| Title: | Cumulative Sum (CUSUM) Charts for Monitoring of Hospital Performance |
| Version: | 0.4.1 |
| Date: | 2019-10-02 |
| Language: | en-GB |
| Description: | Provides functions for constructing and evaluating CUSUM charts and RA-CUSUM charts with focus on false signal probability. |
| Depends: | R (≥ 3.5.0) |
| License: | GPL-2 |
| LazyData: | true |
| SystemRequirements: | C++11 |
| Encoding: | UTF-8 |
| Imports: | stats, graphics, checkmate, data.table, Rcpp |
| Suggests: | testthat, knitr, ggplot2, rmarkdown |
| Enhances: | vdiffr, covr |
| LinkingTo: | Rcpp |
| VignetteBuilder: | knitr |
| RoxygenNote: | 6.1.1 |
| NeedsCompilation: | yes |
| Packaged: | 2019-10-02 08:07:45 UTC; schneiderheinze |
| Author: | Lena Hubig  [aut,
cre] |
| Maintainer: | Lena Hubig <cs@lenahubig.de> |
| Repository: | CRAN |
| Date/Publication: | 2019-10-02 09:30:03 UTC |
Non-risk-adjusted CUSUM Charts
Description
Calculate non-risk-adjusted CUSUM charts for performance data
Provides functions for constructing and evaluating CUSUM charts and RA-CUSUM charts with focus on false signal probability in health care processes.
Usage
cusum(failure_probability, patient_outcomes, limit, weights = NULL,
odds_multiplier = 2, reset = TRUE)
Arguments
failure_probability |
Double. Baseline failure probability |
patient_outcomes |
Integer. Vector of binary patient outcomes (0,1) |
limit |
Double. Control limit for signalling performance change |
weights |
Double. Optional vector of weights, if empty, standard CUSUM weights are calculated with weights_t |
odds_multiplier |
Double. Odds multiplier of adverse event under the alternative hypothesis (<1 looks for decreases) |
reset |
Logical. Reset the CUSUM after a signal to 0; defaults to TRUE |
Author(s)
Lena Hubig
Examples
# control limit can be obtained with cusum_limit_sim(),
# here it is set to an arbitrary value (2.96)
# CUSUM of in-control process
# simulate patient outcomes
set.seed(2046)
patient_outcomes <- as.logical(rbinom(n = 100, size = 1, prob = 0.05))
cs_ic <- cusum(
failure_probability = 0.05,
patient_outcomes,
limit = 2.96
)
# CUSUM of out-of-control process
# simulate patient outcome
set.seed(2046)
patient_outcomes <- as.logical(rbinom(n = 100, size = 1, prob = 0.2))
cs_oc <- cusum(
failure_probability = 0.05,
patient_outcomes,
limit = 2.96
)
Calculate CUSUM
Description
This function calculates the CUSUM chart for the given sequence of successes and failures
Usage
calc_cusum(x, c0, cA)
Arguments
x |
vector of outcomes |
c0 |
accepted failure probability |
cA |
smallest detectable failure probability |
Value
Returns matrix of possible sequences
Simulate false signal probability alpha given control limit for CUSUM charts
Description
Simulate false signal probability alpha given control limit for CUSUM charts
Usage
cusum_alpha_sim(failure_probability, n_patients, odds_multiplier,
n_simulation, limit, seed = NULL)
Arguments
failure_probability |
Double. Baseline failure probability |
n_patients |
Integer. Number of patients in monitoring period /sample size |
odds_multiplier |
Double. Odds multiplier of adverse event under the alternative hypothesis (<1 looks for decreases) |
n_simulation |
Integer. Number of simulation runs |
limit |
Double. Control limit for signalling performance change |
seed |
Integer. Seed for RNG |
Value
Returns False signal probability of specified CUSUM chart.
Examples
#
# control limit can be obtained with cusum_limit_sim(),
# here it is set to an arbitrary value (2.96)
# simulate false positive probability of CUSUM
cusum_alpha_sim(
failure_probability = 0.05,
n_patients = 100,
odds_multiplier = 2,
n_simulation = 10000,
limit = 2.96,
seed = 2046
)
Non-Risk-adjusted Performance Data
Description
Generated performance data of indicator 17/1 54030: Preoperative stay over 24 hours for patients with proximal femur fracture.
Usage
cusum_example_data
Format
A data frame with 2000 rows and 3 variables:
- t
Sequence of observations
- y
Patient outcome
- year
Year of treatment
Details
Patient outcomes were simulated based on average national failure rate. Two years are provided, so Phase I and Phase II can be defined.
Source
Data for simulation was provided by Bavarian Agency of Quality Assurance (BAQ), Munich Germany.
Description of performance indicator (in German): https://iqtig.org/downloads/auswertung/2016/17n1hftfrak/QSKH_17n1-HUEFTFRAK_2016_QIDB_V02_2017-04-26.pdf
Calculate exact control limit given false signal probability alpha for CUSUM charts for very small sample sizes
Description
This function only works for very small sample sizes (<= 15), as it permutes through all possible outcome sequences and estimates the percentage of runs that reach a specific CUSUM values.
Usage
cusum_limit_exact(n_patients, failure_probability, odds_multiplier, alpha)
Arguments
n_patients |
Integer. Number of patients in monitoring period /sample size |
failure_probability |
Double. Baseline failure probability |
odds_multiplier |
Double. Odds multiplier of adverse event under the alternative hypothesis (<1 looks for decreases) |
alpha |
Double. False signal probability of CUSUM |
Value
Returns the control limit for signalling performance change for small sample sizes (double)
Examples
# calculate exact control limits for alpha = 0.05
cusum_limit_exact(
failure_probability = 0.1,
n_patients = 10,
odds_multiplier = 2,
alpha = 0.05
)
Simulate control limit given false signal probability alpha for CUSUM charts
Description
Simulate control limit given false signal probability alpha for CUSUM charts
Usage
cusum_limit_sim(failure_probability, n_patients, odds_multiplier,
n_simulation, alpha, seed = NULL)
Arguments
failure_probability |
Double. Baseline failure probability |
n_patients |
Integer. Number of patients in monitoring period /sample size |
odds_multiplier |
Double. Odds multiplier of adverse event under the alternative hypothesis (<1 looks for decreases) |
n_simulation |
Integer. Number of simulation runs |
alpha |
Double. False signal probability of CUSUM |
seed |
Integer. Seed for RNG |
Value
Returns the control limit for signalling performance change (double)
Examples
# simulate control limits for alpha = 0.05
cusum_limit_sim(
failure_probability = 0.05,
n_patients = 100,
odds_multiplier = 2,
n_simulation = 1000,
alpha = 0.05,
seed = 2046
)
Group-sequential CUSUM chart
Description
Calculate GSCUSUM chart for non-risk-adjusted processes.
Usage
gscusum(input_outcomes, failure_probability, odds_multiplier, limit,
quantiles, max_num_shuffles = 10000L, seed = 0L)
Arguments
input_outcomes |
Matrix. First column are binary patient outcomes (0,1). Second column are continuous sequence of block identifier. |
failure_probability |
Double. Baseline failure probability |
odds_multiplier |
Double. Odds multiplier of adverse event under the alternative hypothesis (<1 looks for decreases) |
limit |
Double. Control limit for signalling performance change |
quantiles |
Double. Vector of requested quantiles of GSCUSUM distribution |
max_num_shuffles |
Integer. Number of shuffles (i.e. different sequences of observations) |
seed |
Integer. Seed for RNG (if = 0 random seed is set (default)) |
Value
gscusum matrix, signal probability, average CUSUM value and specified quantiles for every observation.
Group-sequential Non-Risk-adjusted Performance Data with Block Identifier
Description
Generated performance data of indicator 17/1 54030: Preoperative stay over 24 hours for patients with proximal femur fracture.
Usage
gscusum_example_data
Format
A data frame with 2000 rows and 4 variables:
- t
Sequence of observations
- y
Patient outcome
- year
Year of treatment
- block_identifier
Continuous block identifier
Details
Patient outcomes were simulated based on average national failure rate. Two years are provided, so Phase I and Phase II can be defined.
Source
Data for simulation was provided by Bavarian Agency of Quality Assurance (BAQ), Munich Germany.
Description of performance indicator (in German): https://iqtig.org/downloads/auswertung/2016/17n1hftfrak/QSKH_17n1-HUEFTFRAK_2016_QIDB_V02_2017-04-26.pdf
Make all outcomes
Description
creates all possible sequences of outcomes for a sample size
Usage
make_all_outcomes(npat_outcome)
Arguments
npat_outcome |
Number of patients (sample sizes) |
Value
Returns matrix of possible sequences
Plot CUSUM chart for a cusum Object
Description
Produces a CUSUM chart.
Usage
## S3 method for class 'cusum' plot(x, signal = TRUE, ...)
Arguments
x |
An object of class cusum |
signal |
Logical. If TRUE, signals are plotted (default) |
Risk-adjusted CUSUM Charts
Description
Calculate risk-adjusted CUSUM charts for performance data
Usage
racusum(patient_risks, patient_outcomes, limit, weights = NULL,
odds_multiplier = 2, reset = TRUE, limit_method = c("constant",
"dynamic"))
Arguments
patient_risks |
Double. Vector of patient risk scores (individual risk of adverse event) |
patient_outcomes |
Integer. Vector of binary patient outcomes (0,1) |
limit |
Double. Control limit for signalling performance change |
weights |
Double. Optional vector of weights, if empty, standard CUSUM weights are calculated with weights_t |
odds_multiplier |
Double. Odds multiplier of adverse event under the alternative hypothesis (<1 looks for decreases) |
reset |
Logical. Reset the CUSUM after a signal to 0; defaults to TRUE |
limit_method |
"constant" or "dynamic" |
Examples
# Patients risks are usually known from Phase I.
# If not, these risk scores can be simulated.
# define possible patient risk scores
risks <- c(0.001, 0.01, 0.1, 0.002, 0.02, 0.2)
# sample risk population of size n = 100
set.seed(2046)
patient_risks <- sample(x = risks, size = 100, replace = TRUE)
# control limit can be obtained with racusum_limit_sim(),
# here it is set to an arbitrary value (2.96),
# or dynamic control limits with racusum_limit_dpcl()
##### RA-CUSUM of in-control process
# simulate patient outcome for performace as expected
set.seed(2046)
patient_outcomes <- as.logical(rbinom(
n = 100,
size = 1,
prob = patient_risks
))
racusum(patient_risks,
patient_outcomes,
limit = 2.96
)
#### RA-CUSUM of out-of-control process
# simulate patient outcome for deviating performance
set.seed(2046)
patient_outcomes <- as.logical(rbinom(n = 100, size = 1, prob = patient_risks * 2))
#'
racusum(patient_risks,
patient_outcomes,
limit = 2.96
)
Simulate false signal probability alpha given control limit for RA-CUSUM charts
Description
Simulate false signal probability alpha given control limit for RA-CUSUM charts
Usage
racusum_alpha_sim(patient_risks, odds_multiplier, n_simulation, limit,
seed = NULL)
Arguments
patient_risks |
Double. Vector of patient risk scores (individual risk of adverse event) |
odds_multiplier |
Double. Odds multiplier of adverse event under the alternative hypothesis (<1 looks for decreases) |
n_simulation |
Integer. Number of simulation runs |
limit |
Double. Control limit for signalling performance change |
seed |
Integer. Seed for RNG |
Value
Returns False signal probability of specified RA-CUSUM chart.
Examples
# Patients risks are usually known from Phase I.
# If not, these risk scores can be simulated.
# define possible patient risk scores
risks <- c(0.001, 0.01, 0.1, 0.002, 0.02, 0.2)
# sample risk population of size n = 100
set.seed(2046)
patient_risks <- sample(x = risks, size = 100, replace = TRUE)
# control limit can be obtained with racusum_limit_sim(),
# here it is set to an arbitrary value (2.96)
# simulate false positive probability of RA-CUSUM
racusum_alpha_sim(patient_risks,
odds_multiplier = 2,
n_simulation = 1000,
limit = 2.96,
seed = 2046
)
Risk-adjusted Performance Data
Description
Generated performance data of indicator: Ratio of observed to expected cases of severe stroke or death under open carotid stenosis surgery.
Usage
racusum_example_data
Format
A data frame with 2000 rows and 4 variables:
- t
Sequence of observations
- y
Patient outcome
- score
Patient risk score
- year
Year of treatment
Details
Individual patient risk scores were drawn from actual hospital data and patient outcomes were simulated. Two years are provided, so Phase I and Phase II can be defined.
Source
Data for simulation was provided by Bavarian Agency of Quality Assurance (BAQ), Munich Germany.
Description of performance indicator (in German): https://iqtig.org/downloads/auswertung/2016/10n2karot/QSKH_10n2-KAROT_2016_QIDB_V02_2017-04-26.pdf
Dynamic Probability Control Limits (DPCL)
Description
Set DPCL for risk-adjusted Bernoulli CUSUM Charts
Usage
racusum_limit_dpcl(patient_risks, N = 1e+05, odds_multiplier = 2,
alpha, seed = NULL)
Arguments
patient_risks |
Double. Vector of patient risk scores (individual risk of adverse event) |
N |
Integer. Number of simulation runs |
odds_multiplier |
Double. Odds multiplier of adverse event under the alternative hypothesis (<1 looks for decreases) |
alpha |
Double. False signal probability of RA-CUSUM |
seed |
Integer. Seed for RNG |
Value
Returns vector of dynamic control limit for signalling performance change (double)
References
Zhang, Xiang & Woodall, William. (2016). Dynamic Probability Control Limits for Lower and Two-Sided Risk-Adjusted Bernoulli CUSUM Charts. Quality and Reliability Engineering International. 10.1002/qre.2044.
Examples
patient_risks <- runif(100, min = 0.1, max = 0.8)
dpcl <- racusum_limit_dpcl(
patient_risks = patient_risks,
N = 1000,
odds_multiplier = 2,
alpha = 0.05,
seed = 32423
)
plot(dpcl, type = "l")
Simulate control limit given false signal probability alpha for RA-CUSUM charts
Description
False-signal-probability-simulation of Control Limits h for risk-adjusted CUSUM charts
Usage
racusum_limit_sim(patient_risks, odds_multiplier, n_simulation, alpha,
seed = NULL)
Arguments
patient_risks |
Double. Vector of patient risk scores (individual risk of adverse event) |
odds_multiplier |
Double. Odds multiplier of adverse event under the alternative hypothesis (<1 looks for decreases) |
n_simulation |
Integer. Number of simulation runs |
alpha |
Double. False signal probability of RA-CUSUM |
seed |
Integer. Seed for RNG |
Value
Returns the control limit for signalling performance change (double)
Examples
# Patients risks are usually known from Phase I.
# If not, these risk scores can be simulated.
# define possible patient risk scores
risks <- c(0.001, 0.01, 0.1, 0.002, 0.02, 0.2)
# sample risk population of size n = 100
set.seed(2046)
patient_risks <- sample(x = risks, size = 100, replace = TRUE)
# simulate control limits for alpha = 0.05
racusum_limit_sim(patient_risks,
odds_multiplier = 2,
n_simulation = 1000,
alpha = 0.05,
seed = 2046
)
RA-Grouped-CUSUM chart
Description
Calculate GSCUSUM chart for risk-adjusted processes.
Usage
ragscusum(input_ra_outcomes, limit, quantiles, max_num_shuffles = 10000L,
seed = 0L)
Arguments
input_ra_outcomes |
Matrix. First column are binary patient outcomes (0,1). Second column are patient individual weight for adverse event (failure) and third column patient individual weight for no adverse event (success). Fourth column are continuous sequence of block identifier. |
limit |
Double. Control limit for signalling performance change |
quantiles |
Double. Vector of requested quantiles of RA-GSCUSUM distribution |
max_num_shuffles |
Integer. Number of shuffles (i.e. different sequences of observations) |
seed |
Integer. Seed for RNG (if = 0 random seed is set (default)) |
Value
ragscusum NumericMatix, signal probability, average CUSUM value and specified quantiles for every observation.
Group-sequential Risk-adjusted Performance Data with Block Identifier
Description
Generated performance data of indicator: Ratio of observed to expected cases of severe stroke or death under open carotid stenosis surgery.
Usage
ragscusum_example_data
Format
A data frame with 2000 rows and 4 variables:
- t
Sequence of observations
- y
Patient outcome
- score
Patient risk score
- year
Year of treatment
- block_identifier
Continuous block identifier
Details
Individual patient risk scores were drawn from actual hospital data and patient outcomes were simulated. Two years are provided, so Phase I and Phase II can be defined.
Source
Data for simulation was provided by Bavarian Agency of Quality Assurance (BAQ), Munich Germany.
Description of performance indicator (in German): https://iqtig.org/downloads/auswertung/2016/10n2karot/QSKH_10n2-KAROT_2016_QIDB_V02_2017-04-26.pdf
Weights for observations
Description
Calculate standard CUSUM weights
Usage
weights_t(patient_outcomes, probability_ae, odds_multiplier = 2)
Arguments
patient_outcomes |
Integer. Vector of binary patient outcomes (0,1) |
probability_ae |
Double. Baseline failure probability for adverse event in non-risk-adjusted case, vector of patient risk scores for risk-adjustment. |
odds_multiplier |
Double. Odds multiplier of adverse event under the alternative hypothesis (<1 looks for decreases) |