eocusum_scores: Compute CUSUM scores based on E-O

In vlad: Variable Life Adjusted Display and Other Risk-Adjusted Quality Control Charts

Description

Compute CUSUM scores based on E-O.

Usage

eocusum_scores(z, k1, k2, reset = FALSE, h1 = NULL, h2 = NULL)

Arguments

z	NumericVector. E-O values.
k1	Double. Reference value k for detecting improvement can be determined from function optimal_k.
k2	Double. Reference value k for detecting deteroration can be determined from function optimal_k.
reset	Logical. If FALSE CUSUM statistic is not reset. If TRUE CUSUM statistic is reset to 0 after a signal is issued.
h1	Double. Upper control limit of the CUSUM chart.
h2	Double. Lower control limit of the CUSUM chart.

Value

Returns a list with two components for the CUSUM scores.

Author(s)

Philipp Wittenberg

References

Wittenberg P, Gan FF, Knoth S (2018). A simple signaling rule for variable life-adjusted display derived from an equivalent risk-adjusted CUSUM chart. Statistics in Medicine, 37(16), pp 2455–2473.

Examples

## Not run: 
library("dplyr")
library("tidyr")
library(ggplot2)
data("cardiacsurgery", package = "spcadjust")

## preprocess data to 30 day mortality and subset phase I (In-control) of surgeons 2
SALL <- cardiacsurgery %>% rename(s = Parsonnet) %>%
  mutate(y = ifelse(status == 1 & time <= 30, 1, 0),
         phase = factor(ifelse(date < 2*365, "I", "II")))

## subset phase I (In-control)
SI <- subset(SALL, phase == "I")

## estimate coefficients from logit model
GLM <- glm(y ~ s, data = SI, family = "binomial")

## set up patient mix
pi1 <- predict(GLM, type = "response", newdata = data.frame(s = SI$s))
pmix <- data.frame(SI$y, pi1, pi1)

## determine k for detecting improvement
k1opt <- optimal_k(pmix=pmix, RA = 1/2)

## determine k for detecting deterioration
k2opt <- optimal_k(pmix=pmix, RA = 2)

## subset phase II of surgeons 2
S2II <- filter(SALL, phase == "II", surgeon == 2) %>% select(s, y)
n <- nrow(S2II)
z <- predict(GLM, type = "response", newdata = data.frame(s = S2II$s))-S2II$y

## CUSUM statistic without reset
cv <- eocusum_scores(z = z, k1 = k1opt, k2 = k2opt)
s1 <- cv$s1; s1l <- cv$s1l
dm1 <- data.frame(cbind("n" = 1:length(s1), "Cup" = s1, "Clow" = s1l, "h1" = 2, "h2" = -2))

## CUSUM statistic reset after signal
cv <- eocusum_scores(z = z, k1 = k1opt, k2 = k2opt, reset = TRUE, h1 = 2, h2 = 2)
s1 <- cv$s1; s1l <- cv$s1l
dm2 <- data.frame(cbind("n" = 1:length(s1), "Cup" = s1, "Clow" = s1l, "h1" = 2, "h2" = -2))

dm3 <- bind_rows(dm1, dm2, .id = "type")
dm3$type <- recode_factor(dm3$type, `1`="No resetting", `2`="Resetting")
dm3 %>%
  gather("CUSUM", value, c(-n, - type)) %>%
  ggplot(aes(x = n, y = value, colour = CUSUM, group = CUSUM)) +
  geom_hline(yintercept = 0, colour = "darkgreen", linetype = "dashed") +
  geom_line(size = 0.5) +
  facet_wrap( ~ type, ncol = 1, scales = "free") +
  labs(x = "Patient number n", y = "CUSUM values") + theme_classic() +
  scale_y_continuous(sec.axis = dup_axis(name = NULL, labels = NULL)) +
  scale_x_continuous(sec.axis = dup_axis(name = NULL, labels = NULL)) +
  guides(colour = "none") +
  scale_color_manual(values = c("blue", "orange", "red", "red"))

## End(Not run)

vlad documentation built on Feb. 15, 2021, 5:12 p.m.