Cumulative Sum of Log-Likelihood Ratio

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()