Epidemiology is the study of the frequency, distribution and determinants of health-related states in populations and the application of such knowledge to control health problems (Disease Control and Prevention 2006).

This vignette provides instruction on the way R and `epiR`

can be used for descriptive epidemiological analyses, that is, to describe how the frequency of disease varies by individual, place and time.

Descriptions of disease frequency involves reporting either the **prevalence** or **incidence** of disease.

Some definitions. Strictly speaking, ‘prevalence’ equals the number of cases of a given disease or attribute that exists in a population at a specified point in time. Prevalence risk is the proportion of a population that has a specific disease or attribute at a specified point in time. Many authors use the term ‘prevalence’ when they really mean prevalence risk, and these notes will follow this convention.

Two types of prevalence are reported in the literature: (1) **point prevalence** equals the proportion of a population in a diseased state at a single point in time, (2) **period prevalence** equals the proportion of a population with a given disease or condition over a specific period of time (i.e. the number of existing cases at the start of a follow-up period plus the number of incident cases that occur during the follow-up period).

Incidence provides a measure of how frequently susceptible individuals become disease cases as they are observed over time. An incident case occurs when an individual changes from being susceptible to being diseased. The count of incident cases is the number of such events that occur in a population during a defined follow-up period. There are two ways to express incidence:

**Incidence risk** (also known as cumulative incidence) is the proportion of initially susceptible individuals in a population who become new cases during a defined follow-up period.

**Incidence rate** (also known as incidence density) is the number of new cases of disease that occur per unit of individual time at risk during a defined follow-up period.

In addition to reporting the point estimate of disease frequency, it is important to provide an indication of the uncertainty around that point estimate. The `epi.conf`

function in the `epiR`

package allows you to calculate confidence intervals for prevalence, incidence risk and incidence rates.

Let’s say we’re interested in the prevalence of disease X in a population comprised of 1000 individuals. Two hundred are tested and four returned a positive result. Assuming 100% test sensitivity and specificity, what is the estimated prevalence of disease X in this population?

```
library(epiR); library(ggplot2); library(scales)
ncas <- 4; npop <- 200
tmp <- as.matrix(cbind(ncas, npop))
epi.conf(tmp, ctype = "prevalence", method = "exact", N = 1000, design = 1,
conf.level = 0.95) * 100
#> est lower upper
#> 1 2 0.5475566 5.041361
```

The estimated prevalence of disease X in this population is 2.0 (95% confidence interval [CI] 0.55 – 5.0) cases per 100 individuals at risk.

Another example. A study was conducted by Feychting, Osterlund, and Ahlbom (1998) to report the frequency of cancer among the blind. A total of 136 diagnoses of cancer were made from 22,050 person-years at risk. What was the incidence rate of cancer in this population?

```
ncas <- 136; ntar <- 22050
tmp <- as.matrix(cbind(ncas, ntar))
epi.conf(tmp, ctype = "inc.rate", method = "exact", N = 1000, design = 1,
conf.level = 0.95) * 1000
#> est lower upper
#> ncas 6.1678 5.174806 7.295817
```

The incidence rate of cancer in this population was 6.2 (95% CI 5.2 to 7.3) cases per 1000 person-years at risk.

Now lets say we want to compare the frequency of disease across several populations. An effective way to do this is to use a ranked error bar plot. With a ranked error bar plot the points represent the point estimate of the measure of disease frequency and the error bars indicate the 95% confidence interval around each estimate. The disease frequency estimates are then sorted from lowest to highest.

Generate some data. First we’ll generate a distribution of disease prevalence estimates. Let’s say it has a mode of 0.60 and we’re 80% certain that the prevalence is greater than 0.35. Use the `epi.betabuster`

function to generate parameters that can be used for a beta distribution to satisfy these constraints:

```
tmp <- epi.betabuster(mode = 0.60, conf = 0.80, greaterthan = TRUE, x = 0.35,
conf.level = 0.95, max.shape1 = 100, step = 0.001)
tmp$shape1; tmp$shape2
#> [1] 2.357
#> [1] 1.904667
```

Now take 100 draws from a beta distribution using the `shape1`

and `shape2`

values calculated above and plot them as a frequency histogram:

```
dprob <- rbeta(n = 25, shape1 = tmp$shape1, shape2 = tmp$shape2)
dat.df <- data.frame(dprob = dprob)
ggplot(data = dat.df, aes(x = dprob)) +
theme_bw() +
geom_histogram(binwidth = 0.01, colour = "gray", fill = "dark blue", size = 0.1) +
scale_x_continuous(limits = c(0,1), name = "Prevalence") +
scale_y_continuous(limits = c(0,10), name = "Number of draws")
#> Warning: Removed 2 rows containing missing values (geom_bar).
```

Generate a vector of population sizes using the uniform distribution. Calculate the number of diseased individuals in each population using `dprob`

(calculated above). Finally, calculate the prevalence of disease in each population and its 95% confidence interval using `epi.conf`

. The function `epi.conf`

provides several options for confidence interval calculation methods for prevalence. Here we’ll use the exact method:

```
dat.df$rname <- paste("Region ", 1:25, sep = "")
dat.df$npop <- round(runif(n = 25, min = 20, max = 1500), digits = 0)
dat.df$ncas <- round(dat.df$dprob * dat.df$npop, digits = 0)
tmp <- as.matrix(cbind(dat.df$ncas, dat.df$npop))
tmp <- epi.conf(tmp, ctype = "prevalence", method = "exact", N = 1000, design = 1,
conf.level = 0.95) * 100
dat.df <- cbind(dat.df, tmp)
head(dat.df)
#> dprob rname npop ncas est lower upper
#> 1 0.6589162 Region 1 812 535 65.88670 62.51113 69.14642
#> 2 0.3325450 Region 2 164 55 33.53659 26.36472 41.31582
#> 3 0.3057466 Region 3 447 137 30.64877 26.40333 35.15254
#> 4 0.5273257 Region 4 1413 745 52.72470 50.08277 55.35527
#> 5 0.8444275 Region 5 1253 1058 84.43735 82.30985 86.40179
#> 6 0.5486895 Region 6 84 46 54.76190 43.52135 65.65691
```

Sort the data in order of variable `est`

and assign a 1 to `n`

identifier as variable `rank`

:

Now create a ranked error bar plot. Because its useful to provide the region-area names on the horizontal axis we’ll rotate the horizontal axis labels by 90 degrees.

```
ggplot(data = dat.df, aes(x = rank, y = est)) +
theme_bw() +
geom_errorbar(aes(ymin = lower, ymax = upper), width = 0.1) +
geom_point() +
scale_x_continuous(limits = c(0,25), breaks = dat.df$rank, labels = dat.df$rname, name = "Region") +
scale_y_continuous(limits = c(0,100), name = "Cases per 100 individuals at risk") +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
```

Epidemic curve data are often presented in one of two formats:

One row for each individual identified as a case with an event date assigned to each.

One row for every event date with an integer representing the number of cases identified on that date.

Generate some data, with one row for every individual identified as a case:

```
n.males <- 100; n.females <- 50
odate <- seq(from = as.Date("2004-07-26"), to = as.Date("2004-12-13"), by = 1)
prob <- c(1:100, 41:1); prob <- prob / sum(prob)
modate <- sample(x = odate, size = n.males, replace = TRUE, p = prob)
fodate <- sample(x = odate, size = n.females, replace = TRUE)
dat.df <- data.frame(sex = c(rep("Male", n.males), rep("Female", n.females)),
odate = c(modate, fodate))
# Sort the data in order of odate:
dat.df <- dat.df[sort.list(dat.df$odate),]
```

Plot the epidemic curve using the `ggplot2`

and `scales`

packages:

```
ggplot(data = dat.df, aes(x = as.Date(odate))) +
theme_bw() +
geom_histogram(binwidth = 7, colour = "gray", fill = "dark blue", size = 0.1) +
scale_x_date(breaks = date_breaks("7 days"), labels = date_format("%d %b"),
name = "Date") +
scale_y_continuous(breaks = seq(from = 0, to = 20, by = 2), limits = c(0,20), name = "Number of cases") +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
```

Produce a separate epidemic curve for males and females using the `facet_grid`

option in `ggplot2`

:

```
ggplot(data = dat.df, aes(x = as.Date(odate))) +
theme_bw() +
geom_histogram(binwidth = 7, colour = "gray", fill = "dark blue", size = 0.1) +
scale_x_date(breaks = date_breaks("1 week"), labels = date_format("%d %b"),
name = "Date") +
scale_y_continuous(breaks = seq(from = 0, to = 20, by = 2), limits = c(0,20), name = "Number of cases") +
theme(axis.text.x = element_text(angle = 90, hjust = 1)) +
facet_grid( ~ sex)
```

Let’s say an event occurred on 31 October 2004. Mark this date on your epidemic curve using `geom_vline`

:

```
ggplot(data = dat.df, aes(x = as.Date(odate))) +
theme_bw() +
geom_histogram(binwidth = 7, colour = "gray", fill = "dark blue", size = 0.1) +
scale_x_date(breaks = date_breaks("1 week"), labels = date_format("%d %b"),
name = "Date") +
scale_y_continuous(breaks = seq(from = 0, to = 20, by = 2), limits = c(0,20), name = "Number of cases") +
theme(axis.text.x = element_text(angle = 90, hjust = 1)) +
facet_grid( ~ sex) +
geom_vline(aes(xintercept = as.numeric(as.Date("31/10/2004", format = "%d/%m/%Y"))),
linetype = "dashed")
```

Plot the total number of disease events by day, coloured according to sex:

```
ggplot(data = dat.df, aes(x = as.Date(odate), group = sex, fill = sex)) +
theme_bw() +
geom_histogram(binwidth = 7, colour = "gray", size = 0.1) +
scale_x_date(breaks = date_breaks("1 week"), labels = date_format("%d %b"),
name = "Date") +
scale_y_continuous(breaks = seq(from = 0, to = 20, by = 2), limits = c(0,20), name = "Number of cases") +
theme(axis.text.x = element_text(angle = 90, hjust = 1)) +
geom_vline(aes(xintercept = as.numeric(as.Date("31/10/2004", format = "%d/%m/%Y"))),
linetype = "dashed") +
scale_fill_manual(values = c("#d46a6a", "#738ca6"), name = "Sex") +
theme(legend.position = c(0.90, 0.80))
```

It can be difficult to appreciate differences in male and female disease counts as a function of date with the above plot format so dodge the data instead:

```
ggplot(data = dat.df, aes(x = as.Date(odate), group = sex, fill = sex)) +
theme_bw() +
geom_histogram(binwidth = 7, colour = "gray", size = 0.1, position = "dodge") +
scale_x_date(breaks = date_breaks("1 week"), labels = date_format("%d %b"),
name = "Date") +
scale_y_continuous(breaks = seq(from = 0, to = 20, by = 2), limits = c(0,20), name = "Number of cases") +
theme(axis.text.x = element_text(angle = 90, hjust = 1)) +
geom_vline(aes(xintercept = as.numeric(as.Date("31/10/2004", format = "%d/%m/%Y"))),
linetype = "dashed") +
scale_fill_manual(values = c("#d46a6a", "#738ca6"), name = "Sex") +
theme(legend.position = c(0.90, 0.80))
```

We now provide code to deal with the situation where the data are presented with one row for every case event date and an integer representing the number of cases identified on each date.

Simulate some data in this format. In the code below the variable `ncas`

represents the number of cases identified on a given date. The variable `dcontrol`

is a factor with two levels: `neg`

and `pos`

. Level `neg`

flags dates when no disease control measures were in place; level `pos`

flags dates when disease controls measures were in place.

```
odate <- seq(from = as.Date("1/1/00", format = "%d/%m/%y"),
to = as.Date("1/1/05", format = "%d/%m/%y"), by = "1 month")
ncas <- round(runif(n = length(odate), min = 0, max = 100), digits = 0)
dat.df <- data.frame(odate, ncas)
dat.df$dcontrol <- "neg"
dat.df$dcontrol[dat.df$odate >= as.Date("1/1/03", format = "%d/%m/%y") &
dat.df$odate <= as.Date("1/6/03", format = "%d/%m/%y")] <- "pos"
head(dat.df)
#> odate ncas dcontrol
#> 1 2000-01-01 0 neg
#> 2 2000-02-01 66 neg
#> 3 2000-03-01 84 neg
#> 4 2000-04-01 27 neg
#> 5 2000-05-01 17 neg
#> 6 2000-06-01 69 neg
```

Generate an epidemic curve. Note `weight = ncas`

in the aesthetics argument for `ggplot2`

:

```
ggplot() +
theme_bw() +
geom_histogram(dat.df, mapping = aes(x = odate, weight = ncas, fill = factor(dcontrol)), binwidth = 60, colour = "gray", size = 0.1) +
scale_x_date(breaks = date_breaks("6 months"), labels = date_format("%b %Y"),
name = "Date") +
scale_y_continuous(limits = c(0,200), name = "Number of cases") +
scale_fill_manual(values = c("#738ca6","#d46a6a")) +
guides(fill = "none") +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
```

Now we’ll add a line to the plot to show the cumulative number of cases detected as a function of calendar date. The coding here requires some thought. First question: What was the cumulative number of cases at the end of the follow-up period? Here we use the `cumsum`

(cumulative sum) function in base R:

```
cumsum(dat.df$ncas)
#> [1] 0 66 150 177 194 263 273 307 337 415 427 482 548 627 657
#> [16] 659 715 727 756 820 844 868 889 905 957 1032 1089 1144 1198 1254
#> [31] 1261 1264 1350 1357 1414 1472 1499 1586 1682 1697 1794 1850 1928 1969 1996
#> [46] 2048 2127 2171 2263 2279 2310 2328 2401 2420 2472 2477 2526 2590 2659 2684
#> [61] 2771
```

At the end of the follow-up period the cumulative number of cases was in the order of 3100 (exact numbers will vary because we’ve used a simulation approach to generate this data). What we need to do is to get our 0 to 3100 cumulative cases to ‘fit’ into the 0 to 200 vertical axis limits of the epidemic curve. A reasonable approach would be to: (1) divide cumulative case numbers by 10; (2) set 350 as the upper limit of the vertical axis; and (3) set `sec.axis = sec_axis(~ . * 10)`

to multiply the values that appear on the primary vertical axis by 10 for the labels that appear on the secondary vertical axis:

```
ggplot() +
theme_bw() +
geom_histogram(data = dat.df, mapping = aes(x = odate, weight = ncas, fill = factor(dcontrol)), binwidth = 60, colour = "gray", size = 0.1) +
geom_line(data = dat.df, mapping = aes(x = odate, y = cumsum(ncas) / 10)) +
scale_x_date(breaks = date_breaks("6 months"), labels = date_format("%b %Y"),
name = "Date") +
scale_y_continuous(limits = c(0,350), name = "Number of cases",
sec.axis = sec_axis(~ . * 10, name = "Cumulative number of cases")) +
scale_fill_manual(values = c("#738ca6","#d46a6a")) +
guides(fill = "none") +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
```

Two types of maps are often used when describing patterns of disease by place:

Choropleth maps. Choropleth mapping involves producing a summary statistic of the outcome of interest (e.g. count of disease events, prevalence, incidence) for each component area within a study region. A map is created by ‘filling’ (i.e. colouring) each component area with colour, providing an indication of the magnitude of the variable of interest and how it varies geographically.

Point maps.

**Choropleth maps**

For illustration we make a choropleth map of sudden infant death syndrome (SIDS) babies in North Carolina counties for 1974 using the `nc.sids`

data provided with the `spData`

package.

```
library(sf); library(spData); library(rgdal); library(plyr); library(RColorBrewer); library(spatstat)
ncsids.sf <- st_read(dsn = system.file("shapes/sids.shp", package = "spData")[1])
#> Reading layer `sids' from data source
#> `C:\Program Files\R\R-4.1.1\library\spData\shapes\sids.shp'
#> using driver `ESRI Shapefile'
#> Simple feature collection with 100 features and 22 fields
#> Geometry type: MULTIPOLYGON
#> Dimension: XY
#> Bounding box: xmin: -84.32385 ymin: 33.88199 xmax: -75.45698 ymax: 36.58965
#> CRS: NA
ncsids.sf <- ncsids.sf[,c("BIR74","SID74")]
head(ncsids.sf)
#> Simple feature collection with 6 features and 2 fields
#> Geometry type: MULTIPOLYGON
#> Dimension: XY
#> Bounding box: xmin: -81.74107 ymin: 36.07282 xmax: -75.77316 ymax: 36.58965
#> CRS: NA
#> BIR74 SID74 geometry
#> 1 1091 1 MULTIPOLYGON (((-81.47276 3...
#> 2 487 0 MULTIPOLYGON (((-81.23989 3...
#> 3 3188 5 MULTIPOLYGON (((-80.45634 3...
#> 4 508 1 MULTIPOLYGON (((-76.00897 3...
#> 5 1421 9 MULTIPOLYGON (((-77.21767 3...
#> 6 1452 7 MULTIPOLYGON (((-76.74506 3...
```

The `ncsids.sf`

simple features object lists for each county in the North Carolina USA the number SIDS deaths for 1974. Plot a choropleth map of the counties of the North Carolina showing SIDS counts for 1974:

```
ggplot() +
theme_bw() +
geom_sf(data = ncsids.sf, aes(fill = SID74), colour = "dark grey") +
scale_fill_gradientn(limits = c(0,60), colours = brewer.pal(n = 5, "Reds"), guide = "colourbar") +
scale_x_continuous(name = "Longitude") +
scale_y_continuous(name = "Latitude") +
labs(fill = "SIDS 1974")
```

**Point maps**

For this example we will used the `epi.incin`

data set included with `epiR`

. Between 1972 and 1980 an industrial waste incinerator operated at a site about 2 kilometres southwest of the town of Coppull in Lancashire, England. Addressing community concerns that there were greater than expected numbers of laryngeal cancer cases in close proximity to the incinerator Diggle (1990) conducted a study investigating risks for laryngeal cancer, using recorded cases of lung cancer as controls. The study area is 20 km x 20 km in size and includes location of residence of patients diagnosed with each cancer type from 1974 to 1983.

Load the `epi.incin`

data set and create negative and positive labels for each point location. We don’t have a boundary map for these data so we’ll use `spatstat`

to create a convex hull around the points and dilate the convex hull by 1000 metres as a proxy boundary. The point locations in this data are projected using the British National Grid coordinate reference system (EPSG code 27700). Create an observation window for the data as `coppull.ow`

and a `ppp`

object for plotting:

```
data(epi.incin); incin.df <- epi.incin
incin.df$status <- factor(incin.df$status, levels = c(0,1), labels = c("Neg", "Pos"))
names(incin.df)[3] <- "Status"
incin.sf <- st_as_sf(incin.df, coords = c("xcoord","ycoord"), remove = FALSE)
st_crs(incin.sf) <- 27700
coppull.ow <- convexhull.xy(x = incin.df[,1], y = incin.df[,2])
coppull.ow <- dilation(coppull.ow, r = 1000)
```

Create a simple features polygon object from `coppull.ow`

. First we convert `coppull.ow`

to a `SpatialPolygonsDataFrame`

object:

```
coords <- matrix(c(coppull.ow$bdry[[1]]$x, coppull.ow$bdry[[1]]$y), ncol = 2, byrow = FALSE)
pol <- Polygon(coords, hole = FALSE)
pol <- Polygons(list(pol),1)
pol <- SpatialPolygons(list(pol))
coppull.spdf <- SpatialPolygonsDataFrame(Sr = pol, data = data.frame(id = 1), match.ID = TRUE)
```

Convert the `SpatialPolygonsDataFrame`

to an `sf`

object and set the coordinate reference system:

The `mformat`

function is used to plot the axis labels in kilometres (instead of metres):

```
ggplot() +
theme_bw() +
geom_sf(data = incin.sf, aes(colour = Status, shape = Status)) +
geom_sf(data = coppull.sf, fill = "transparent", colour = "black") +
coord_sf(datum = st_crs(coppull.sf)) +
scale_colour_manual(values = c("grey","red")) +
scale_shape_manual(values = c(1,16)) +
scale_x_continuous(name = "Easting (km)", labels = mformat()) +
scale_y_continuous(name = "Northing (km)", labels = mformat()) +
theme(legend.position = c(0.10, 0.15))
```

Diggle, PJ. 1990. “A Point Process Modeling Approach to Raised Incidence of a Rare Phenomenon in the Vicinity of a Prespecified Point.” *Journal of the Royal Statistical Society Series A* 153: 349–62.

Disease Control, Centers for, and Prevention. 2006. *Principles of Epidemiology in Public Health Practice: An Introduction to Applied Epidemiology and Biostatistics*. Atlanta, Georgia: Centers for Disease Control; Prevention.

Feychting, M, B Osterlund, and A Ahlbom. 1998. “Reduced Cancer Incidence Among the Blind.” *Epidemiology* 9: 490–94.