

Prevalence measures the total number of cases (old and new) in a population at a specific point in time.

Formula: \[P = \frac{\text{Number of existing cases}}{\text{Total Population}} \times 10^n\]

Real-Life Example: HIV/AIDS

In a country with 1,000,000 people, if 50,000 people are currently living with HIV, the prevalence is $5\%$. Prevalence is useful for resource planning (e.g., how many hospital beds or doses of medication are needed today).

4. Incidence (The “Video”)

Incidence measures the flow of new cases into a population.

4.1 Cumulative Incidence (Risk)

The probability that an individual will develop the disease over a specific period. \[CI = \frac{\text{New cases during period}}{\text{Population at risk at the start}}\]

4.2 Incidence Rate (Person-Time)

Used when people are followed for different amounts of time. \[IR = \frac{\text{New cases}}{\text{Sum of person-time units}}\]

5. Visualizing the Relationship

The relationship between Incidence and Prevalence is often described using the “Bathtub Analogy.”

Incidence = The water coming out of the faucet.
Prevalence = The level of water in the tub.
Recovery/Death = The drain.

6. Real-Life Application Case Study

Scenario: A Flu Outbreak in a Nursing Home

Total Residents: 200
January 1st: 10 residents already have the flu.
During January: 30 more residents catch the flu.
Deaths: 2 residents die from the flu.

Calculations:

Point Prevalence (Jan 1): $10 / 200 = 5\%$
Cumulative Incidence (Jan): $30 / (200 - 10) = 15.7\%$ (Note: We subtract the 10 who already had it because they weren’t ‘at risk’ of catching it again).
Case Fatality Rate (CFR): $2 / (10 + 30) = 5\%$ (Deaths divided by total people who had the disease).

7. Summary of Measures

Measure	Numerator	Denominator	Utility
Prevalence	All cases	Total population	Planning / Burden
Incidence	New cases	Population at risk	Etiology / Risk
Case Fatality	Deaths from disease	Total cases	Disease Severity

8. Practice Exercise

A community of 10,000 people is monitored for “Disease X” over one year. - At the start, 500 have it. - During the year, 200 new cases are diagnosed. - 50 people die from the disease.

Task: Calculate the Period Prevalence and the Cumulative Incidence using R.

pop <- 10000
existing <- 500
new_cases <- 200

# Calculate
period_prevalence <- ((existing + new_cases) / pop) * 100
cum_incidence <- (new_cases / (pop - existing)) * 1000

print(paste("Period Prevalence:", period_prevalence, "%"))

## [1] "Period Prevalence: 7 %"

print(paste("Cumulative Incidence:", round(cum_incidence, 2), "per 1,000 at risk"))

## [1] "Cumulative Incidence: 21.05 per 1,000 at risk"

```

Why the error happened:

In R, :: allows you to access a function from a package without loading it. However, opts_chunk is not a function; it is a list (specifically an internal object) within the knitr package.

Wrong: knitr::opts_chunk_set() (R looks for a function named exactly that and fails).
Right: knitr::opts_chunk$set() (R finds the list opts_chunk and then uses the $ to call the set function inside it).

Module III: Measurement of Disease Frequency

barkhado ali

2025-12-29