epiR (version 2.0.75)

epi.edr: Estimated dissemination ratio

Description

Computes estimated dissemination ratios on the basis of a vector of count data (usually incident disease cases identified on each day of an epidemic).

Usage

epi.edr(dat, n = 4, conf.level = 0.95, nsim = 99, na.zero = TRUE)

Value

Returns the point estimate of the EDR and the lower and upper bounds of the confidence interval of the EDR.

Arguments

dat

a numeric vector listing the number of incident cases for each day of an epidemic.

n

scalar, defining the number of days to be used when computing the estimated dissemination ratio.

conf.level

magnitude of the returned confidence interval. Must be a single number between 0 and 1.

nsim

scalar, defining the number of simulations to be used for the confidence interval calculations.

na.zero

logical, replace NaN or Inf values with zeros?

Details

In infectious disease outbreaks the n-day estimated dissemination ratio (EDR) at day i equals the total number of incident disease cases between day i and day [i - (n - 1)] (inclusive) divided by the total number of incident disease cases between day (i - n) and day (i - 2n) + 1 (inclusive). EDR values are often calculated for each day of an outbreak and presented as a time series analysis. If the EDR is consistently less than one, the epidemic is said to be `under control'.

A simulation approach is used to calculate confidence intervals for each daily EDR estimate. The numerator and denominator of the EDR estimate for each day is taken in turn and a random number drawn from a Poisson distribution, using the calculated numerator and denominator value as the mean. EDR is then calculated for these simulated values and the process repeated nsim times. Confidence intervals are then derived from the vector of simulated values for each day.

References

Miller W (1976). A state-transition model of epidemic foot-and-mouth disease. In: Proceedings of an International Symposium: New Techniques in Veterinary Epidemiology and Economics, University of Reading, Reading, pp. 56 - 72.

Morris R, Sanson R, Stern M, Stevenson M, Wilesmith J (2002). Decision-support tools for foot-and-mouth disease control. Revue Scientifique et Technique de l'Office International des Epizooties 21, 557 - 567.

Perez-Reche FJ, Taylor N, McGuigan C, Conaglen P, Forbes K, Strachan N, Honhold N (2021) Estimated Dissemination Ratio --- A practical alternative to the reproduction number for infectious diseases. Frontiers in Public Health 9. DOI: 10.3389/fpubh.2021.675065.

Examples

## EXAMPLE 1 Foot and mouth disease, Cumbria 2001:

## Counts of incident FMD positive farms by date:
edate <- seq(from = as.Date("2001-02-28", format = "%Y-%m-%d"), 
   to = as.Date("2001-06-15", format = "%Y-%m-%d"), by = 1)
ncas <- c(1,2,0,0,1,1,0,0,4,2,3,3,5,2,8,2,5,0,5,7,15,13,6,7,11,8,7,11,
   6,5,10,7,8,8,7,5,6,3,3,3,3,4,1,4,6,2,1,4,3,3,1,1,1,2,2,2,2,0,4,1,1,
   0,0,2,1,2,1,0,1,2,2,4,0,1,0,1,0,0,0,1,0,3,1,1,3,0,0,1,1,2,0,0,1,1,1,
   3,3,1,1,1,0,0,0,1,1,1,1,1)
dat.df01 <- data.frame(edate = edate, ncas = ncas)


## Seven day EDR:
edr <- epi.edr(dat.df01$ncas, n = 7, conf.level = 0.95, nsim = 99, 
   na.zero = FALSE)

dat.df01$edr.500 <- edr$est
dat.df01$edr.025 <- edr$lower
dat.df01$edr.975 <- edr$upper

## log2 transformed EDRs:
dat.df01$ledr.500 <- log(edr$est, base = 2)
dat.df01$ledr.025 <- log(edr$lower, base = 2)
dat.df01$ledr.975 <- log(edr$upper, base = 2)

## You may want to smooth the EDRs:
dat.df01$sedr.500 <- lowess(dat.df01$edate, dat.df01$est, f = 0.15)$y
dat.df01$sedr.025 <- lowess(dat.df01$edate, dat.df01$lower, f = 0.15)$y
dat.df01$sedr.975 <- lowess(dat.df01$edate, dat.df01$upper, f = 0.15)$y

if (FALSE) {
library(ggplot2); library(scales)

## Frequency histogram of the number of incident FMD positive farms as a
## function of date:
ggplot() +
  theme_bw() +
  geom_histogram(data = dat.df01, aes(x = edate, weight = ncas), 
     binwidth = 1, fill = "#008080", alpha = 0.45) +
  scale_x_date(breaks = date_breaks("7 days"), name = "Date") +
  scale_y_continuous(limits = c(0,15), 
     name = "Number of events") + 
  theme(axis.text.x = element_text(angle = 90, hjust = 1))


## EDR line plot (and its 95% confidence interval) as a function of 
## date:
ybreaks <- -5:5
ylabels <- 2^(-5:5)


## Drop EDR estimates outside of the 0.03125 and 32 range since distracting on
## plot:
dat.df01$ledr.025[dat.df01$ledr.025^2 < 0.03125 | 
   dat.df01$ledr.025^2 > 32] <- NA
dat.df01$ledr.975[dat.df01$ledr.975^2 < 0.03125 | 
   dat.df01$ledr.975^2 > 32] <- NA

ggplot() +
  theme_bw() +
  geom_line(data = dat.df01, aes(x = edate, y = ledr.500), 
     col = "black", linewidth = 1) +
  geom_line(data = dat.df01, aes(x = edate, y = ledr.025), 
     col = "black", linetype = "dashed", linewidth = 0.5) +
  geom_line(data = dat.df01, aes(x = edate, y = ledr.975), 
     col = "black", linetype = "dashed", linewidth = 0.5) +
  scale_x_date(breaks = date_breaks("7 days"), name = "Date") +
  scale_y_continuous(name = "Estimated dissemination ratio (EDR)",
     breaks = ybreaks, labels = ylabels, limits = range(ybreaks)) + 
  geom_hline(yintercept = 0, col = "red", linetype = "dashed") +
  theme(axis.text.x = element_text(angle = 90, hjust = 1))  


## EDR line plot (and its 95% confidence interval) as a function of 
## date superimposed on the epidemic curve. Set the upper limit for the 
## vertical axis of the histogram as ymax. The vertical position of 
## the EDR curve will be shifted by ymax / 2 (i.e., half way up the plot):
ymax <- 20; shift <- ymax / 2
ybreaks <- -5:5 + shift
ylabels <- 2^(-5:5)

ggplot() +
  theme_bw() +
  geom_histogram(data = dat.df01, aes(x = edate, weight = ncas), 
     binwidth = 1, fill = "#008080", alpha = 0.45) +
  geom_line(data = dat.df01, aes(x = edate, y = ledr.500 + shift), 
     col = "black", linewidth = 1) +
  geom_line(data = dat.df01, aes(x = edate, y = ledr.025 + shift), 
     col = "black", linetype = "dashed", linewidth = 0.5) +
  geom_line(data = dat.df01, aes(x = edate, y = ledr.975 + shift), 
      col = "black", linetype = "dashed", linewidth = 0.5) +
  scale_x_date(breaks = date_breaks("7 days"), name = "Date") +
  scale_y_continuous(limits = c(0,ymax), 
     name= "Estimated dissemination ratio (EDR)",
     sec.axis = sec_axis(trans = ~ ., name = "Number of events"),
     breaks = ybreaks, labels = ylabels) + 
  geom_hline(yintercept = shift, col = "red", linetype = "dashed") +
  theme(axis.text.x = element_text(angle = 90, hjust = 1), 
     panel.grid.minor = element_blank())
 }