vlad (version 0.2.2)

racusum_beta_arl: ARL of Beta RA-CUSUM charts

Description

Compute the ARL of risk-adjusted CUSUM charts assuming a beta distributed patient mix.

Usage

racusum_beta_arl_mc(h, shape1, shape2, g0, g1, RA, RQ = 1, r = 600, method = 1)
racusum_beta_arl_int(h, shape1, shape2, g0, g1, RA, RQ, N, pw)
racusum_beta_arl_sim(h, shape1, shape2, g0, g1, r, RA = 2, RQ = 1, rs = 71)

Arguments

h

Double. h is the control limit (>0).

shape1

Double. Shape parameter \(\alpha\) > 0 of the beta distribution.

shape2

Double. Shape parameter \(\beta\) > 0 of the beta distribution.

g0

Double. Estimated intercept coefficient from a binary logistic regression model.

g1

Double. Estimated slope coefficient from a binary logistic regression model.

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. Odds ratio of death under the null hypotheses is 1.

RQ

Double. Defines the performance of a surgeon with the odds ratio ratio of death.

r

Integer. Number of runs.

method

Character. If method = "1" a combination of Sequential Probability Ratio Test and Toeplitz matrix structure is used to calculate the ARL. "2" solves a linear equation system using the classical approach of Brook and Evans (1972) to calculate the ARL.

N

Integer. Number of quadrature nodes, dimension of the resulting linear equation system is equal to N.

pw

Logical. If FALSE full collocation is applied. If TRUE a piece-wise collocation method is used.

rs

Integer. Maximum risk score.

Value

Returns a single value which is the Average Run Length for "racusum_beta_arl_mc" and "racusum_beta_arl_int", and the Run Length for "racusum_beta_arl_sim".

References

Brook D and Evans DA (1972) An approach to the probability distribution of CUSUM run length. Biometrika, 59(3), pp. 539--549

Examples

# NOT RUN {
library(vlad)
## Markov Chain
racusum_beta_arl_mc(h=4.5, shape1=1, shape2=6, g0=-3.6798, g1=0.0768*71, RA=2, r=1e4)
## Full collocation
racusum_beta_arl_int(h=4.5, shape1=1, shape2=6, g0=-3.6798, g1=0.0768*71, RA=2, RQ=1, N=150,
 pw=FALSE)
## Piece-wise collocation
racusum_beta_arl_int(h=4.5, shape1=1, shape2=6, g0=-3.6798, g1=0.0768*71, RA=2, RQ=1, N=49,
 pw=TRUE)
## Monte Carlo simulation
m <- 1e3
RLS <- sapply(1:m, racusum_beta_arl_sim, h=4.5, shape1=1, shape2=6, g0=-3.6798, g1=0.0768,
RA = 2, RQ = 1, rs = 71)
data.frame(cbind(ARL=mean(RLS), ARLSE=sd(RLS)/sqrt(m)))
# }