Cumulative Sum of Observed Minus Expected Outcome

Calculates the cumulative observed-minus-expected failure for a series of procedures which can be used to create CUSUM charts.

Usage

cusum_ome(xi, p0, by = NULL)

Arguments

xi

An integer. The dichotomous outcome variable (1 = Failure, 0 = Success) for the i-th procedure.

p0

A double. The acceptable event rate.

by

A factor. Optional variable to stratify procedures by.

Value

An object of class data.frame.

References

Rogers, C. A., Reeves, B. C., Caputo, M., Ganesh, J. S., Bonser, R. S., & Angelini, G. D. (2004). Control chart methods for monitoring cardiac surgical performance and their interpretation. The Journal of Thoracic and Cardiovascular Surgery, 128(6), 811-819.

Examples

library(purrr)
library(ggplot2)

# Data
df <- data.frame(
  xi = simplify(
    map(
      c(.1,.08,.05,.1,.13,.14,.14,.09,.25),
      ~ rbinom(50,1,.x))),
   p0 = simplify(
    map(
      c(.1,.1,.1,.1,.1,.1,.1,.15,.2),
      ~ rnorm(50,.x,.03))),
   by = rep(
    factor(paste('Subject', c('A','B','C'))),
    times = c(150,150,150))
 )

# Create CUSUM plot
cusum_ome(
 xi = df$xi,
 p0 = df$p0,
 by = df$by
) |>
ggplot(aes(x = i, y = cusum)) +
geom_hline(yintercept = 0, linetype = 6, linewidth = 0.5) +
  geom_step() +
  ylab("Cumulative Observed Minus Expected Failures") +
  xlab("Case Number") +
  facet_wrap(~ by) +
  theme_bw()