Faster alternative to stats:binom.test

[adamkucharski]

We're currently using stats::binom.test to generate uncertainty in estimates (i.e. 95% CI using Clopper-Pearson method). For most use cases the slowdown will be limited, but this could be made much faster for longer time series estimation (e.g. cfr_time_varying()).

For example, we could switch to Wilson method:

binom_wilson <- function(x, n, conf.level = 0.95) {
  p_hat <- x / n
  z <- qnorm(1 - (1 - conf.level) / 2)
  denom <- 1 + z^2 / n
  center <- (p_hat + z^2 / (2 * n)) / denom
  half_width <- z * sqrt((p_hat * (1 - p_hat) + z^2 / (4 * n)) / n) / denom
  lower <- center - half_width
  upper <- center + half_width
  
  # Ensure boundaries within [0,1]
  lower <- max(0, lower)
  upper <- min(1, upper)
  
  list(estimate = p_hat, conf.int = c(lower, upper))
}

# Example usage
binom_wilson(50, 100)

[sbfnk]

Just noting that this and several other methods are available in the binom R package.