Rename ID and IDEA

[Rnaught] / R / idea.R

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+#' IDEA method
+#'
+#' This function implements a least squares estimation method of R0 due to
+#' Fisman et al. (PloS One, 2013). See details for implementation notes.
+#'
+#' This method is closely related to that implemented in \code{ID}. The method
+#' is based on an incidence decay model. The estimate of R0 is the value which
+#' minimizes the sum of squares between observed case counts and cases counts
+#' expected under the model.
+#'
+#' 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.
+#'
+#' @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.
+#'
+#' @return \code{IDEA} returns a single value, the estimate of R0.
+#'
+#' @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.
+#' IDEA(NT, mu = 5 / 7)
+#'
+#' # Obtain R0 when the serial distribution has a mean of three days.
+#' IDEA(NT, mu = 3 / 7)
+#'
+#' @export
+IDEA <- function(NT, mu) {
+  if (length(NT) < 2)
+    print("Warning: length of NT should be at least two.")
+  else {
+    NT <- as.numeric(NT)
+    TT <- length(NT)
+    s <- (1:TT) / mu
+
+    y1 <- log(NT) / s
+    y2 <- s^2
+    y3 <- log(NT)
+
+    IDEA1 <- sum(y2) * sum(y1) - sum(s) * sum(y3)
+    IDEA2 <- TT * sum(y2) - sum(s)^2
+    IDEA <- exp(IDEA1 / IDEA2)
+
+    return(IDEA)
+  }
+}