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#' Excess counts in an interval
#'
#' Helper function to compute excess deaths statistics for a
#'
#' @param start First day of interval
#' @param end Last day of interval
#' @param obs Observed counts
#' @param mu Expected counts
#' @param cov Covariance matrix for percent change
#' @param pop Population size
#' @param frequency Observations per year
#' @param fhat Estimated percent increase
#' @param X Design matrix used to estimate fhat
#' @param betacov Covariance matrix for parameter estimates used to estimate fhat
#'
#' @importFrom stats ARMAacf
#'
#'
excess_stats <- function(start, end, obs, mu, cov, pop, frequency,
fhat = NULL, X = NULL, betacov = NULL){
mu <- matrix(mu, nrow = 1)
observed <- sum(obs)
expected <- sum(mu)
excess <- observed - expected
## cov is the variance-covariance of the percent increase (obs - exp) / exp
sd <- sqrt(mu %*% cov %*% t(mu))
res <- data.frame(
start = start,
end = end,
obs_death_rate = observed / sum(pop) * frequency * 1000,
exp_death_rate = expected / sum(pop) * frequency * 1000,
sd_death_rate = sd / sum(pop) * frequency * 1000,
observed = observed,
expected = expected,
excess = excess,
sd = sd)
if(!is.null(fhat)){
res$fitted <- mu %*% fhat
res$se <- sqrt(mu %*% X %*% betacov %*% t(X) %*% t(mu))
}
return(res)
}
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