vlad (version 0.2.0)

racusum_arl_sim: Compute ARLs of RA-CUSUM control charts using simulation

Description

Computes the Average Run Length of a risk-adjusted cumulative sum control chart using simulation.

Usage

racusum_arl_sim(r, coeff, h, df, R0 = 1, RA = 2, yemp = TRUE)

Arguments

r

Integer Vector. Number of runs.

coeff

Numeric Vector. Estimated coefficients \(\alpha\) and \(\beta\) from the binary logistic regression model.

h

Double. Control Chart limit for detecting deterioration/improvement.

df

Data Frame. First column are Parsonnet Score values within a range of 0 to 100 representing the preoperative patient risk. The second column are binary (0/1) outcome values of each operation.

R0

Double. Odds ratio of death under the null hypotheses.

RA

Double. Odds ratio of death under the alternative hypotheses. Detecting deterioration in performance with increased mortality risk by doubling the odds Ratio RA = 2. Detecting improvement in performance with decreased mortality risk by halving the odds ratio of death RA = 1/2.

yemp

Logical. If TRUE use observed outcome value, if FALSE use estimated binary logistc regression model.

Value

Returns a single value which is the Run Length.

References

Steiner SH, Cook RJ, Farewell VT and Treasure T (2000). Monitoring surgical performance using risk-adjusted cumulative sum charts. Biostatistics, 1(4), pp. 441--452.

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(vlad)
set.seed(1234)
data("cardiacsurgery", package="spcadjust")
df1 <- subset(cardiacsurgery, select=c(Parsonnet, status))
coeff1 <- round(coef(glm(status ~ Parsonnet, data=df1, family="binomial")), 3)

## Parallel Simulation 1: y = random (10^4 runs, RA=2)
m <- 10^4; h_vec <- 2.7; yemp <- FALSE
no_cores <- parallel::detectCores()
cl <- parallel::makeCluster(no_cores)
parallel::clusterExport(cl, c("h_vec", "racusum_arl_sim", "coeff1", "df1", "yemp"))
time <- system.time( {
  ARL <- array(NA, dim=c( length(h_vec), m))
  for (h in h_vec) {
    ARL[which(h_vec==h), ] <- parallel::parSapply(cl, 1:m, racusum_arl_sim, h=h, coeff=coeff1,
                                                 df=df1, yemp=yemp, USE.NAMES=FALSE) }
} )
simMean <- apply(ARL, c(1), mean)
simSE <- sqrt(apply(ARL, c(1), var)/m)
print(list(simMean, simSE, time))
parallel::stopCluster(cl)
df.sim1 <- data.frame("RA"=2, "h"=h, "ARL"=simMean, "ARLSE"=simSE, "nsim"=m)

## Parallel Simulation 2: y = empirical (10^4 runs, RA=2)
m <- 10^4; h_vec <- 2.7
no_cores <- parallel::detectCores()
cl <- parallel::makeCluster(no_cores)
parallel::clusterExport(cl, c("h_vec", "racusum_arl_sim", "coeff1", "df1"))
time <- system.time( {
  ARL <- array(NA, dim=c( length(h_vec), m))
  for (h in h_vec) {
    ARL[which(h_vec==h), ] <- parallel::parSapply(cl, 1:m, racusum_arl_sim, h=h, coeff=coeff1,
                                                 df=df1, USE.NAMES=FALSE) }
} )
simMean <- apply(ARL, c(1), mean)
simSE <- sqrt(apply(ARL, c(1), var)/m)
print(list(simMean, simSE, time))
parallel::stopCluster(cl)
df.sim2 <- data.frame("RA"=2, "h"=h, "ARL"=simMean, "ARLSE"=simSE, "nsim"=m)

rbind(df.sim1, df.sim2)
# }