vlad (version 0.2.2)

racusum_beta_crit: Alarm thresholds of Beta RA-CUSUM charts

Description

Compute alarm threshold of risk-adjusted CUSUM charts assuming a beta distributed patient mix.

Usage

racusum_beta_crit_mc(L0, shape1, shape2, g0, g1, RA, RQ = 1, method = 1,
  r = 600, jmax = 4, verbose = TRUE)
racusum_beta_crit_sim(L0, shape1, shape2, g0, g1, RA = 2, RQ = 1, nc = 1,
  rs = 71, hmax = 30, jmax = 4, m = 10000, verbose = FALSE)

Arguments

L0

Double. Prespecified Average Run Length.

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 true performance of a surgeon with the odds ratio ratio of death RQ. Use RQ = 1 to compute the in-control ARL and other values to compute the out-of-control ARL.

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.

r

Double. Matrix system dimension.

jmax

Integer. Number of digits for grid search.

verbose

Logical. If FALSE a quiet calculation of h is done. If TRUE verbose output of the search procedure (see details) is included.

nc

Integer. Number of cores used for parallel processing. Value is passed to parSapply.

rs

Integer. Maximum risk score.

hmax

Integer. Maximum value of h for the grid search.

m

Integer. Number of simulation runs.

Value

Returns a single value which is the control limit h for a given In-control ARL.

Details

Determines the control limit ("h") for a given in-control ARL ("L0") using racusum_beta_arl_mc or racusum_beta_arl_sim and parSapply by applying a grid search.

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_crit_mc(L0=7500, shape1=.61, shape2=4.09, g0=-3.6798, g1=0.0768*71, RA=2, RQ=1,
 r=1e3)
## Monte Carlo simulation
racusum_beta_crit_sim(L0=7500, shape1=.61, shape2=4.09, g0=-3.6798, g1=0.0768, RA = 2, RQ = 1,
rs = 71, verbose=TRUE, m=1e3)
# }