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measures_of_disease_in_epidemiology_2024_bjk.rmd
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---
title: "Measures of Disease in Clinical Epidemiology<br/>"
subtitle: "<hr/>"
author: "Brendan J. Kelly, MD, MS"
institute: "Infectious Diseases & Epidemiology<br/><br/>{width=160px}"
date: "updated: `r format(Sys.Date(), '%d %B %Y')`"
output:
xaringan::moon_reader:
self_contained: true
css: xaringan-themer-inferno-grids-fade.css
lib_dir: libs
chakra: libs/remark-latest.min.js
seal: false
nature:
ratio: 16:9
highlightStyle: github
highlightLines: true
countIncrementalSlides: false
slideNumberFormat: "%current%"
---
exclude: true
```{r setup, include=FALSE}
options(htmltools.dir.version = FALSE)
xaringan::summon_remark()
```
```{r xaringan-tile-view, echo=FALSE}
xaringanExtra::use_tile_view()
xaringanExtra::use_webcam()
xaringanExtra::use_tachyons()
xaringanExtra::use_animate_css()
xaringanExtra::use_share_again()
#xaringanExtra::use_scribble(pen_color = "#56106E")
```
---
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<br>Clinical Epidemiology</span>]
]
.callout-url-leftcorner[
.title-nametext[
Brendan J. Kelly, MD, MS
Infectious Diseases, Epidemiology & Microbiology
University of Pennsylvania
19 November 2024
]
]
.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>
]
---
## Disclosures
.pad-left[
- No conflicts of interest.
]
---
## Learning Objectives
.pad-left[
- Measures of disease occurrence: use population data to describe health and disease.
- Key concepts -- explain the meaning of:
- data types and terminology
- prevalence
- incidence (<ins>warning</ins>: multiple types)
- relative risk (RR)
- odds ratio (OR)
- Implementation: prevalence, incidence, RR, and OR from study data (2x2 tables!).
]
---
## 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>Data Types<br>&<br>Distributions</div></div>
</div>
---
layout: false
class: full-screen hide-count
<div class="grid-3-2">
<div class="extension-tile gridset-a"><div>Data Types<br>&<br>Distributions</div></div>
<div class="extension-tile gridset-b animated flipInX"><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>Data Types<br>&<br>Distributions</div></div>
<div class="extension-tile gridset-b"><div>Case from 1981</div></div>
<div class="extension-tile gridset-c animated bounceInDown"><div>Prevalence</div></div>
</div>
---
layout: false
class: full-screen hide-count
<div class="grid-3-2">
<div class="extension-tile gridset-a"><div>Data Types<br>&<br>Distributions</div></div>
<div class="extension-tile gridset-b"><div>Case from 1981</div></div>
<div class="extension-tile gridset-c"><div>Prevalence</div></div>
<div class="extension-tile gridset-d animated fadeInRight"><div>Incidence</div></div>
</div>
---
layout: false
class: full-screen hide-count
<div class="grid-3-2">
<div class="extension-tile gridset-a"><div>Data Types<br>&<br>Distributions</div></div>
<div class="extension-tile gridset-b"><div>Case from 1981</div></div>
<div class="extension-tile gridset-c"><div>Prevalence</div></div>
<div class="extension-tile gridset-d"><div>Incidence</div></div>
<div class="extension-tile gridset-e animated bounceInUp"><div>Inference from<br>Exposures &<br>Outcomes</div></div>
</div>
---
class: full-screen hide-count
<div class="grid-3-2">
<div class="extension-tile gridset-a"><div>Data Types<br>&<br>Distributions</div></div>
<div class="extension-tile gridset-b"><div>Case from 1981</div></div>
<div class="extension-tile gridset-c"><div>Prevalence</div></div>
<div class="extension-tile gridset-d"><div>Incidence</div></div>
<div class="extension-tile gridset-e"><div>Inference from<br>Exposures &<br>Outcomes</div></div>
<div class="extension-tile gridset-f animated slideInLeft"><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 animated flipInY"><div>Data Types<br>&<br>Distributions</div></div>
<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-grey"><div>Relative Risk<br>&<br>Odds Ratios</div></div>
</div>
---
## Data Types
.pad-left[
- __Dichotomous__: binary 0 / 1, true / false
- the focus of most methods in this course (e.g., pneumonia, MI)
- __Continuous__: real values, infinite scale
- discussed in diagnostics lecture (e.g., age, height)
- __Nominal__: discrete data
- categories without intrinsic order (e.g., state)
- __Ordinal__: discrete data
- categories with intrinsic order (e.g., age category)
]
---
## How to Characterize Continuous Data
.pad-left[
- Pair a measure of central tendency with a measure of dispersion:
- mean and SD (both affected by outliers)
- median and IQR
- In doing so, account for <ins>uncertainty</ins> in measures.
]
---
## Characterize Continuous Data: Central Tendency
.pad-left[
- **Mean ( $\mu$)**:
$$\mu=\frac{1}{N}\sum_{i=1}^Nx_i$$
- **Median**: middle value, when values ordered / ranked
- **Mode**: most frequently occurring value
]
<p style="text-align: center;"><mark> (you do <strong>NOT</strong> need to memorize these formulas) </mark></p>
---
## Characterize Continuous Data: Variation/Spread
.pad-left[
- **Standard deviation (SD or $\sigma$)**:
$$\sigma=\sqrt{\frac{1}{N}*\sum_{i=1}^N(x_i - \mu)^2}$$
- **Interquartile range (IQR)** depends on ranking the values:
- the first quartile is the "middle" value of the first half of the ordered set
- the third quartile is the "middle" value of the second half of the ordered set
- IQR is the range of values between first and third quartiles
]
<p style="text-align: center;"><mark> (you do <strong>NOT</strong> need to memorize these formulas) </mark></p>
---
## Describing Continuous Data
.pad-left[
- "Normally distributed": data well characterized by **mean** and **standard deviation (SD)**.
- “Non-parametric” data have a mean and standard deviation, but these parameters do NOT characterize the data well...
]
---
## "Normally Distributed" Continuous Data
```{r parametric_data, echo=FALSE, warning=FALSE, message=FALSE, fig.height=6, fig.width=12, fig.align='center', fig.retina=2}
library(tidyverse)
library(NHANES)
library(ggtext)
set.seed(16)
NHANES |>
as_tibble() |>
filter(Age >= 18) |>
mutate(Gender = paste0("Gender: ", Gender)) |>
ggplot(data = _) +
geom_histogram(aes(x = Height, fill = Gender), colour = "black") +
scale_fill_viridis_d(option = "turbo", begin = 0.15, end = 0.95) +
theme_classic() +
theme(legend.position = 'none', line = element_line(colour = "black"), text = element_text(size = 22), plot.title = ggtext::element_markdown(size = 22), axis.title.x = ggtext::element_markdown(size = 22)) +
labs(title = "Height (cm) from a Population Survey of US Citizens", subtitle = "7,481 subjects with age >= 18 years", x = "Height (cm)", y = "Subject Count") +
facet_wrap(facets = ~ Gender, scales = "free_x")
```
.footnote[[CDC National Health and Nutrition Examination Survey (NHANES)](https://www.cdc.gov/nchs/nhanes/index.htm)]
---
## "Non-Parametric" Continuous Data: Skewed
```{r skewed_data, echo=FALSE, warning=FALSE, message=FALSE, fig.height=6, fig.width=12, fig.align='center', fig.retina=2}
library(tidyverse)
library(NHANES)
library(ggtext)
set.seed(16)
NHANES |>
as_tibble() |>
filter(Age >= 18) |>
mutate(Gender = paste0("Gender: ", Gender)) |>
ggplot(data = _) +
geom_histogram(aes(x = BMI, fill = Gender), colour = "black") +
scale_fill_viridis_d(option = "turbo", begin = 0.15, end = 0.95) +
theme_classic() +
theme(legend.position = 'none', line = element_line(colour = "black"), text = element_text(size = 22), plot.title = ggtext::element_markdown(size = 22), axis.title.x = ggtext::element_markdown(size = 22)) +
labs(title = "BMI (kg/m^2^) from a Population Survey of US Citizens", subtitle = "7,481 subjects with age >= 18 years", x = "BMI (kg/m^2^)", y = "Subject Count") +
facet_wrap(facets = ~ Gender, scales = "free_x")
```
.footnote[[CDC National Health and Nutrition Examination Survey (NHANES)](https://www.cdc.gov/nchs/nhanes/index.htm)]
---
## "Non-Parametric" Continuous Data: Uniform
```{r uniform_data, echo=FALSE, warning=FALSE, message=FALSE, fig.height=6, fig.width=12, fig.align='center', fig.retina=2}
library(tidyverse)
library(NHANES)
library(ggtext)
set.seed(16)
NHANES |>
as_tibble() |>
#filter(Age >= 18) |>
mutate(Gender = paste0("Gender: ", Gender)) |>
ggplot(data = _) +
geom_histogram(aes(x = Age, fill = Gender), colour = "black") +
scale_fill_viridis_d(option = "turbo", begin = 0.15, end = 0.95) +
theme_classic() +
theme(legend.position = 'none', line = element_line(colour = "black"), text = element_text(size = 22), plot.title = ggtext::element_markdown(size = 22), axis.title.x = ggtext::element_markdown(size = 22)) +
labs(title = "Age (years) from a Population Survey of US Citizens", subtitle = " ", x = "Age (years)", y = "Subject Count") +
facet_wrap(facets = ~ Gender, scales = "free_x")
```
.footnote[[CDC National Health and Nutrition Examination Survey (NHANES)](https://www.cdc.gov/nchs/nhanes/index.htm)]
---
## Describing Continuous Data
.pad-left[
- "Normally distributed": data well characterized by **mean** and **standard deviation (SD)**.
- “Non-parametric” data have a mean and standard deviation, but these parameters do NOT characterize the data well:
- **skewed** data: distribution not symmetric around a central value
- **uniform** data: distributed with equal probability of each value
- For "non-parametric" data, we prefer to use **median** and **interquartile range (IQR)** to describe the distribution of a continuous variable because these are less affected by extreme values.
- You can always calculate mean and SD from continuous data. But these parameters might not represent the data well.
]
---
## Dichotomizing Continuous Data
.pad-left[
- Using a threshold to transform continuous data into dichotomous data means <mark>losing information about uncertainty</mark>.
- This is on top of the fundamental uncertainty we face with any epidemiologic measure: does the measured population represent the population of interest?
- See the diagnosis lecture: for example, threshold of oxygen saturation (or $\beta$-D glucan) to diagnose _Pneumocystis_ pneumonia (PCP) means trade-off between sensitivity and specificity.
]
---
## Dichotomania
.pad-left[
- As we discuss prevalence, incidence, RR, and OR, we focus on <ins>dichotomous</ins> exposures and outcomes.
- Remember -- with dichotomous data:
- information about uncertainty is lost
- misclassification is a risk
- But we're doing it anyway 😀 ... why?
- Medicine focuses on dichotomous diagnostic and treatment decisions.
.footnote[[Altman & Royston _BMJ_ 2006](https://www.bmj.com/content/332/7549/1080.1.full)]
]
---
## What About Regression?
.pad-left[
- As we discuss prevalence, incidence, RR, and OR, we focus on <ins>dichotomous</ins> exposures and outcomes.
- Regression methods account for different data types:
- linear models: continuous outcomes
- generalized linear models: dichotomous, nominal, ordinal, etc outcomes
- can incorporate different exposure data types & multiple exposures
- Regression methods are <u>beyond the scope of this course</u>.
.footnote[[Altman & Royston _BMJ_ 2006](https://www.bmj.com/content/332/7549/1080.1.full)]
]
---
class: full-screen hide-count
<div class="grid-3-2">
<div class="extension-tile gridset-grey"><div>Data Types<br>&<br>Distributions</div></div>
<div class="extension-tile gridset-b animated flipInX"><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>
---
## HIV Pandemic: MMWR June 5, 1981
.center[
<img src="figs/hiv_timeline_mmwr_1981.png" alt="MMWR 1981" style="box-shadow: 3px 3px 3px gray;">
]
---
exclude: true
background-image: url(figs/cover_mmwr_1981.jpg)
background-size: 750px
background-position: 50% 50%
## HIV Pandemic: MMWR June 5, 1981
---
## HIV Pandemic: MMWR June 5, 1981
.bg-washed-gray.b--dark-gray.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
]]
---
## HIV Pandemic: Stigma & Discrimination
.pull-left[
- Socially vulnerable groups often at higher infection risk:
- HIV, COVID-19
- how we name infectious diseases has exacerbated stigma
- _bad epidemiology exacerbates stigma_
- Prejudice is used to gain political power:
- homophobia in the 1980s
- anti-Asian racism in the 2020s
]
.pull-right[
<img src="img/radiolab_ashes_on_the_lawn_tall.png" alt="Radiolab" style="box-shadow: 3px 3px 3px gray;">
]
.footnote[[Radiolab "The Ashes on the Lawn"](https://radiolab.org/podcast/ashes-lawn)]
---
## COVID-19 Pandemic: Stigma & Discrimination
.pull-left[
- As we proceed in course, think about causal versus proxy variables. For example:
- Race is not a proxy for biology.
- Race exerts large effects on health: structural racism & direct / interpersonal racism
- High-risk work, access to care, and social networks are some ways social determinants and racism impact health.
]
.pull-right[
<img src="img/covid_disparities_discrimination.png" alt="Radiolab" style="box-shadow: 3px 3px 3px gray;">
]
.footnote[Bilal U et al _Lancet Reg Health Am_ 2022;<br> Chastain DB et al _NEJM_ 2020; Lee JH _NEJM_ 2021]
---
## Case from 1981... _Pneumocystis_ pneumonia?
.pad-left[
- 36-year-old man presents with a 4-month history of fever, dyspnea, and cough.
- What is his diagnosis? Does he have _Pneumocystis_ pneumonia (PCP)?
- As you collect data (history, vital signs, physical exam, laboratory test values, radiology results), you are making inferences about the diagnosis based on __associations__ between your findings and disease states.
]
---
## 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
- PCP is a fungal pneumonia caused by _Pneumocystis jirovecii_ (formerly _Pneumocystis carinii_), which causes dyspnea, hypoxemia, and nonproductive cough, and eventually cystic lung changes.
- In 1981, _Pneumocystis_ was known to be a low <ins>prevalence</ins> disease.
- New data would show an increasing <ins>incidence</ins>.
]
---
## 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>Data Types<br>&<br>Distributions</div></div>
<div class="extension-tile gridset-grey"><div>Case from 1981</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>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: full-screen hide-count
<div class="grid-3-2">
<div class="extension-tile gridset-grey"><div>Data Types<br>&<br>Distributions</div></div>
<div class="extension-tile gridset-grey"><div>Case from 1981</div></div>
<div class="extension-tile gridset-c animated flipInY"><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>
---
## 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_
```{r pcp_study, echo=FALSE, warning=FALSE, message=FALSE, fig.height=7, fig.width=12, fig.align='center', fig.retina=2}
library(tidyverse)
set.seed(16)
tibble(subject_id = factor(seq(50)),
enrollment = rep(0,50),
exit = sample(x = c(rep(2,35),runif(n = 15, min = 1.7, max = 2)), size = 50, replace = FALSE),
pcp_start = c(rep(NA,5),1.2,rep(NA,5),0.4,rep(NA,4),1.1,rep(NA,6),0.8,rep(NA,4),1.4,NA,0.3,rep(NA,3),1.0,rep(NA,6),0.1,rep(NA,4),0.9,rep(NA,3)),
pcp_stop = pcp_start + 0.0577,
ppx_start = c(rep(NA,4),1.5,rep(NA,5),1.6,rep(NA,6),1.4,rep(NA,3),1.7,rep(NA,3),1.4,rep(NA,1),1.3,rep(NA,2),1.55,rep(NA,9),1.2,rep(NA,5),1.5,rep(NA,3))) %>%
group_by(subject_id) %>%
nest() %>%
mutate(exit_adjust = map_dbl(data, ~ ifelse(is.na(.x[["pcp_start"]]) & is.na(.x[["ppx_start"]]), sample(x = seq(1.5,2,0.1), size = 1), .x[["exit"]]))) %>%
unnest(cols = c(data)) %>%
ungroup() %>%
mutate(ppx_stop = exit_adjust) %>%
group_by(subject_id) %>%
mutate(follow_start1 = enrollment,
follow_stop1 = min(pcp_start, ppx_start, exit_adjust, na.rm = TRUE),
follow_start2 = pcp_stop,
follow_stop2 = min(ppx_start, exit_adjust, na.rm = TRUE)) %>%
ungroup() %>%
ggplot(data = .) +
geom_segment(aes(x = enrollment, xend = exit_adjust, y = subject_id, yend = subject_id), colour = "grey", size = 1) +
geom_segment(aes(x = pcp_start, xend = pcp_stop, y = subject_id, yend = subject_id), colour = "red", size = 1) +
geom_point(aes(x = pcp_start, y = subject_id), colour = "red", size = 2) +
geom_segment(aes(x = ppx_start, xend = ppx_stop, y = subject_id, yend = subject_id), colour = "blue", size = 1, size = 2) +
labs(x = "Duration of Study Enrollment (years)", y = "Subject ID") +
theme_classic() +
theme(text = element_text(size = 22), axis.text.y = element_text(size = 10)) -> p
```
```{r print_pcp_study, echo=FALSE, warning=FALSE, message=FALSE, fig.height=7, fig.width=12, fig.align='center', fig.retina=2, dependson= "pcp_study"}
p
```
---
## Cohort at Risk for _Pneumocystis_
```{r print_pcp_study_label_case, echo=FALSE, warning=FALSE, message=FALSE, fig.height=7, fig.width=12, fig.align='center', fig.retina=2, dependson= "pcp_study"}
p +
annotate(geom = "text", x = 0.1, y = 42, label = "Case &\nTreatment")
```
---
## Cohort at Risk for _Pneumocystis_
```{r print_pcp_study_label_followup, echo=FALSE, warning=FALSE, message=FALSE, fig.height=7, fig.width=12, fig.align='center', fig.retina=2, dependson= "pcp_study"}
p +
annotate(geom = "text", x = 1.9, y = 3, label = "End of Follow-up")
```
---
## Cohort at Risk for _Pneumocystis_
```{r print_pcp_study_label_prophylaxis, echo=FALSE, warning=FALSE, message=FALSE, fig.height=7, fig.width=12, fig.align='center', fig.retina=2, dependson= "pcp_study"}
p +
annotate(geom = "text", x = 1.9, y = 22, label = "Prophylactic\nAntibiotic")
```
---
## Cohort at Risk: Point Prevalence
```{r pcp_point_prev, echo=FALSE, warning=FALSE, message=FALSE, fig.height=7, fig.width=12, fig.align='center', fig.retina=2, dependson= "pcp_study"}
p + annotate("rect", xmin=0.9, xmax=0.91, ymin=0, ymax=Inf, alpha=0.6, fill="purple")
#+ geom_vline(aes(xintercept = 0.9), colour = "purple", size = 3, alpha = 0.4)
```
---
## Cohort at Risk: Period Prevalence
```{r pcp_period_prev, echo=FALSE, warning=FALSE, message=FALSE, fig.height=7, fig.width=12, fig.align='center', fig.retina=2, dependson= "pcp_study"}
p + annotate("rect", xmin=0.9, xmax=1.2, ymin=0, ymax=Inf, alpha=0.6, fill="purple")
```
---
## 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?).
- Prevalence can provide a useful snapshot of the burden of disease.
]
---
## 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>Data Types<br>&<br>Distributions</div></div>
<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-d animated flipInX"><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: full-screen hide-count
<div class="grid-3-2">
<div class="extension-tile gridset-grey"><div>Data Types<br>&<br>Distributions</div></div>
<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-d animated flipInX"><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>
---
## Case from 1981... _Pneumocystis_ pneumonia?
.pull-left[
<img src="figs/nejm_combined.png" alt="Masur & Gottlieb" style="box-shadow: 3px 3px 3px gray;">
]
.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[
- _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>