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diff --git a/R/seqB.R b/R/seqB.R deleted file mode 100644 index 1dcf927..0000000 --- a/R/seqB.R +++ /dev/null @@ -1,129 +0,0 @@ -#' 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. -#' -#' 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. -#' -#' 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. -#' -#' @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 -#' # Weekly data. -#' NT <- c(1, 4, 10, 5, 3, 4, 19, 3, 3, 14, 4) -#' -#' ## Obtain R0 when the serial distribution has a mean of five days. -#' res1 <- seqB(NT, mu = 5 / 7) -#' res1$Rhat -#' -#' ## Obtain R0 when the serial distribution has a mean of three days. -#' res2 <- seqB(NT, mu = 3 / 7) -#' res2$Rhat -#' -#' # Compute posterior mode instead of posterior mean and plot. -#' -#' Rpost <- res1$posterior -#' loc <- which(Rpost$pmf == max(Rpost$pmf)) -#' Rpost$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", "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 - } - - 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 - - if (maxll > 700) - const <- maxll - 700 - - loglik <- loglik - const - posterior <- exp(loglik) * prior - posterior <- posterior / sum(posterior) - prior <- posterior - } - - Rhat <- sum(R * posterior) - - return(list(Rhat = Rhat, - posterior = list(supp = R, pmf = posterior), - group = group)) - } -} |