#' seqB method
#'
-#' This function implements a sequential Bayesian estimation method of R0 due to Bettencourt and Riberio (PloS One, 2008).
-#' See details for important implementation notes.
+#' This function implements a sequential Bayesian estimation method of R0 due to
+#' Bettencourt and Riberio (PloS One, 2008). See details for important
+#' implementation notes.
#'
-#' The method sets a uniform prior distribution on R0 with possible values between zero and \code{kappa}, discretized to a fine grid.
-#' The distribution of R0 is then updated sequentially, with one update for each new case count observation.
-#' The final estimate of R0 is \code{Rhat}, the mean of the (last) posterior distribution.
-#' The prior distribution is the initial belief of the distribution of R0; which in this implementation is the uninformative uniform
-#' distribution with values between zero and \code{kappa}. Users can change the value of /code{kappa} only (i.e., the prior distribution
-#' cannot be changed from the uniform). As more case counts are observed, the influence of the prior distribution should lessen on
-#' the final estimate \code{Rhat}.
+#' The method sets a uniform prior distribution on R0 with possible values
+#' between zero and \code{kappa}, discretized to a fine grid. The distribution
+#' of R0 is then updated sequentially, with one update for each new case count
+#' observation. The final estimate of R0 is \code{Rhat}, the mean of the (last)
+#' posterior distribution. The prior distribution is the initial belief of the
+#' distribution of R0, which is the uninformative uniform distribution with
+#' values between zero and \code{kappa}. Users can change the value of
+#' \code{kappa} only (i.e., the prior distribution cannot be changed from the
+#' uniform). As more case counts are observed, the influence of the prior
+#' distribution should lessen on the final estimate \code{Rhat}.
#'
-#' This method is based on an approximation of the SIR model, which is most valid at the beginning of an epidemic. The method assumes
-#' that the mean of the serial distribution (sometimes called the serial interval) is known. The final estimate can be quite sensitive
-#' to this value, so sensitivity testing is strongly recommended. Users should be careful about units of time (e.g., are counts observed
-#' daily or weekly?) when implementing.
+#' This method is based on an approximation of the SIR model, which is most
+#' valid at the beginning of an epidemic. The method assumes that the mean of
+#' the serial distribution (sometimes called the serial interval) is known. The
+#' final estimate can be quite sensitive to this value, so sensitivity testing
+#' is strongly recommended. Users should be careful about units of time (e.g.,
+#' are counts observed daily or weekly?) when implementing.
#'
-#' Our code has been modified to provide an estimate even if case counts equal to zero are present in some time intervals. This is done
-#' by grouping the counts over such periods of time. Without grouping, and in the presence of zero counts, no estimate can be provided.
+#' Our code has been modified to provide an estimate even if case counts equal
+#' to zero are present in some time intervals. This is done by grouping the
+#' counts over such periods of time. Without grouping, and in the presence of
+#' zero counts, no estimate can be provided.
#'
#' @param NT Vector of case counts.
-#' @param mu Mean of the serial distribution. This needs to match case counts in time units. For example, if case counts
-#' are weekly and the serial distribution has a mean of seven days, then \code{mu} should be set to one. If case
-#' counts are daily and the serial distribution has a mean of seven days, then \code{mu} should be set to seven.
-#' @param kappa Largest possible value of uniform prior (defaults to 20). This describes the prior belief on ranges of R0,
-#' and should be set to a higher value if R0 is believed to be larger.
+#' @param mu Mean of the serial distribution. This needs to match case counts in
+#' time units. For example, if case counts are weekly and the serial
+#' distribution has a mean of seven days, then \code{mu} should be set
+#' to one. If case counts are daily and the serial distribution has a
+#' mean of seven days, then \code{mu} should be set to seven.
+#' @param kappa Largest possible value of uniform prior (defaults to 20). This
+#' describes the prior belief on ranges of R0, and should be set to
+#' a higher value if R0 is believed to be larger.
#'
-#' @return \code{secB} returns a list containing the following components: \code{Rhat} is the estimate of R0 (the posterior mean),
-#' \code{posterior} is the posterior distribution of R0 from which alternate estimates can be obtained (see examples),
-#' and \code{group} is an indicator variable (if \code{group=TRUE}, zero values of NT were input and grouping was done
-#' to obtain \code{Rhat}). The variable \code{posterior} is returned as a list made up of \code{supp} (the support of
-#' the distribution) and \code{pmf} (the probability mass function).
+#' @return \code{seqB} returns a list containing the following components:
+#' \code{Rhat} is the estimate of R0 (the posterior mean),
+#' \code{posterior} is the posterior distribution of R0 from which
+#' alternate estimates can be obtained (see examples), and \code{group}
+#' is an indicator variable (if \code{group == TRUE}, zero values of NT
+#' were input and grouping was done to obtain \code{Rhat}). The variable
+#' \code{posterior} is returned as a list made up of \code{supp} (the
+#' support of the distribution) and \code{pmf} (the probability mass
+#' function).
#'
#' @examples
-#' ## ===================================================== ##
-#' ## Illustrate on weekly data ##
-#' ## ===================================================== ##
-#'
+#' # Weekly data.
#' NT <- c(1, 4, 10, 5, 3, 4, 19, 3, 3, 14, 4)
-#' ## obtain Rhat when serial distribution has mean of five days
-#' res1 <- seqB(NT=NT, mu=5/7)
+#'
+#' ## Obtain R0 when the serial distribution has a mean of five days.
+#' res1 <- seqB(NT, mu = 5 / 7)
#' res1$Rhat
-#' ## obtain Rhat when serial distribution has mean of three days
-#' res2 <- seqB(NT=NT, mu=3/7)
+#'
+#' ## Obtain R0 when the serial distribution has a mean of three days.
+#' res2 <- seqB(NT, mu = 3 / 7)
#' res2$Rhat
#'
-#' ## ============================================================= ##
-#' ## Compute posterior mode instead of posterior mean and plot ##
-#' ## ============================================================= ##
+#' # Compute posterior mode instead of posterior mean and plot.
#'
-#' Rpost <- res1$posterior
+#' Rpost <- res1$posterior
#' loc <- which(Rpost$pmf == max(Rpost$pmf))
-#' Rpost$supp[loc] # posterior mode
-#' res1$Rhat # compare with posterior mean
+#' Rpost$supp[loc] # Posterior mode.
+#' res1$Rhat # Compare with the posterior mean.
#'
-#' par(mfrow=c(2, 1), mar=c(2, 2, 1, 1))
-#' plot(Rpost$supp, Rpost$pmf, col="black", type="l", xlab="", ylab="")
-#' abline(h=1/(20/0.01+1), col="red")
-#' abline(v=res1$Rhat, col="blue")
-#' abline(v=Rpost$supp[loc], col="purple")
-#' legend("topright", legend=c("prior", "posterior", "posterior mean (Rhat)", "posterior mode"), col=c("red", "black", "blue", "purple"), lty=1)
-#' plot(Rpost$supp, Rpost$pmf, col="black", type="l", xlim=c(0.5, 1.5), xlab="", ylab="")
-#' abline(h=1/(20/0.01+1), col="red")
-#' abline(v=res1$Rhat, col="blue")
-#' abline(v=Rpost$supp[loc], col="purple")
-#' legend("topright", legend=c("prior", "posterior", "posterior mean (Rhat)", "posterior mode"), col=c("red", "black", "blue", "purple"), lty=1)
+#' par(mfrow = c(2, 1), mar = c(2, 2, 1, 1))
#'
-#' ## ========================================================= ##
-#' ## Compute Rhat using only the first five weeks of data ##
-#' ## ========================================================= ##
-#'
-#' res3 <- seqB(NT=NT[1:5], mu=5/7) # serial distribution has mean of five days
-#' res3$Rhat
+#' plot(Rpost$supp, Rpost$pmf, col = "black", type = "l", xlab = "", ylab = "")
+#' abline(h = 1 / (20 / 0.01 + 1), col = "red")
+#' abline(v = res1$Rhat, col = "blue")
+#' abline(v = Rpost$supp[loc], col = "purple")
+#' legend("topright",
+#' legend = c("Prior", "Posterior", "Posterior mean", "Posterior mode"),
+#' col = c("red", "black", "blue", "purple"), lty = 1)
#'
#' @export
-seqB <- function(NT, mu, kappa=20) {
- if (length(NT) < 2)
- print("Warning: length of NT should be at least two.")
- else {
- if (min(NT) > 0) {
- times <- 1:length(NT)
- tau <- diff(times)
- }
- group <- FALSE
- if (min(NT) == 0) {
- times <- which(NT > 0)
- NT <- NT[times]
- tau <- diff(times)
- group <- TRUE
- }
+seqB <- function(NT, mu, kappa = 20) {
+ if (length(NT) < 2)
+ print("Warning: length of NT should be at least two.")
+ else {
+ if (min(NT) > 0) {
+ times <- 1:length(NT)
+ tau <- diff(times)
+ }
+ group <- FALSE
+ if (min(NT) == 0) {
+ times <- which(NT > 0)
+ NT <- NT[times]
+ tau <- diff(times)
+ group <- TRUE
+ }
- R <- seq(0, kappa, 0.01)
- prior0 <- rep(1, kappa / 0.01 + 1)
- prior0 <- prior0 / sum(prior0)
- k <- length(NT) - 1
- R0.post <- matrix(0, nrow=k, ncol=length(R))
- prior <- prior0
- posterior <- seq(0, length(prior0))
- gamma <- 1 / mu
+ R <- seq(0, kappa, 0.01)
+ prior0 <- rep(1, kappa / 0.01 + 1)
+ prior0 <- prior0 / sum(prior0)
+ k <- length(NT) - 1
+ R0.post <- matrix(0, nrow = k, ncol = length(R))
+ prior <- prior0
+ posterior <- seq(0, length(prior0))
+ gamma <- 1 / mu
- for (i in 1:k) {
- mm1 <- NT[i]
- mm2 <- NT[i+1]
- lambda <- tau[i] * gamma * (R - 1)
- lambda <- log(mm1) + lambda
- loglik <- mm2 * lambda - exp(lambda)
- maxll <- max(loglik)
- const <- 0
+ for (i in 1:k) {
+ mm1 <- NT[i]
+ mm2 <- NT[i + 1]
+ lambda <- tau[i] * gamma * (R - 1)
+ lambda <- log(mm1) + lambda
+ loglik <- mm2 * lambda - exp(lambda)
+ maxll <- max(loglik)
+ const <- 0
- if (maxll > 700)
- const <- maxll - 700
+ if (maxll > 700)
+ const <- maxll - 700
- loglik <- loglik-const
- posterior <- exp(loglik) * prior
- posterior <- posterior / sum(posterior)
- prior <- posterior
- }
+ loglik <- loglik - const
+ posterior <- exp(loglik) * prior
+ posterior <- posterior / sum(posterior)
+ prior <- posterior
+ }
- Rhat <- sum(R * posterior)
+ Rhat <- sum(R * posterior)
- return(list(Rhat=Rhat, posterior=list(supp=R, pmf=posterior), group=group))
- }
+ return(list(Rhat = Rhat,
+ posterior = list(supp = R, pmf = posterior),
+ group = group))
+ }
}
git.nmode.ca / Rnaught / blobdiff
