Calculates the cumulative sum of failures for a series of procedures which can be used to create CUSUM charts.
Arguments
- xi
An integer. The dichotomous outcome variable (1 = Failure, 0 = Success) for the i-th procedure.
- p0
A double. The acceptable event rate.
- p1
A double. The unacceptable event rate.
- by
A factor. Optional variable to stratify procedures by.
- alpha
A double. The Type I Error rate. Probability of rejecting the null hypothesis when `p0` is the true rate.
- beta
A double. The Type II Error rate. Probability of failing to reject null hypothesis when it is false.
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))
)
# Overall event rate
p0 <- sum(df$xi) / nrow(df)
# Create CUSUM plot
cusum_failure(
xi = df$xi,
p0 = p0,
p1 = p0 * 1.5,
by = df$by
) |>
ggplot(aes(y = cusum, x = i)) +
geom_step() +
geom_line(mapping = aes(y = l0), linetype = 2) +
geom_line(mapping = aes(y = l1), linetype = 2) +
ylab("Cumulative Failures") +
xlab("Case Number") +
facet_wrap(~ by) +
theme_bw()
