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<!DOCTYPE html>
<html lang="" xml:lang="">
<head>
<title>Measures of Disease in Clinical Epidemiology </title>
<meta charset="utf-8" />
<meta name="author" content="Brendan J. Kelly, MD, MS" />
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<textarea id="source">
exclude: true
---
class: top left hide-count
background-image: url(img/Pneumocystis_jirovecii_AO_AL_wikipedia_crop.png)
background-size: cover
.move-top20[
.title-text[<span style="font-size:0.8em">Measures of Disease in Clinical Epidemiology</span>]
]
.callout-url-leftcorner[
.title-nametext[
Brendan J. Kelly, MD, MS
Infectious Diseases & Epidemiology
University of Pennsylvania
updated: 08 February 2022
]
]
.footnote-right[
<span style='color:white'>image: Federica Viazzi "Microscopy image of <i>P. jirovecii</i>" [(Wikipedia)](https://en.wikipedia.org/wiki/Pneumocystis_jirovecii#/media/File:Pneumocystis_jirovecii_AO_AL.jpg)</span>
]
---
## Learning Objectives
.pad-left[
- Measures of disease occurrence: use population data to describe health and disease.
- Key concepts -- explain the meaning of:
- prevalence
- incidence (<ins>warning</ins>: multiple types)
- relative risk (RR)
- odds ratio (OR)
- Implementation: prevalence, incidence, RR, and OR from study data (2x2 tables!).
- Back to the beginning:
- how do we measure?
- data types and data distributions
]
---
## Why Do I Care? ...
.pad-left[
- Why use these tools (prevalence, incidence, RR, OR)?
- inform differential diagnoses & counsel patients (<ins>your job</ins>)
- design public health interventions & direct new diagnostics/therapies (society!)
- understand distributions and determinants of diseases (science!)
]
---
## ... What Do I Need to Know for the Test?
.pad-left[
.grey-text[
- Why use these tools (prevalence, incidence, RR, OR)?
- inform differential diagnoses & counsel patients (<ins>your job</ins>)
- design public health interventions & direct new diagnostics/therapies (society!)
- understand distributions and determinants of diseases (science!)
]
- How to use these tools:
- precise definitions
(e.g., RR vs OR, cumulative incidence vs incidence density)
- a bit of arithmetic
]
---
class: full-screen hide-count
<div class="grid-3-2">
<div class="extension-tile gridset-a animated flipInY"><div>Case from 1981</div></div>
</div>
---
layout: false
class: full-screen hide-count
<div class="grid-3-2">
<div class="extension-tile gridset-a"><div>Case from 1981</div></div>
<div class="extension-tile gridset-b animated flipInX"><div>Prevalence</div></div>
</div>
---
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<div class="grid-3-2">
<div class="extension-tile gridset-a"><div>Case from 1981</div></div>
<div class="extension-tile gridset-b"><div>Prevalence</div></div>
<div class="extension-tile gridset-c animated bounceInDown"><div>Incidence</div></div>
</div>
---
layout: false
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<div class="grid-3-2">
<div class="extension-tile gridset-a"><div>Case from 1981</div></div>
<div class="extension-tile gridset-b"><div>Prevalence</div></div>
<div class="extension-tile gridset-c"><div>Incidence</div></div>
<div class="extension-tile gridset-d animated fadeInRight"><div>Inference from<br>Exposures &<br>Outcomes</div></div>
</div>
---
layout: false
class: full-screen hide-count
<div class="grid-3-2">
<div class="extension-tile gridset-a"><div>Case from 1981</div></div>
<div class="extension-tile gridset-b"><div>Prevalence</div></div>
<div class="extension-tile gridset-c"><div>Incidence</div></div>
<div class="extension-tile gridset-d"><div>Inference from<br>Exposures &<br>Outcomes</div></div>
<div class="extension-tile gridset-e animated bounceInUp"><div>Relative Risk<br>&<br>Odds Ratios</div></div>
</div>
---
class: full-screen hide-count
<div class="grid-3-2">
<div class="extension-tile gridset-a"><div>Case from 1981</div></div>
<div class="extension-tile gridset-b"><div>Prevalence</div></div>
<div class="extension-tile gridset-c"><div>Incidence</div></div>
<div class="extension-tile gridset-d"><div>Inference from<br>Exposures &<br>Outcomes</div></div>
<div class="extension-tile gridset-e"><div>Relative Risk<br>&<br>Odds Ratios</div></div>
<div class="extension-tile gridset-f animated slideInLeft"><div>Data Types<br>&<br>Distributions</div></div>
</div>
---
class: full-screen hide-count
<div class="grid-3-2">
<div class="extension-tile gridset-a animated flipInY"><div>Case from 1981</div></div>
<div class="extension-tile gridset-grey"><div>Prevalence</div></div>
<div class="extension-tile gridset-grey"><div>Incidence</div></div>
<div class="extension-tile gridset-grey"><div>Inference from<br>Exposures &<br>Outcomes</div></div>
<div class="extension-tile gridset-grey"><div>Relative Risk<br>&<br>Odds Ratios</div></div>
<div class="extension-tile gridset-grey"><div>Data Types<br>&<br>Distributions</div></div>
</div>
---
## Case from 1981...
.pad-left[
- 36-year-old man presents with a 4-month history of fever, dyspnea, and cough.
]
---
background-image: url(figs/hiv_timeline_mmwr_1981.png)
background-size: contain
???
Image credit: [MMWR](https://www.hiv.gov/hiv-basics/overview/history/hiv-and-aids-timeline)
---
background-image: url(figs/cover_mmwr_1981.jpg)
background-size: 750px
background-position: 50% 50%
## MMWR June 5, 1981
---
## MMWR June 5, 1981
.bg-washed-blue.b--dark-blue.ba.bw2.br3.shadow-5.ph4.mt5.f4[
All the above observations suggest the possibility of a <mark>cellular-immune dysfunction related to a common exposure that predisposes individuals to opportunistic infections such as pneumocystosis and candidiasis</mark>. Although the role of CMV infection in the pathogenesis of pneumocystosis remains unknown, the possibility of _P. carinii_ infection must be carefully considered in a differential diagnosis for previously healthy homosexual males with dyspnea and pneumonia.
.tr[
— Gottlieb MS et al <ins>MMWR</ins> 1981
]]
---
## Stigma and Discrimination
.pad-left[
- vulnerable groups and infection risk
- HIV, COVID-19
- how we name infectious diseases
]
---
## Case from 1981... _Pneumocystis_ pneumonia?
.pad-left[
- 36-year-old man presents with a 4-month history of fever, dyspnea, and cough.
- What do you want to know and why?
- history
- vital signs
- physical exam
- laboratory test values
- radiology
- What is his diagnosis? Does he have _Pneumocystis_ pneumonia (PCP)?
]
---
## Case from 1981... _Pneumocystis_ pneumonia?
.pad-left[
- Differential diagnosis must be grounded in understanding:
- distributions of disease: we'll learn about **prevalence** & **incidence**
- determinants of disease: we'll learn **2x2 tables** to relate exposures and outcomes
- In 1981, _Pneumocystis_ was known to be a low <ins>prevalence</ins> disease.
- New data would show an increasing <ins>incidence</ins>.
<br/>
.center[<mark>(In ID, the differential is always evolving).</mark>]
]
---
## Case from 1981... _Pneumocystis_ pneumonia?
.pad-left[
- Does our patient have _Pneumocystis_ pneumonia (PCP)?
- How is the distribution of _Pneumocystis_ pneumonia changing?
- What are the determinants of _Pneumocystis_ pneumonia?
<br/>
.center[<mark>Note: questions depend on <strong>dichotomous</strong> definition of disease (yes/no <em>Pneumocystis</em>)</mark>]
]
---
class: full-screen hide-count
<div class="grid-3-2">
<div class="extension-tile gridset-grey"><div>Case from 1981</div></div>
<div class="extension-tile gridset-b animated flipInX"><div>Measuring<br>Disease<br>Occurrence</div></div>
<div class="extension-tile gridset-grey"><div>Incidence</div></div>
<div class="extension-tile gridset-grey"><div>Inference from<br>Exposures &<br>Outcomes</div></div>
<div class="extension-tile gridset-grey"><div>Relative Risk<br>&<br>Odds Ratios</div></div>
<div class="extension-tile gridset-grey"><div>Data Types<br>&<br>Distributions</div></div>
</div>
---
class: full-screen hide-count
<div class="grid-3-2">
<div class="extension-tile gridset-grey"><div>Case from 1981</div></div>
<div class="extension-tile gridset-b animated flipInX"><div>Prevalence</div></div>
<div class="extension-tile gridset-grey"><div>Incidence</div></div>
<div class="extension-tile gridset-grey"><div>Inference from<br>Exposures &<br>Outcomes</div></div>
<div class="extension-tile gridset-grey"><div>Relative Risk<br>&<br>Odds Ratios</div></div>
<div class="extension-tile gridset-grey"><div>Data Types<br>&<br>Distributions</div></div>
</div>
---
## Prevalence
.pad-left[
- How common is _Pneumocystis_ pneumonia (PCP)?
- Prevalence:
- number with the disease / number in specified population
- **point prevalence**: at a specific point in time
- **period prevalence**: during a given period (e.g., 12-month prevalence)
- a proportion (unitless, ranges from 0-1)
- numerator includes all people who have the disease, both new and ongoing cases
- represents a <ins>cross-sectional</ins> “snapshot” of the population
]
---
## Prevalence of _Pneumocystis_ pneumonia
.pad-left[
- In 1967, CDC became the sole supplier of pentamidine in the United States and began collecting data on cases of PCP:
- period prevalence published in 1974<sup>*</sup>: 579 cases (194 confirmed) over 3 years
- what’s the denominator?
- what’s the prevalence?
- __Point prevalence__ of _Pneumocystis_ would be vanishingly small given limited duration of disease.
- From 1967-1974, even the __period prevalence__ was very small.
.footnote[[*] Walzer PD et al _Annals Int Med_ 1974]
]
---
## Point Prevalence versus Period Prevalence
.pad-left[
- To understand the difference between point and period prevalence, let's imagine a cohort of people living with HIV/AIDS at risk for _Pneumocystis_:
- 50 high-risk subjects enrolled at the start of a two-year observation period
- cases of PCP each receive 3 weeks of antibiotic treatment (red on plot)
- incomplete follow-up (grey on plot)
- some subjects started on _Pneumocystis_ prophylaxis (blue on plot)
]
---
## Cohort at Risk for _Pneumocystis_
<img src="measures_of_disease_in_epidemiology_2021_bjk_files/figure-html/print_pcp_study-1.png" width="864" style="display: block; margin: auto;" />
---
## Cohort at Risk for _Pneumocystis_
<img src="measures_of_disease_in_epidemiology_2021_bjk_files/figure-html/print_pcp_study_label_case-1.png" width="864" style="display: block; margin: auto;" />
---
## Cohort at Risk for _Pneumocystis_
<img src="measures_of_disease_in_epidemiology_2021_bjk_files/figure-html/print_pcp_study_label_followup-1.png" width="864" style="display: block; margin: auto;" />
---
## Cohort at Risk for _Pneumocystis_
<img src="measures_of_disease_in_epidemiology_2021_bjk_files/figure-html/print_pcp_study_label_prophylaxis-1.png" width="864" style="display: block; margin: auto;" />
---
## Cohort at Risk: Point Prevalence
<img src="measures_of_disease_in_epidemiology_2021_bjk_files/figure-html/pcp_point_prev-1.png" width="864" style="display: block; margin: auto;" />
---
## Cohort at Risk: Period Prevalence
<img src="measures_of_disease_in_epidemiology_2021_bjk_files/figure-html/pcp_period_prev-1.png" width="864" style="display: block; margin: auto;" />
---
## Prevalence
.pad-left[
- Prevalence is **NOT** the same as risk.
- Prevalence numerator includes all people who have the disease, both new and ongoing cases, so represents a cross-sectional “snapshot” of the population.
- Prevalence does **NOT** estimate the risk of developing the disease because <mark>prevalence does **NOT** fully account for time </mark> (are the measured cases old cases or new cases?).
]
---
## Reflection Question
.pad-left[
How can an infection have high prevalence if it occurs infrequently?
- (A) the infection is rapidly fatal
- (B) the infection rapidly resolves
- (C) a few children get the infection every year, but the infection persists for the rest of their lives
- (D) the infection results in lifelong protective immunity
]
---
class: full-screen hide-count
<div class="grid-3-2">
<div class="extension-tile gridset-grey"><div>Case from 1981</div></div>
<div class="extension-tile gridset-grey"><div>Prevalence</div></div>
<div class="extension-tile gridset-c animated flipInY"><div>Measuring<br>Disease<br>Occurrence</div></div>
<div class="extension-tile gridset-grey"><div>Inference from<br>Exposures &<br>Outcomes</div></div>
<div class="extension-tile gridset-grey"><div>Relative Risk<br>&<br>Odds Ratios</div></div>
<div class="extension-tile gridset-grey"><div>Data Types<br>&<br>Distributions</div></div>
</div>
---
class: full-screen hide-count
<div class="grid-3-2">
<div class="extension-tile gridset-grey"><div>Case from 1981</div></div>
<div class="extension-tile gridset-grey"><div>Prevalence</div></div>
<div class="extension-tile gridset-c animated flipInY"><div>Incidence</div></div>
<div class="extension-tile gridset-grey"><div>Inference from<br>Exposures &<br>Outcomes</div></div>
<div class="extension-tile gridset-grey"><div>Relative Risk<br>&<br>Odds Ratios</div></div>
<div class="extension-tile gridset-grey"><div>Data Types<br>&<br>Distributions</div></div>
</div>
---
## Case from 1981... _Pneumocystis_ pneumonia?
.pull-left[
]
.pull-right[
<br/>
- new _Pneumocystis_ cases (NYC<sup>1</sup>): 13 cases over 21 months
- new _Pneumocystis_ cases (LA<sup>2</sup>): 5 cases over 7 months
- concurrent opportunistic infections:
- CMV
- _Candida_
- Kaposi's sarcoma
]
.footnote[[1,2] Masur H et al _NEJM_ 1981; Gottlieb MS et al _NEJM_ 1981]
---
## Incidence
.pad-left[
- Among MSM, _Pneumocystis_ pneumonia (PCP) is occurring more frequently...
- Incidence: occurrence of new cases over a given period of time.
- **cumulative incidence**:
`$$cumulative\ incidence = \frac{{new\ cases}}{persons\ at\ risk\\at\ start\ time\ interval}$$`
- **incidence density**: (more precise)
`$$incidence\ density = \frac{new\ cases}{person\ time\\at\ risk}$$`
]
---
## Cumulative Incidence
.pad-left[
- Cumulative incidence:
- must specify population consisting of at-risk individuals
- must specify a time period of observation
- <ins>numerator</ins> = all new cases during a specified time period
- <ins>denominator</ins> = all individuals at risk in the specified population at the start of the specified time period (does NOT account for deaths due to other causes)
- ranges from 0 to 1 (a.k.a., “incidence proportion”)
- like prevalence, is a proportion and therefore has no units (but only makes sense if you specify the time period of observation, e.g., % per year)
]
---
## Incidence Density
.pad-left[
- Incidence density:
- in a specified population consisting of at risk individuals over a specified period of observation, more precisely quantifies the person-time at risk
- <ins>numerator</ins> = all new cases during a specified time period
- <ins>denominator</ins> = the sum, over all individuals in the population, of time at risk until the event of interest, death, loss to follow-up, the end of the study, or when they are no longer at risk for whatever reason
- not a proportion; range depends on the units of person-time (0 to infinity)
- <mark>accounts for death from other causes!</mark>
]
---
## Incidence: Which Denominator?
.pad-left[
- To understand the difference between cumulative incidence and incidence density, let's return to our imagined study of people living with HIV/AIDS at risk for _Pneumocystis_:
- 50 high-risk subjects enrolled at the start of a two-year observation period
- cases of PCP each receive 3 weeks of antibiotic treatment (red on plot)
- incomplete follow-up (grey on plot)
- some subjects started on _Pneumocystis_ prophylaxis (blue on plot)
]
---
## Cohort at Risk for _Pneumocystis_
<img src="measures_of_disease_in_epidemiology_2021_bjk_files/figure-html/reprint_pcp_study-1.png" width="864" style="display: block; margin: auto;" />
---
## Cohort at Risk for _Pneumocystis_
<img src="measures_of_disease_in_epidemiology_2021_bjk_files/figure-html/print_pcp_study_label_case2-1.png" width="864" style="display: block; margin: auto;" />
---
## Cohort at Risk for _Pneumocystis_
<img src="measures_of_disease_in_epidemiology_2021_bjk_files/figure-html/print_pcp_study_label_followup2-1.png" width="864" style="display: block; margin: auto;" />
---
## Cohort at Risk for _Pneumocystis_
<img src="measures_of_disease_in_epidemiology_2021_bjk_files/figure-html/print_pcp_study_label_prophylaxis2-1.png" width="864" style="display: block; margin: auto;" />
---
## Cohort at Risk: Cumulative Incidence (at risk at start)
<img src="measures_of_disease_in_epidemiology_2021_bjk_files/figure-html/pcp_incid_proportion-1.png" width="864" style="display: block; margin: auto;" />
---
## Cohort at Risk: Incidence Density (person-time at risk)
<img src="measures_of_disease_in_epidemiology_2021_bjk_files/figure-html/pcp_incid_density-1.png" width="864" style="display: block; margin: auto;" />
---
## Incidence: Which Denominator?
.pad-left[
- Cumulative incidence of _Pneumocystis_ versus incidence density:
- if the end of the grey line is death / loss to follow-up, how does incidence density compare to annual cumulative incidence?
- if you don’t count time on prophylaxis or treatment antibiotics as “time at risk”, how does the incidence density compare to the annual cumulative incidence?
]
---
## Notes on Population at Risk
.pad-left[
- In a population, individuals are at risk of disease if they:
- (1) do not have the disease at baseline
- (2) are capable of developing the disease (e.g., have the organ of interest; have not been successfully immunized against the disease; haven’t developed lifelong immunity)
- The difference between cumulative incidence and incidence density is that the latter attempts a more precise quantification of population at risk -- it’s harder to evaluate, but more informative if you can.
]
---
## Notes on Person-Time
.pad-left[
- To improve precision of risk estimate (<ins>incidence density</ins>), we measure:
- population at risk of outcome
- actual time at risk (during which outcome could occur)
- **Person-time**:
- denominator for incidence density
- the product of population at risk and time at risk (e.g., patient-months)
]
---
## Beware the Phrase “Incidence Rate”!
.pad-left[
- “Incidence rate” is used to mean two different things:
- number new cases / number persons at risk @ start (short) time interval (e.g., “annual incidence rate” to mean cumulative incidence over one year)
- number new cases / person-time at risk (i.e., incidence density, the precise rate)
]
---
## Reflection Question
.pad-left[
Your patient with HIV is considering starting prophylactic antibiotics for PCP. You have PCP prevalence, cumulative incidence, and incidence density data available. Which data provide the most precise information on the patient’s risk of PCP off of prophylaxis?
- (A) prevalence
- (B) cumulative incidence
- (C) incidence density
]
---
background-image: url(figs/bathtub_labelled.svg)
background-size: 520px
background-position: 50% 70%
## Can You Tell Prevalence from Incidence?
---
## Can You Tell Prevalence from Incidence?
.pad-left[
- HIV in Rakai, Uganda 1994-2003*:
- intensive “ABC” intervention (Abstinence, Be faithful, Condoms)
- prevalence declined!
- incidence remained constant at 1.5% per year
- what happened?
.footnote[[*] Wawer M et al _CROI_ 2005; Roehr B _BMJ_ 2005]
]
---
class: full-screen hide-count
<div class="grid-3-2">
<div class="extension-tile gridset-grey"><div>Case from 1981</div></div>
<div class="extension-tile gridset-grey"><div>Prevalence</div></div>
<div class="extension-tile gridset-grey"><div>Incidence</div></div>
<div class="extension-tile gridset-d animated flipInX"><div>What<br>determines<br>risk?</div></div>
<div class="extension-tile gridset-grey"><div>Relative Risk<br>&<br>Odds Ratios</div></div>
<div class="extension-tile gridset-grey"><div>Data Types<br>&<br>Distributions</div></div>
</div>
---
class: full-screen hide-count
<div class="grid-3-2">
<div class="extension-tile gridset-grey"><div>Case from 1981</div></div>
<div class="extension-tile gridset-grey"><div>Prevalence</div></div>
<div class="extension-tile gridset-grey"><div>Incidence</div></div>
<div class="extension-tile gridset-d animated flipInX"><div>Inference from<br>Exposures &<br>Outcomes</div></div>
<div class="extension-tile gridset-grey"><div>Relative Risk<br>&<br>Odds Ratios</div></div>
<div class="extension-tile gridset-grey"><div>Data Types<br>&<br>Distributions</div></div>
</div>
---
## Basics of Study Types
.pad-left[
- We want to understand the <mark>relationship between risk factors (exposures) and disease (outcomes)</mark>. For example, between CD4 count and PCP in HIV.
- To calculate incidence need to know how many are in a population:
- randomized trials: pick the population, randomize, control the treatment, and measure the outcome
- cohort studies: pick the population, divide into preselected exposure (treatment or risk factor) groups, and measure the outcome
- But do NOT know this in case control studies: pick the cases and control groups, then measure rates of exposure (do NOT know size of population at risk).
]
---
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---
## 2x2 Table
.pull-left[
- Dichotomous exposures and outcomes.
- Examine relationships between exposures and outcomes.
- <ins>Goal</ins>: inference about larger world.
]
.pull-right[
<img src="measures_of_disease_in_epidemiology_2021_bjk_files/figure-html/unnamed-chunk-2-1.png" width="360" style="display: block; margin: auto;" />
]
---
## 2x2 Table
.pull-left[
- Dichotomous exposures and outcomes.
- Examine relationships between exposures and outcomes.
- <ins>Goal</ins>: inference about larger world.
]
.pull-right[
<img src="measures_of_disease_in_epidemiology_2021_bjk_files/figure-html/unnamed-chunk-3-1.png" width="360" style="display: block; margin: auto;" />
]
---
## 2x2 Table
.pull-left[
- Dichotomous exposures and outcomes.
- Examine relationships between exposures and outcomes.
- <ins>Goal</ins>: inference about larger world.
- <mark>Is study RCT/cohort or case-control?</mark>
- Can always calculate a <ins>relative risk (RR)</ins> from 2x2 table but only appropriate for <ins>RCT/cohort</ins>
- Can always calculate an <ins>odds ratio (OR)</ins> from 2x2 table but only appropriate for <ins>case-control study</ins><br/>(can do better with RR if RCT/cohort)
]
.pull-right[
<img src="measures_of_disease_in_epidemiology_2021_bjk_files/figure-html/unnamed-chunk-4-1.png" width="360" style="display: block; margin: auto;" />
]
---
class: full-screen hide-count
<div class="grid-3-2">
<div class="extension-tile gridset-grey"><div>Case from 1981</div></div>
<div class="extension-tile gridset-grey"><div>Prevalence</div></div>
<div class="extension-tile gridset-grey"><div>Incidence</div></div>
<div class="extension-tile gridset-grey"><div>Inference from<br>Exposures &<br>Outcomes</div></div>
<div class="extension-tile gridset-e animated flipInY"><div>2x2 tables<br>are HARD!</div></div>
<div class="extension-tile gridset-grey"><div>Data Types<br>&<br>Distributions</div></div>
</div>
---
class: full-screen hide-count
<div class="grid-3-2">
<div class="extension-tile gridset-grey"><div>Case from 1981</div></div>
<div class="extension-tile gridset-grey"><div>Prevalence</div></div>
<div class="extension-tile gridset-grey"><div>Incidence</div></div>
<div class="extension-tile gridset-grey"><div>Inference from<br>Exposures &<br>Outcomes</div></div>
<div class="extension-tile gridset-e animated flipInY"><div>Relative Risk<br>&<br>Odds Ratios</div></div>
<div class="extension-tile gridset-grey"><div>Data Types<br>&<br>Distributions</div></div>
</div>
---
## 2x2 Table: Calculate Relative Risk for Cohort/Trial
.pull-left[
- Relative Risk (RR): risk (incidence) exposed / risk (incidence) unexposed:
`$$RR = \frac{\frac{A}{(A + B)}}{\frac{C}{(C + D)}}$$`
- Risk difference (RD): risk (incidence) exposed - risk (incidence) unexposed:
`$$RD = \frac{A}{(A + B)} - \frac{C}{(C + D)}$$`
]
.pull-right[
<img src="measures_of_disease_in_epidemiology_2021_bjk_files/figure-html/unnamed-chunk-5-1.png" width="360" style="display: block; margin: auto;" />
]
---
## PCP ~ AIDS: Relative Risk (RR)
.pull-left[
- Imagine a cohort study examining incidence (risk) for _Pneumocystis_ among patients with or without an Acquired Immunodeficiency Syndrome (AIDS):
- Relative Risk (RR):
`$$RR = \frac{\frac{10}{(10 + 10)}}{\frac{5}{(5 + 15)}} = \frac{0.5}{0.25} = 2$$`
- Risk difference (RD):
`$$RD = \frac{10}{(10 + 10)} - \frac{5}{(5 + 15)} = 0.25$$`
]
.pull-right[
<img src="measures_of_disease_in_epidemiology_2021_bjk_files/figure-html/unnamed-chunk-6-1.png" width="360" style="display: block; margin: auto;" />
]