Calculates the cumulative log likelihood ratio of failure for a series of procedures which can be used to create CUSUM charts.

## Usage

cusum_loglike(xi, p0, p1, by = NULL, alpha = 0.05, beta = 0.05)

## 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 true.

beta

A double. The Type II Error rate. Probability of failing to reject null hypothesis when it is false.

## 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))
)

# Overall event rate
p0 <- sum(df$xi) / nrow(df) # Create CUSUM plot cusum_loglike( xi = df$xi,
p0 = p0,
p1 = p0 * 1.5,
by = df\$by
) |>
ggplot(aes(y = cusum, x = i)) +
geom_step() +
geom_hline(aes(yintercept = h0), linetype = 2) +
geom_hline(aes(yintercept = h1), linetype = 2) +
ylab("Cumulative Log-likelihood Ratio") +
xlab("Case Number") +
facet_wrap(~ by) +
theme_bw()