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 (Centers for 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); library(lubridate)
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
#> ncas 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 used 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
```

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)) +
geom_histogram(binwidth = 0.01, colour = "gray", 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 0.5975903 Region 1 851 509 59.81199 56.42990 63.12588
#> 2 0.4315116 Region 2 1466 633 43.17872 40.62490 45.75992
#> 3 0.9001671 Region 3 1250 1125 90.00000 88.20166 91.60749
#> 4 0.8289258 Region 4 1282 1063 82.91732 80.74330 84.93918
#> 5 0.8805447 Region 5 1124 990 88.07829 86.03913 89.91558
#> 6 0.4054125 Region 6 1171 475 40.56362 37.73532 43.43944
```

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)) +
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 = "Prevalence (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),]
```

We’d like to have the flexibility to plot counts of cases by calendar week or by epidemiological (‘epi’) week. We assign to each date the corresponding epidemiology week number using the `epiweek`

function from the `lubridate`

package.

Plot the epidemic curve using the `ggplot2`

and `scales`

packages:

```
ggplot(data = dat.df, aes(x = as.Date(odate))) +
geom_histogram(binwidth = 7, colour = "gray", 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))
```

The same plot but this time showing epidemiology week on the horizontal axis:

```
ggplot(data = dat.df, aes(x = eweek)) +
geom_histogram(binwidth = 1, colour = "gray", size = 0.1) +
scale_x_continuous(breaks = seq(from = 30, to = 50, by = 1), name = "Epidemiology week") +
scale_y_continuous(breaks = seq(from = 0, to = 20, by = 2), limits = c(0,20), name = "Number of cases")
```

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))) +
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)) +
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))) +
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)) +
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)) +
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 we dodge the data instead.

```
ggplot(data = dat.df, aes(x = as.Date(odate), group = sex, fill = sex)) +
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 98 neg
#> 2 2000-02-01 61 neg
#> 3 2000-03-01 61 neg
#> 4 2000-04-01 1 neg
#> 5 2000-05-01 30 neg
#> 6 2000-06-01 86 neg
```

Generate an epidemic curve. Note `weight = ncas`

in the aesthetics argument for `ggplot2`

:

```
ggplot(dat.df, aes(x = odate, weight = ncas, fill = factor(dcontrol))) +
geom_histogram(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("#2f4f4f", "red")) +
guides(fill = FALSE) +
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(spData); library(rgeos); library(rgdal); library(plyr); library(RColorBrewer); library(spatstat)
ncsids.shp <- readOGR(system.file("shapes/sids.shp", package = "spData")[1])
#> OGR data source with driver: ESRI Shapefile
#> Source: "C:\Program Files\R\R-4.0.5\library\spData\shapes\sids.shp", layer: "sids"
#> with 100 features
#> It has 22 fields
ncsids.shp@data <- ncsids.shp@data[,c("BIR74","SID74")]
head(ncsids.shp@data)
#> BIR74 SID74
#> 0 1091 1
#> 1 487 0
#> 2 3188 5
#> 3 508 1
#> 4 1421 9
#> 5 1452 7
```

The `ncsids.shp`

spatialPolygonsDataframe lists for each county in the North Carolina USA the number SIDS deaths for 1974.

Prepare the spatialPolygonsDataframe by creating a 1 to *n* identifier called `id`

. We then `fortify`

the spatialPolygonsDataframe to allow it to be used with `ggplot2`

. Finally, join the attribute data from spatialPolygonsDataframe `ncsids.shp`

to the fortified `ncsids.df`

, using variable `id`

as the key:

```
ncsids.shp$id <- 1:nrow(ncsids.shp@data)
ncsids.df <- fortify(ncsids.shp, region = "id")
ncsids.df <- join(x = ncsids.df, y = ncsids.shp@data, by = "id")
```

Choropleth map of the counties of the North Carolina showing SIDS counts for 1974:

```
ggplot(data = ncsids.df) +
theme_bw() +
geom_polygon(aes(x = long, y = lat, group = group, fill = SID74)) +
geom_path(aes(x = long, y = lat, group = group), colour = "grey", size = 0.25) +
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") +
coord_map()
```

**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. Create an observation window for the data as `dat.w`

and a `ppp`

object for plotting:

```
data(epi.incin); dat.df <- epi.incin
dat.df$status <- factor(dat.df$status, levels = c(0,1), labels = c("Neg", "Pos"))
names(dat.df)[3] <- "Status"
dat.w <- convexhull.xy(x = dat.df[,1], y = dat.df[,2])
dat.w <- dilation(dat.w, r = 1000)
dat.ppp <- ppp(x = dat.df[,1], y = dat.df[,2], marks = factor(dat.df[,3]), window = dat.w)
```

Create a SpatialPolygonsDataFrame from `dat.w`

:

```
coords <- matrix(c(dat.w$bdry[[1]]$x, dat.w$bdry[[1]]$y), ncol = 2, byrow = FALSE)
pol <- Polygon(coords, hole = FALSE)
pol <- Polygons(list(pol),1)
pol <- SpatialPolygons(list(pol))
pol.spdf <- SpatialPolygonsDataFrame(Sr = pol, data = data.frame(id = 1), match.ID = TRUE)
pol.map <- fortify(pol.spdf)
#> Regions defined for each Polygons
```

Plot the data as a point map:

```
ggplot() +
geom_point(data = dat.df, aes(x = xcoord, y = ycoord, colour = Status, shape = Status)) +
geom_polygon(data = pol.map, aes(x = long, y = lat, group = group), col = "black",
fill = "transparent") +
scale_colour_manual(values = c("blue", "red")) +
scale_shape_manual(values = c(1,16)) +
labs(x = "Easting (m)", y = "Northing (m)", fill = "Status") +
coord_equal() +
theme_bw()
```

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

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.

Feychting, M, B Osterlund, and A Ahlbom. 1998. “Reduced cancer incidence among the blind.” *Epidemiology* 9: 490–94.