cusum_failure | R Documentation |
Calculates the cumulative sum of failures for a series of procedures which can be used to create CUSUM charts.
cusum_failure(xi, p0, p1, by = NULL, alpha = 0.05, beta = 0.05)
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. |
An object of class data.frame
.
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.
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()
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