Help for package DySS

Type:

Package

Title:

Dynamic Screening Systems

Version:

1.0

Date:

2022-07-04

Maintainer:

Lu You <Lu.You@epi.usf.edu>

Description:

In practice, we will encounter problems where the longitudinal performance of processes needs to be monitored over time. Dynamic screening systems (DySS) are methods that aim to identify and give signals to processes with poor performance as early as possible. This package is designed to implement dynamic screening systems and the related methods. References: Qiu, P. and Xiang, D. (2014) <doi:10.1080/00401706.2013.822423>; Qiu, P. and Xiang, D. (2015) <doi:10.1002/sim.6477>; Li, J. and Qiu, P. (2016) <doi:10.1080/0740817X.2016.1146423>; Li, J. and Qiu, P. (2017) <doi:10.1002/qre.2160>; You, L. and Qiu, P. (2019) <doi:10.1080/00949655.2018.1552273>; Qiu, P., Xia, Z., and You, L. (2020) <doi:10.1080/00401706.2019.1604434>; You, L., Qiu, A., Huang, B., and Qiu, P. (2020) <doi:10.1002/bimj.201900127>; You, L. and Qiu, P. (2021) <doi:10.1080/00224065.2020.1767006>.

License:

GPL-2 | GPL-3

Imports:

Rcpp (≥ 1.0.0), utils, stats, graphics, ggplot2, gridExtra

LinkingTo:

Rcpp, RcppArmadillo

RoxygenNote:

7.1.2

Encoding:

UTF-8

Suggests:

knitr, rmarkdown

VignetteBuilder:

knitr

Depends:

R (≥ 2.10)

LazyData:

true

NeedsCompilation:

yes

Packaged:

2022-07-15 23:39:41 UTC; luyou

Author:

Lu You [aut, cre], Peihua Qiu [aut]

Repository:

CRAN

Date/Publication:

2022-07-16 09:50:05 UTC

Calculate ATS

Description

The function calculate_ATS calculates the average time to signals (ATS) given a control chart matrix and a specified control limit (CL). ATS is defined as the average time from the start of process monitoring to signal times.

Usage

calculate_ATS(
  chart_matrix,
  time_matrix,
  nobs,
  starttime,
  endtime,
  design_interval,
  n_time_units,
  time_unit,
  CL,
  no_signal_action = "omit"
)

Arguments

chart_matrix

charting statistic values arranged as a numeric matrix.
chart_matrix[i,j] is the jth charting statistic of the ith subject.

time_matrix

observation times arranged as a numeric matrix.
time_matrix[i,j] is the jth observation time of the ith subject, corresponding to the time the charting statistic chart_matrix[i,j] is computed.

nobs

number of observations arranged as an integer vector.
nobs[i] is the number of observations for the ith subject.

starttime

a numeric vector that gives the start times.
starttime[i] is the time that the ith subject starts to be monitored.

endtime

a numeric vector that gives the end times.
endtime[i] is the time that the ith subject is lost to be monitored.

design_interval

a numeric vector of length two that gives the left- and right- limits of the design interval. By default, design_interval=range(time_matrix,na.rm=TRUE).

n_time_units

an integer value that gives the number of basic time units in the design time interval.
The design interval will be discretized to
seq(design_interval[1],design_interval[2],length.out=n_time_units)

time_unit

an optional numeric value of basic time unit. Only used when n_time_units is missing.
The design interval will be discretized to
seq(design_interval[1],design_interval[2],by=time_unit)

CL

a numeric value specifying the control limit.
CL is the control limit, signals will be given if charting statistics are greater than the control limit.

no_signal_action

a character specifying the method to use when a signal is not given to a process. If no_signal_action="omit" take averages by omitting the processes with no signals, namely, average only the processes with signals.
If no_signal_action="maxtime" impute the signal times by the maximum time, which is the right limit of design time interval.
If no_signal_action="endtime" impute the signal times by the end times.

Details

Calculate ATS

Value

a numeric value, the ATS given the charting statistics and the control limit.

References

Examples

data("data_example_long_1d")

result_pattern<-estimate_pattern_long_1d(
  data_matrix=data_example_long_1d$data_matrix_IC,
  time_matrix=data_example_long_1d$time_matrix_IC,
  nobs=data_example_long_1d$nobs_IC,
  design_interval=data_example_long_1d$design_interval,
  n_time_units=data_example_long_1d$n_time_units,
  estimation_method="meanvar",
  smoothing_method="local linear",
  bw_mean=0.1,
  bw_var=0.1)

result_monitoring<-monitor_long_1d(
  data_matrix_new=data_example_long_1d$data_matrix_OC,
  time_matrix_new=data_example_long_1d$time_matrix_OC,
  nobs_new=data_example_long_1d$nobs_OC,
  pattern=result_pattern,
  side="upward",
  chart="CUSUM",
  method="standard",
  parameter=0.5)

result_ATS<-calculate_ATS(
  chart_matrix=result_monitoring$chart,
  time_matrix=data_example_long_1d$time_matrix_OC,
  nobs=data_example_long_1d$nobs_OC,
  starttime=rep(0,nrow(data_example_long_1d$time_matrix_OC)),
  endtime=rep(1,nrow(data_example_long_1d$time_matrix_OC)),
  design_interval=data_example_long_1d$design_interval,
  n_time_units=data_example_long_1d$n_time_units,
  CL=2.0)

Calculate Signal Times

Description

The function calculate_signal_times calculates the time to signals given a control chart matrix and a specified control limit (CL).

Usage

calculate_signal_times(
  chart_matrix,
  time_matrix,
  nobs,
  starttime,
  endtime,
  design_interval,
  n_time_units,
  time_unit,
  CL
)

Arguments

chart_matrix

a matrix of charting statistic values.
chart_matrix[i,j] is the jth charting statistic of the ith subject.

time_matrix

a matrix of observation times.
time_matrix[i,j] is the jth observation time of the ith subject, corresponding to the time the charting statistic chart_matrix[i,j] is computed.

nobs

number of observations arranged as an integer vector.
nobs[i] is the number of observations for the ith subject.

starttime

a vector of times from the start of monitoring.
starttime[i] is the time that the ith subject starts to be monitored.

endtime

a vector of times from the start of monitoring.
endtime[i] is the time that the ith subject is lost to be monitored.

design_interval

a numeric vector of length two that gives the left- and right- limits of the design interval. By default, design_interval=range(time_matrix,na.rm=TRUE).

n_time_units

an integer value that gives the number of basic time units in the design time interval.
The design interval will be discretized to
seq(design_interval[1],design_interval[2],length.out=n_time_units)

time_unit

an optional numeric value of basic time unit. Only used when n_time_units is missing.
The design interval will be discretized to
seq(design_interval[1],design_interval[2],by=time_unit)

CL

a numeric value specifying the control limit.
CL is the control limit, signals will be given if charting statistics are greater than the control limit.

Details

Calculate Signal Times

Value

A list of two vectors:

$signal_times

times to signals, a numeric vector.

$signals

whether the subject received signals, a logical vector.

References

Examples

data("data_example_long_1d")

result_pattern<-estimate_pattern_long_1d(
  data_matrix=data_example_long_1d$data_matrix_IC,
  time_matrix=data_example_long_1d$time_matrix_IC,
  nobs=data_example_long_1d$nobs_IC,
  design_interval=data_example_long_1d$design_interval,
  n_time_units=data_example_long_1d$n_time_units,
  estimation_method="meanvar",
  smoothing_method="local linear",
  bw_mean=0.1,
  bw_var=0.1)

result_monitoring<-monitor_long_1d(
  data_matrix_new=data_example_long_1d$data_matrix_OC,
  time_matrix_new=data_example_long_1d$time_matrix_OC,
  nobs_new=data_example_long_1d$nobs_OC,
  pattern=result_pattern,
  side="upward",
  chart="CUSUM",
  method="standard",
  parameter=0.5)
result_signal_times<-calculate_signal_times(
  chart_matrix=result_monitoring$chart,
  time_matrix=data_example_long_1d$time_matrix_OC,
  nobs=data_example_long_1d$nobs_OC,
  starttime=rep(0,nrow(data_example_long_1d$time_matrix_OC)),
  endtime=rep(1,nrow(data_example_long_1d$time_matrix_OC)),
  design_interval=data_example_long_1d$design_interval,
  n_time_units=data_example_long_1d$n_time_units,
  CL=2.0)

A simulated dataset with univariate data

Description

A simulated univariate longitudinal dataset for demonstration.

Usage

data(data_example_long_1d)

Format

An object of class list of length 9.

Details

Data Example: Univariate Longitudinal Data

Value

A list of the following components

$data_matrix_IC

The data matrix for IC data.

$time_matrix_IC

The time matrix for IC data.

$nobs_IC

Number of observations for each IC process.

$data_matrix_OC

The data matrix for OC data.

$time_matrix_OC

The time matrix for OC data.

$nobs_OC

Number of observations for each OC process.

$design_interval

The design interval.

$n_time_units

Number of time units in the design interval.

$time_unit

The time unit.

Examples

data(data_example_long_1d)

A simulated dataset with multivariate longitudinal data

Description

A simulated univariate longitudinal dataset for demonstration.

Usage

data(data_example_long_md)

Format

An object of class list of length 9.

Details

Data Example: Multivariate Longitudinal Data

Value

A list of the following components

$data_array_IC

The data array for IC data.

$time_matrix_IC

The time matrix for IC data.

$nobs_IC

Number of observations for each IC process.

$data_array_OC

The data array for OC data.

$time_matrix_OC

The time matrix for OC data.

$nobs_OC

Number of observations for each OC process.

$design_interval

The design interval.

$n_time_units

Number of time units in the design interval.

$time_unit

The time unit.

Examples

data(data_example_long_md)

A simulated dataset with longitudinal and survival data

Description

A simulated univariate longitudinal dataset for demonstration.

Usage

data(data_example_long_surv)

Format

An object of class list of length 15.

Details

Data Example: Longitudinal and Survival Data

Value

A list of the following components

$data_array_IC

The data array for IC data.

$time_matrix_IC

The time matrix for IC data.

$nobs_IC

Number of observations for each IC process.

$starttime_IC

Start time of monitoring for IC processes.

$survtime_IC

End time of monitoring for IC processes.

$survevent_IC

Survival events of IC processes.

$data_array_OC

The data array for OC data.

$time_matrix_OC

The time matrix for OC data.

$nobs_OC

Number of observations for each OC process.

$starttime_OC

Start time of monitoring for OC processes.

$survtime_OC

End time of monitoring for OC processes.

$survevent_OC

Survival events of OC processes.

$design_interval

The design interval.

$n_time_units

Number of time units in the design interval.

$time_unit

The time unit.

Examples

data(data_example_long_surv)

A real data example on stroke

Description

In this dataset, there are 27 subjects with stroke and 1028 subjects without stroke. Three risk factors, systolic blood pressures, diastolic blood pressures, cholesterol levels, are collected over time at different ages.

Usage

data(data_stroke)

Format

An object of class list of length 8.

Details

Real Data Example: Stroke Data

Value

A list of the following components

$systolic_ctrl

A matrix of systolic blood pressures for controls. The [i,j] element is the jth observation of the ith control.

$diastolic_ctrl

A matrix of diastolic blood pressures for controls. The [i,j] element is the jth observation of the ith control.

$cholesterol_ctrl

A matrix of cholesterol levels for controls. The [i,j] element is the jth observation of the ith control.

$age_ctrl

A matrix of the age of observations for controls. The [i,j] element is the age of jth observation for the ith control.

$systolic_case

A matrix of systolic blood pressures for cases. The [i,j] element is the jth observation of the ith case.

$diastolic_case

A matrix of diastolic blood pressures for cases. The [i,j] element is the jth observation of the ith case.

$cholesterol_case

A matrix of cholesterol levels for cases. The [i,j] element is the jth observation of the ith case.

$age_case

A matrix of the age of observations for cases. The [i,j] element is the age of jth observation for the ith case.

Examples

data(data_stroke)

Estimate the Regular Longitudinal Pattern of Univariate Data

Description

Function estimate_pattern_long_1d estimate the regular longitudinal pattern of a univariate variable from a dataset of n subjects. This is usually the first step of dynamic screening. The pattern can be described by mean, variance, covariance, and distribution depending on the estimation method. When the estimated pattern is used for monitoring new subjects, the collected data from new subjects are compared to the estimated pattern for monitoring abnormality.

Usage

estimate_pattern_long_1d(
  data_matrix,
  time_matrix,
  nobs,
  design_interval,
  n_time_units,
  time_unit,
  estimation_method,
  smoothing_method = "local linear",
  bw_mean,
  bw_var,
  bw_cov,
  bw_t,
  bw_y
)

Arguments

data_matrix

observed data arranged in a numeric matrix format.
data_matrix[i,j] is the jth observation of the kth dimension of the ith subject.

time_matrix

observation times arranged in a numeric matrix format.
time_matrix[i,j] is the jth observation time of the ith subject.
data_matrix[i,j] is observed at time_matrix[i,j].

nobs

number of observations arranged as an integer vector.
nobs[i] is the number of observations for the ith subject.

design_interval

a numeric vector of length two that gives the left- and right- limits of the design interval. By default, design_interval=range(time_matrix,na.rm=TRUE).

n_time_units

an integer value that gives the number of basic time units in the design time interval.
The design interval will be discretized to
seq(design_interval[1],design_interval[2],length.out=n_time_units)

time_unit

an optional numeric value of basic time unit. Only used when n_time_units is missing.
The design interval will be discretized to
seq(design_interval[1],design_interval[2],by=time_unit)

estimation_method

a character specifying the estimation method.
If estimation_method="meanvar", the function will estimate the mean and variance functions using local smoothing (c.f., Qiu and Xiang, 2014). Parameters bw_mean and bw_var are required.
If estimation_method="meanvarcov", the function will estimate the mean, variance and covariance functions using local smoothing (c.f., Li and Qiu, 2016). Parameters bw_mean, bw_var and bw_cov are required.
If estimation_method="meanvarcovmean", the function will estimate the mean, variance and covariance functions (c.f., Li and Qiu, 2016). In the last step, the mean function will be updated using the covariance function. Parameters bw_mean, bw_var and bw_cov are required.
If estimation_method="distribution", the function will estimate the distribution function (c.f., You and Qiu, 2020). Parameters bw_t and bw_y are required.
If estimation_method="distributionvarcov", the function will estimate the distribution function and the covariance function of standardized values (c.f., You and Qiu 2020). Parameters bw_cov, bw_t and bw_y are required.

smoothing_method

a character value specifying the smoothing method.
If smoothing_method="local constant", apply local constant approximation.
If smoothing_method="local linear", apply local linear approximation.

bw_mean

a numeric value.
The bandwidth parameter for estimating mean function.

bw_var

a numeric value.
The bandwidth parameter for estimating variance function.

bw_cov

a numeric value.
The bandwidth parameter for estimating covariance function.

bw_t

a numeric value.
The bandwidth parameter in time axis for estimating distribution function.

bw_y

a numeric value.
The bandwidth parameter in y-axis for estimating distribution function.

Details

Estimate the Regular Longitudinal Pattern of Univariate Data

Value

a list that stores the estimated longitudinal pattern and model parameters.
If estimation_method="meanvar", returns a list of class pattern_long_1d_meanvar
If estimation_method="meanvarcov" or "meanvarcovmean", returns a list of class pattern_long_1d_meanvarcov
If estimation_method="distribution", returns a list of class pattern_long_1d_distribution
If estimation_method="distributionvarcov", returns a list of class pattern_long_1d_distributionvarcov

$grid

Discretized design interval.

$mean_est

Estimated mean function.

$var_est

Estimated variance function.

$cov_est

Estimated covariance function.

References

Qiu, P. and Xiang, D. (2014). Univariate dynamic screening system: an approach for identifying individuals with irregular longitudinal behavior. Technometrics, 56:248-260.
Li, J. and Qiu, P. (2016). Nonparametric dynamic screening system for monitoring correlated longitudinal data. IIE Transactions, 48(8):772-786.
You, L. and Qiu, P. (2019). Fast computing for dynamic screening systems when analyzing correlated data. Journal of Statistical Computation and Simulation, 89(3):379-394.
You, L., Qiu, A., Huang, B., and Qiu, P. (2020). Early detection of severe juvenile idiopathic arthritis by sequential monitoring of patients' health-related quality of life scores. Biometrical Journal, 62(5).
You, L. and Qiu, P. (2021). A robust dynamic screening system by estimation of the longitudinal data distribution. Journal of Quality Technology, 53(4).

Examples

data("data_example_long_1d")

result_pattern<-estimate_pattern_long_1d(
  data_matrix=data_example_long_1d$data_matrix_IC,
  time_matrix=data_example_long_1d$time_matrix_IC,
  nobs=data_example_long_1d$nobs_IC,
  design_interval=data_example_long_1d$design_interval,
  n_time_units=data_example_long_1d$n_time_units,
  estimation_method="meanvar",
  smoothing_method="local linear",
  bw_mean=0.1,
  bw_var=0.1)

Estimate the Regular Longitudinal Pattern of Multivariate Data

Description

Function estimate_pattern_long_md estimate the regular longitudinal pattern of multivariate processes from a dataset of n subjects. This is usually the first step of dynamic screening. The pattern can be described by mean, variance, covariance, and distribution depending on the estimation method. When the estimated pattern is used for monitoring new subjects, the collected data from new subjects are compared to the estimated pattern for monitoring abnormality.

Usage

estimate_pattern_long_md(
  data_array,
  time_matrix,
  nobs,
  design_interval,
  n_time_units,
  time_unit,
  estimation_method,
  bw_mean,
  bw_var,
  bw_cov
)

Arguments

data_array

observed data arranged in a 3d array format.
data_array[i,j,k] is the jth observation of the kth dimension of the ith subject.

time_matrix

observation times arranged in a numeric matrix format.
time_matrix[i,j] is the jth observation time of the ith subject.
data_array[i,j,] is observed at time_matrix[i,j].

nobs

number of observations arranged as an integer vector.
nobs[i] is the number of observations for the ith subject.

design_interval

a numeric vector of length two that gives the left- and right- limits of the design interval. By default, design_interval=range(time_matrix,na.rm=TRUE).

n_time_units

an integer value that gives the number of basic time units in the design time interval.
The design interval will be discretized to
seq(design_interval[1],design_interval[2],length.out=n_time_units)

time_unit

an optional numeric value of basic time unit. Only used when n_time_units is missing.
The design interval will be discretized to
seq(design_interval[1],design_interval[2],by=time_unit)

estimation_method

a string.
If estimation_method="meanvar", the function will estimate the mean function (\mathrm{E}[\mathbf{y}(t)]), and variance function (\mathrm{Var}(\mathbf{y}(t))). Parameters bw_mean_int and bw_var_int are needed.
If estimation_method="meanvarcov", the function will estimate the mean function (\mathrm{E}[\mathbf{y}(t)]), variance function (\mathrm{Var}(\mathbf{y}(t))), and covariance function (\mathrm{Cov}(\mathbf{y}(s),\mathbf{y}(t))). Parameters bw_mean_int, bw_var_int and bw_cov_int.

bw_mean

a numeric value.
The bandwidth parameter for estimating mean function.

bw_var

a numeric value.
The bandwidth parameter for estimating variance function.

bw_cov

a numeric value.
The bandwidth parameter for estimating covariance function.

Details

Estimate the Regular Longitudinal Pattern of Multivariate Data

Value

an object that stores the estimated longitudinal pattern and model parameters.
If estimation_method="meanvar", returns an object of class pattern_long_md_meanvar.
If estimation_method="meanvarcov", returns an object of class pattern_long_md_meanvarcov.

$grid

Discretized design interval.

$mean_est

Estimated mean function.

$var_est

Estimated variance function.

$cov_est

Estimated covariance function.

References

Qiu, P. and Xiang, D. (2015). Surveillance of cardiovascular diseases using a multivariate dynamic screening system. Statistics in Medicine, 34:2204-2221.
Li, J. and Qiu, P. (2017). Construction of an efficient multivariate dynamic screening system. Quality and Reliability Engineering International, 33(8):1969-1981.
You, L., Qiu, A., Huang, B., and Qiu, P. (2020). Early detection of severe juvenile idiopathic arthritis by sequential monitoring of patients' health-related quality of life scores. Biometrical Journal, 62(5).

Examples

data("data_example_long_md")

result_pattern<-estimate_pattern_long_md(
  data_array=data_example_long_md$data_array_IC,
  time_matrix=data_example_long_md$time_matrix_IC,
  nobs=data_example_long_md$nobs_IC,
  design_interval=data_example_long_md$design_interval,
  n_time_units=data_example_long_md$n_time_units,
  estimation_method="meanvar",
  bw_mean=0.1,
  bw_var=0.1)

Estimate the Pattern of Longitudinal and Survival Data

Description

Function estimate_pattern_long_surv estimate the pattern of longitudinal and survival data from a dataset of n subjects. This is usually the first step of dynamic screening. The risk of a subject to event is quantified by a linear combination of longitudinal data by a Cox model. The risk pattern can be described by mean and variance depending on the estimation method. When the estimated pattern is used for monitoring new subjects, the collected data from new subjects are compared to the estimated pattern for monitoring abnormality.

Usage

estimate_pattern_long_surv(
  data_array,
  time_matrix,
  nobs,
  starttime,
  survtime,
  survevent,
  design_interval,
  n_time_units,
  time_unit,
  estimation_method = "risk",
  smoothing_method = "local linear",
  bw_beta,
  bw_mean,
  bw_var
)

Arguments

data_array

observed data arranged in a 3d array format.
data_array[i,j,k] is the jth observation of the kth dimension of the ith subject.

time_matrix

observation times arranged in a numeric matrix format.
time_matrix[i,j] is the jth observation time of the ith subject.
data_array[i,j,] is observed at time_matrix[i,j].

nobs

number of observations arranged as an integer vector.
nobs[i] is the number of observations for the ith subject.

starttime

a vector of entry times
starttime[i] is the entry time of the ith subject.

survtime

a vector of survival times
survtime[i] is the survival time of the ith subject.

survevent

a logical vector of survival events
If survevents[i]==TRUE, then a survival event is observed at survtime[i].
If survevents[i]==FALSE, then no survival event is observed at survtime[i].

design_interval

a numeric vector of length two that gives the left- and right- limits of the design interval. By default, design_interval=range(time_matrix,na.rm=TRUE).

n_time_units

an integer value that gives the number of basic time units in the design time interval.
The design interval will be discretized to seq(design_interval[1],design_interval[2],length.out=n_time_units)

time_unit

an optional numeric value of basic time unit. Only used when n_time_units is missing.
The design interval will be discretized to seq(design_interval[1],design_interval[2],by=time_unit)

estimation_method

a string.
If estimation_method="risk", apply the risk monitoring method (c.f., You and Qiu 2020).
(Currently only the method "risk" is available.)

smoothing_method

a string.
If smoothing_method="local constant", apply local constant smoothing
If smoothing_method="local linear", apply local linear smoothing

bw_beta

an integer value.
The bandwidth parameter for estimating the regression coefficients beta in the Cox model.

bw_mean

an integer value.
The bandwidth parameter for estimating mean function.

bw_var

an integer value.
The bandwidth parameter for estimating variance function.

Details

Estimate the Pattern of Longitudinal and Survival Data

Value

an object that stores the estimated longitudinal pattern and model parameters.
If estimation_method="risk", returns an object of class pattern_long_surv_risk.

$grid

discretized design interval.

$beta_est

Estimated regression coefficients.

$mean_risk_est

Estimated mean function.

$var_risk_est

Estimated variance function.

References

You, L. and Qiu, P. (2020). An effective method for online disease risk monitoring. Technometrics, 62(2):249-264.

Examples

data("data_example_long_surv")

result_pattern<-estimate_pattern_long_surv(
  data_array=data_example_long_surv$data_array_IC,
  time_matrix=data_example_long_surv$time_matrix_IC,
  nobs=data_example_long_surv$nobs_IC,
  starttime=data_example_long_surv$starttime_IC,
  survtime=data_example_long_surv$survtime_IC,
  survevent=data_example_long_surv$survevent_IC,
  design_interval=data_example_long_surv$design_interval,
  n_time_units=data_example_long_surv$n_time_units,
  estimation_method="risk",
  smoothing_method="local linear",
  bw_beta=0.05,
  bw_mean=0.1,
  bw_var=0.1)

Evaluate Control Charts (in a single dataset)

Description

The function evaluate_control_chart_one_group evaluates a control chart when the in-control (IC) and out-of-control (OC) charting statistics are supplied together in one matrix chart_matrix. The logical vector status indicates if the ith subject is IC or OC.

Usage

evaluate_control_chart_one_group(
  chart_matrix,
  time_matrix,
  nobs,
  starttime,
  endtime,
  status,
  design_interval,
  n_time_units,
  time_unit,
  no_signal_action = "omit"
)

Arguments

chart_matrix

charting statistics arranged as a numeric matrix.
chart_matrix[i,j] is the jth charting statistic of the ith subject.

time_matrix

observation times arranged as a numeric matrix.
time_matrix[i,j] is the jth observation time of the ith subject.
chart_matrix[i,j] is the charting statistic of the ith subject at time_matrix[i,j].

nobs

number of observations arranged as an integer vector.
nobs[i] is the number of observations for the ith subject.

starttime

a numeric vector. starttime[i] is the time when monitoring starts for ith subject.

endtime

a numeric vector, times when monitoring end. endtime[i] is the time when monitoring ends for ith subject.

status

a logical vector. status[i]=FALSE if the ith subject is IC, while status[i]=TRUE indicates the the ith subject is OC.

design_interval

a numeric vector of length two that gives the left- and right- limits of the design interval. By default, design_interval=range(time_matrix,na.rm=TRUE).

n_time_units

an integer value that gives the number of basic time units in the design time interval.
The design interval will be discretized to seq(design_interval[1],design_interval[2],length.out=n_time_units)

time_unit

an optional numeric value of basic time unit. Only used when n_time_units is missing.
The design interval will be discretized to seq(design_interval[1],design_interval[2],by=time_unit)

no_signal_action

a character value specifying how to set signal times when processes with no signals.
If no_signal_action=="omit", the signal time is set to be missing.
If no_signal_action=="maxtime", the signal time is set to be the time from start time to the end of the design interval.
If no_signal_action=="endtime", the signal time is set to be the time from start time to the end time.

Details

Evaluate Control Charts

Value

an list that stores the evaluation measures.

$thres

A numeric vector. Threshold values for control limits.

$FPR

A numeric vector. False positive rates.

$TPR

A numeric vector. True positive rates.

$ATS0

A numeric vector. In-control ATS.

$ATS1

A numeric vector. Out-of-control ATS.

References

Examples

result_pattern<-estimate_pattern_long_surv(
  data_array=data_example_long_surv$data_array_IC,
  time_matrix=data_example_long_surv$time_matrix_IC,
  nobs=data_example_long_surv$nobs_IC,
  starttime=data_example_long_surv$starttime_IC,
  survtime=data_example_long_surv$survtime_IC,
  survevent=data_example_long_surv$survevent_IC,
  design_interval=data_example_long_surv$design_interval,
  n_time_units=data_example_long_surv$n_time_units,
  estimation_method="risk",
  smoothing_method="local linear",
  bw_beta=0.05,
  bw_mean=0.1,
  bw_var=0.1)

result_monitoring<-monitor_long_surv(
  data_array_new=data_example_long_surv$data_array_IC,
  time_matrix_new=data_example_long_surv$time_matrix_IC,
  nobs_new=data_example_long_surv$nobs_IC,
  pattern=result_pattern,
  method="risk",
  parameter=0.5)

output_evaluate<-evaluate_control_chart_one_group(
  chart_matrix=result_monitoring$chart[1:200,],
  time_matrix=data_example_long_surv$time_matrix_IC[1:200,],
  nobs=data_example_long_surv$nobs_IC[1:200],
  starttime=rep(0,200),
  endtime=rep(1,200),
  status=data_example_long_surv$survevent_IC[1:200],
  design_interval=data_example_long_surv$design_interval,
  n_time_units=data_example_long_surv$n_time_units,
  no_signal_action="maxtime")

Evaluate Control Charts

Description

The function evaluate_control_chart_two_groups evaluates control charts when the in-control (IC) and out-of-control (OC) charting statistics are supplied separately in two matrices chart_matrix_IC and chart_matrix_OC.

Usage

evaluate_control_chart_two_groups(
  chart_matrix_IC,
  time_matrix_IC,
  nobs_IC,
  starttime_IC,
  endtime_IC,
  chart_matrix_OC,
  time_matrix_OC,
  nobs_OC,
  starttime_OC,
  endtime_OC,
  design_interval,
  n_time_units,
  time_unit,
  no_signal_action = "omit"
)

Arguments

chart_matrix_IC, chart_matrix_OC

charting statistics arranged as a numeric matrix.
chart_matrix_IC[i,j] is the jth charting statistic of the ith IC subject.
chart_matrix_OC[i,j] is the jth charting statistic of the ith OC subject.

time_matrix_IC, time_matrix_OC

observation times arranged as a numeric matrix.
time_matrix_IC[i,j] is the jth observation time of the ith IC subject.
time_matrix_OC[i,j] is the jth observation time of the ith OC subject.
chart_matrix_IC[i,j] is the charting statistic of the ith IC subject at time_matrix[i,j].
chart_matrix_OC[i,j] is the charting statistic of the ith OC subject at time_matrix[i,j].

nobs_IC, nobs_OC

number of observations arranged as an integer vector.
nobs_IC[i] is the number of observations for the ith subject.
nobs_OC[i] is the number of observations for the ith subject.

starttime_IC, starttime_OC

a numeric vector that gives the start times.
starttime_IC[i] is the time that the ith IC subject starts to be monitored.
starttime_OC[i] is the time that the ith OC subject starts to be monitored.

endtime_IC, endtime_OC

a numeric vector that gives the end times.
endtime_IC[i] is the time that the ith IC subject is lost to be monitored.
endtime_OC[i] is the time that the ith OC subject is lost to be monitored.

design_interval

a numeric vector of length two that gives the left- and right- limits of the design interval. By default, design_interval=range(time_matrix,na.rm=TRUE).

n_time_units

an integer value that gives the number of basic time units in the design time interval.
The design interval will be discretized to seq(design_interval[1],design_interval[2],length.out=n_time_units)

time_unit

an optional numeric value of basic time unit. Only used when n_time_units is missing.
The design interval will be discretized to seq(design_interval[1],design_interval[2],by=time_unit)

no_signal_action

Details

Evaluate Control Charts

Value

an list that stores the evaluation measures.

$thres

A numeric vector. Threshold values for control limits.

$FPR

A numeric vector. False positive rates.

$TPR

A numeric vector. True positive rates.

$ATS0

A numeric vector. In-control ATS.

$ATS1

A numeric vector. Out-of-control ATS.

References

Examples

pattern<-estimate_pattern_long_1d(
  data_matrix=data_example_long_1d$data_matrix_IC,
  time_matrix=data_example_long_1d$time_matrix_IC,
  nobs=data_example_long_1d$nobs_IC,
  design_interval=data_example_long_1d$design_interval,
  n_time_units=data_example_long_1d$n_time_units,
  estimation_method="meanvar",
  smoothing_method="local linear",
  bw_mean=0.1,
  bw_var=0.1)

chart_IC_output<-monitor_long_1d(
  data_example_long_1d$data_matrix_IC,
  data_example_long_1d$time_matrix_IC,
  data_example_long_1d$nobs_IC,
  pattern=pattern,side="upward",chart="CUSUM",
  method="standard",parameter=0.2)

chart_OC_output<-monitor_long_1d(
  data_example_long_1d$data_matrix_OC,
  data_example_long_1d$time_matrix_OC,
  data_example_long_1d$nobs_OC,
  pattern=pattern,side="upward",chart="CUSUM",
  method="standard",parameter=0.2)

output_evaluate<-evaluate_control_chart_two_groups(
  chart_matrix_IC=chart_IC_output$chart[1:50,],
  time_matrix_IC=data_example_long_1d$time_matrix_IC[1:50,],
  nobs_IC=data_example_long_1d$nobs_IC[1:50],
  starttime_IC=rep(0,50),
  endtime_IC=rep(1,50),
  chart_matrix_OC=chart_OC_output$chart[1:50,],
  time_matrix_OC=data_example_long_1d$time_matrix_OC[1:50,],
  nobs_OC=data_example_long_1d$nobs_OC[1:50],
  starttime_OC=rep(0,50),
  endtime_OC=rep(1,50),
  design_interval=data_example_long_1d$design_interval,
  n_time_units=data_example_long_1d$n_time_units,
  no_signal_action="maxtime")

Monitor Univariate Longitudinal Data

Description

Monitor Univariate Longitudinal Data

Usage

monitor_long_1d(
  data_matrix_new,
  time_matrix_new,
  nobs_new,
  pattern,
  side = "upward",
  chart = "CUSUM",
  method = "standard",
  parameter = 0.5,
  CL = Inf
)

Arguments

data_matrix_new

observed data arranged in a numeric matrix format.
data_matrix_new[i,j] is the jth observation of the ith subject.

time_matrix_new

observation times arranged in a numeric matrix format.
time_matrix_new[i,j] is the jth observation time of the ith subject.
data_matrix_new[i,j] is observed at time_matrix_new[i,j].

nobs_new

number of observations arranged as an integer vector.
nobs_new[i] is the number of observations for the ith subject.

pattern

the estimated regular longitudinal pattern

side

a character value specifying the sideness/direction of process monitoring
If side="upward"apply control charts that aim to detect upward shifts.
If side="downward"apply control charts that aim to detect downward shifts.
If side="both"apply control charts that aim to detect shifts in both sides

chart

a string specifying the control charts to use. If chart="CUSUM"apply CUSUM charts.
If chart="EWMA"apply EWMA charts.

method

a string
If method="standard", standardize observations by mean and variance (cf., Qiu and Xiang, 2014).
If method="decorrelation", standardize and decorrelate observations by mean and covariance (cf., Li and Qiu, 2016).
If method="sprint", standardize and decorrelate observations within sprint length by mean and covariance (cf., You and Qiu 2018).
If method="distribution and standard", standardize observations by distribution (cf., You and Qiu, 2020).
If method="distribution and decorrelation", standardize observations by distribution and covariance (cf., You and Qiu, 2020).
If method="distribution and sprint",standardize and decorrelate observations within sprint length by distribution and covariance (cf., You and Qiu, 2020).
method="nonparametric and standard" currently not supported.
method="nonparametric and decorrelation" currently not supported

parameter

a numeric value
If chart="CUSUM", parameter is the allowance constant in the control chart.
If chart="EWMA", parameter is the weighting in the control chart.

CL

a numeric value speficying the control limit.
A signal will be given if charting statistics are larger than the control limit. (Note: in this package, signs of charting statistics may be reversed such that larger values of charting statistics indicate worse performance of processes.) After the signal is given, the algorithm stops calculating the charting statistics for the remaining observation times. The default value of control limit is infinity, which means we will calculate the charting statistics for all observation times.

Value

a list that stores the result.

$chart

a numeric matrix, $chart[i,j] is the jth charting statistic of the ith subject.

$standardized_values

a numeric matrix, $standardized_values[i,j] is the standardized value of the jth observation of the ith subject.

References

Examples

data("data_example_long_1d")

result_pattern<-estimate_pattern_long_1d(
  data_matrix=data_example_long_1d$data_matrix_IC,
  time_matrix=data_example_long_1d$time_matrix_IC,
  nobs=data_example_long_1d$nobs_IC,
  design_interval=data_example_long_1d$design_interval,
  n_time_units=data_example_long_1d$n_time_units,
  estimation_method="meanvar",
  smoothing_method="local linear",
  bw_mean=0.1,
  bw_var=0.1)

result_monitoring<-monitor_long_1d(
  data_matrix_new=data_example_long_1d$data_matrix_OC,
  time_matrix_new=data_example_long_1d$time_matrix_OC,
  nobs_new=data_example_long_1d$nobs_OC,
  pattern=result_pattern,
  side="upward",
  chart="CUSUM",
  method="standard",
  parameter=0.5)

Monitor Multivariate Longitudinal Data

Description

Monitor Multivariate Longitudinal Data

Usage

monitor_long_md(
  data_array_new,
  time_matrix_new,
  nobs_new,
  pattern,
  side = "both",
  method = "multivariate EWMA",
  parameter = 0.5,
  CL = Inf
)

Arguments

data_array_new

an array of longitudinal observations.
data_array_new[i,j,k] is the jth observation of the kth dimension of the ith subject.

time_matrix_new

a matrix of observation times.
time_matrix_new[i,j] is the jth observation time of the ith subject.
data_array_new[i,j,] is observed at time_matrix[i,j].

nobs_new

an integer vector for number of observations.
nobs_new[i] is the number of observations for the ith subject.

pattern

the estimated regular longitudinal pattern

side

a string
If side="upward", control charts aim to detect upward shifts.
If side="downward", control charts aim to detect downward shifts.
If side="both", control charts aim to detect shifts in both sides.

method

a string
If method="simultaneous CUSUM", apply simultaneous CUSUM charts. (See SIMUL in You et al, 2020.)
If method="simultaneous EWMA", apply simultaneous EWMA charts. (See SIMUL in You et al, 2020.)
If method="multivariate CUSUM", apply multivariate CUSUM charts.
If method="multivariate EWMA", apply multivariate EWMA charts. (See Qiu and Xiang, 2015 or QX-1S/QS-2S in You et al, 2020.)
If method="decorrelation CUSUM", apply decorrelation CUSUM charts. (See Li and Qiu, 2017 or LQ-1S/LQ-2S in You et al, 2020)
If method="decorrelation EWMA", apply decorrelation EWMA charts. (See Li and Qiu, 2017 or LQ-1S/LQ-2S in You et al, 2020)
If method="nonparametric CUSUM"
If method="nonparametric EWMA"

parameter

a numeric value.
parameter is the allowance constant if method is a CUSUM chart.
parameter is the weighting parameter if method is an EWMA chart.

CL

a numeric value
CL is the control limit. A signal will be given if charting statistics are larger than the control limit. (Note: in this package, signs of charting statistics may be reversed such that larger values of charting statistics indicate worse performance of processes.) After the signal is given, the algorithm stops calculating the charting statistics for the remaining observation times. The default value of control limit is infinity, which means we will calculate the charting statistics for all observation times.

Value

a list that stores the result.

$chart

a numeric matrix, $chart[i,j] is the jth charting statistic of the ith subject calculated at time time_matrix_new[i,j].

$SSijk

a numeric array, the multivariate statistics used in the calculation of control charts. $SSijk[i,j,] is the jth multivariate statistic for the ith subject.

$standardized_values

a numeric array. $standardized_values[i,j,] is the jth standardized vector for the ith subject.

References

Examples

data("data_example_long_md")

result_pattern<-estimate_pattern_long_md(
  data_array=data_example_long_md$data_array_IC,
  time_matrix=data_example_long_md$time_matrix_IC,
  nobs=data_example_long_md$nobs_IC,
  design_interval=data_example_long_md$design_interval,
  n_time_units=data_example_long_md$n_time_units,
  estimation_method="meanvar",
  bw_mean=0.1,
  bw_var=0.1)

result_monitoring<-monitor_long_md(
data_array_new=data_example_long_md$data_array_OC,
time_matrix_new=data_example_long_md$time_matrix_OC,
nobs_new=data_example_long_md$nobs_OC,
pattern=result_pattern,
side="both",
method="multivariate EWMA",
parameter=0.5)

result_ATS<-calculate_ATS(
  chart_matrix=result_monitoring$chart_matrix,
  time_matrix=data_example_long_md$time_matrix_OC,
  nobs=data_example_long_md$nobs_OC,
  starttime=rep(0,nrow(data_example_long_md$time_matrix_OC)),
  endtime=rep(1,nrow(data_example_long_md$time_matrix_OC)),
  design_interval=data_example_long_md$design_interval,
  n_time_units=data_example_long_md$n_time_units,
  CL=16.0)

Monitor Longitudinal Data for Survival Outcomes

Description

Monitor Longitudinal Data for Survival Outcomes

Usage

monitor_long_surv(
  data_array_new,
  time_matrix_new,
  nobs_new,
  pattern,
  method,
  parameter = 0.5,
  CL = Inf
)

Arguments

data_array_new

observed data arranged in a numeric array format.
data_array_new[i,j,k] is the jth observation of the kth dimension of the ith subject.

time_matrix_new

observation times arranged in a numeric matrix format.
time_matrix_new[i,j] is the jth observation time of the ith subject.
data_array_new[i,j,] is observed at time_matrix[i,j].

nobs_new

number of observations arranged as an integer vector.
nobs_new[i] is the number of observations for the ith subject.

pattern

the estimated longitudinal and survival pattern from estimate_pattern_long_surv.

method

a character value specifying the smoothing method
If method="risk", apply the risk monitoring method by You and Qiu (2020).

parameter

a numeric value.
The weighting parameter in the modified EWMA charts.

CL

a numeric value specifying the control limit

Value

a list that stores the result.

$chart

charting statistics arranged in a matrix.

$standardized_values

standardized values arranged in a matrix.

References

You, L. and Qiu, P. (2020). An effective method for online disease risk monitoring. Technometrics, 62(2):249-264.

Examples

data("data_example_long_surv")

result_pattern<-estimate_pattern_long_surv(
  data_array=data_example_long_surv$data_array_IC,
  time_matrix=data_example_long_surv$time_matrix_IC,
  nobs=data_example_long_surv$nobs_IC,
  starttime=data_example_long_surv$starttime_IC,
  survtime=data_example_long_surv$survtime_IC,
  survevent=data_example_long_surv$survevent_IC,
  design_interval=data_example_long_surv$design_interval,
  n_time_units=data_example_long_surv$n_time_units,
  estimation_method="risk",
  smoothing_method="local linear",
  bw_beta=0.05,
  bw_mean=0.1,
  bw_var=0.1)

result_monitoring<-monitor_long_surv(
  data_array_new=data_example_long_surv$data_array_OC,
  time_matrix_new=data_example_long_surv$time_matrix_OC,
  nobs_new=data_example_long_surv$nobs_OC,
  pattern=result_pattern,
  method="risk",
  parameter=0.5)

Evaluate and Visualize Control Charts by PM-ROC curves

Description

Evaluate and Visualize Control Charts by PM-ROC curves

Usage

plot_PMROC(evaluate_control_chart)

Arguments

evaluate_control_chart

an object of class evaluate_control_chart.
evaluate_control_chart is an output from evaluate_control_chart_one_group or evaluate_control_chart_two_group.

Value

No return value, called for drawing one PM-ROC plot.

Examples

pattern<-estimate_pattern_long_1d(
  data_matrix=data_example_long_1d$data_matrix_IC,
  time_matrix=data_example_long_1d$time_matrix_IC,
  nobs=data_example_long_1d$nobs_IC,
  design_interval=data_example_long_1d$design_interval,
  n_time_units=data_example_long_1d$n_time_units,
  estimation_method="meanvar",
  smoothing_method="local linear",
  bw_mean=0.1,
  bw_var=0.1)

chart_IC_output<-monitor_long_1d(
  data_example_long_1d$data_matrix_IC,
  data_example_long_1d$time_matrix_IC,
  data_example_long_1d$nobs_IC,
  pattern=pattern,side="upward",chart="CUSUM",
  method="standard",parameter=0.2)

chart_OC_output<-monitor_long_1d(
  data_example_long_1d$data_matrix_OC,
  data_example_long_1d$time_matrix_OC,
  data_example_long_1d$nobs_OC,
  pattern=pattern,side="upward",chart="CUSUM",
  method="standard",parameter=0.2)

output_evaluate<-evaluate_control_chart_two_groups(
  chart_matrix_IC=chart_IC_output$chart[1:50,],
  time_matrix_IC=data_example_long_1d$time_matrix_IC[1:50,],
  nobs_IC=data_example_long_1d$nobs_IC[1:50],
  starttime_IC=rep(0,50),
  endtime_IC=rep(1,50),
  chart_matrix_OC=chart_OC_output$chart[1:50,],
  time_matrix_OC=data_example_long_1d$time_matrix_OC[1:50,],
  nobs_OC=data_example_long_1d$nobs_OC[1:50],
  starttime_OC=rep(0,50),
  endtime_OC=rep(1,50),
  design_interval=data_example_long_1d$design_interval,
  n_time_units=data_example_long_1d$n_time_units,
  no_signal_action="maxtime")

plot_evaluation(output_evaluate)
plot_PMROC(output_evaluate)

Evaluate and Visualize Control Charts by ROC curves

Description

Evaluate and Visualize Control Charts by ROC curves

Usage

plot_evaluation(evaluate_control_chart)

Arguments

evaluate_control_chart

an object of class evaluate_control_chart.
evaluate_control_chart is an output from evaluate_control_chart_one_group or evaluate_control_chart_two.

Value

No return value, called for drawing two ROC plots.

Examples

result_pattern<-estimate_pattern_long_surv(
  data_array=data_example_long_surv$data_array_IC,
  time_matrix=data_example_long_surv$time_matrix_IC,
  nobs=data_example_long_surv$nobs_IC,
  starttime=data_example_long_surv$starttime_IC,
  survtime=data_example_long_surv$survtime_IC,
  survevent=data_example_long_surv$survevent_IC,
  design_interval=data_example_long_surv$design_interval,
  n_time_units=data_example_long_surv$n_time_units,
  estimation_method="risk",
  smoothing_method="local linear",
  bw_beta=0.05,
  bw_mean=0.1,
  bw_var=0.1)

result_monitoring<-monitor_long_surv(
  data_array_new=data_example_long_surv$data_array_IC,
  time_matrix_new=data_example_long_surv$time_matrix_IC,
  nobs_new=data_example_long_surv$nobs_IC,
  pattern=result_pattern,
  method="risk",
  parameter=0.5)

output_evaluate<-evaluate_control_chart_one_group(
  chart_matrix=result_monitoring$chart,
  time_matrix=data_example_long_surv$time_matrix_IC,
  nobs=data_example_long_surv$nobs_IC,
  starttime=rep(0,nrow(data_example_long_surv$time_matrix_IC)),
  endtime=rep(1,nrow(data_example_long_surv$time_matrix_IC)),
  status=data_example_long_surv$survevent_IC,
  design_interval=data_example_long_surv$design_interval,
  n_time_units=data_example_long_surv$n_time_units,
  no_signal_action="maxtime")

plot_evaluation(output_evaluate)
plot_PMROC(output_evaluate)

Search Control Limit

Description

Given a chart matrix, the function search_CL searches the control limit (CL) so that the specified average time to signals (ATS) can be attained.

Usage

search_CL(
  chart_matrix,
  time_matrix,
  nobs,
  starttime,
  endtime,
  design_interval,
  n_time_units,
  time_unit,
  ATS_nominal,
  CL_lower,
  CL_step,
  CL_upper,
  no_signal_action = "omit",
  ATS_tol,
  CL_tol
)

Arguments

chart_matrix

charting statistics arranged as a numeric matrix.
chart_matrix[i,j] is the jth charting statistic of the ith subject.

time_matrix

observation times arranged as a numeric matrix.
time_matrix[i,j] is the jth observation time of the ith subject, corresponding to the time the charting statistic chart_matrix[i,j] is computed.

nobs

number of observations arranged as an integer vector.
nobs[i] is the number of observations for the ith subject.

starttime

a vector of times from the start of monitoring.
starttime[i] is the time that the ith subject starts to be monitored.

endtime

a vector of times from the start of monitoring.
endtime[i] is the time that the ith subject is lost to be monitored.

design_interval

a numeric vector of length two that gives the left- and right- limits of the design interval. By default, design_interval=range(time_matrix,na.rm=TRUE).

n_time_units

an integer value that gives the number of basic time units in the design time interval.
The design interval will be discretized to
seq(design_interval[1],design_interval[2],length.out=n_time_units)

time_unit

an optional numeric value of basic time unit. Only used when n_time_units is missing.
The design interval will be discretized to
seq(design_interval[1],design_interval[2],by=time_unit)

ATS_nominal

a numeric value.
ATS_nominal is the nominal (or say targeted) ATS that is intended to achieve.

CL_lower, CL_step, CL_upper

three numeric values.
The control limit will be searched within the interval [CL_lower,CL_upper].
When applying grid search, the algorithm will use a step size of CL_step.
(Namely, the algorithm will start with CL_lower, and search through the sequences CL_lower, CL_lower+CL_step, CL_lower+2*CL_step, ... until CL_upper.)

no_signal_action

ATS_tol

a numeric value.
Error tolerance for ATS.

CL_tol

a numeric value.
Error tolerance for control limit.

Details

Search Control Limit

Value

a numeric value, the control limit that gives the desired ATS.

Examples


result_pattern<-estimate_pattern_long_1d(
  data_matrix=data_example_long_1d$data_matrix_IC,
  time_matrix=data_example_long_1d$time_matrix_IC,
  nobs=data_example_long_1d$nobs_IC,
  design_interval=data_example_long_1d$design_interval,
  n_time_units=data_example_long_1d$n_time_units,
  estimation_method="meanvar",
  smoothing_method="local linear",
  bw_mean=0.1,
  bw_var=0.1)

result_monitoring<-monitor_long_1d(
  data_matrix_new=data_example_long_1d$data_matrix_IC,
  time_matrix_new=data_example_long_1d$time_matrix_IC,
  nobs_new=data_example_long_1d$nobs_IC,
  pattern=result_pattern,
  side="upward",
  chart="CUSUM",
  method="standard",
  parameter=0.5)

CL<-search_CL(
  chart_matrix=result_monitoring$chart,
  time_matrix=data_example_long_1d$time_matrix_IC,
  nobs=data_example_long_1d$nobs_IC,
  starttime=rep(0,nrow(data_example_long_1d$time_matrix_IC)),
  endtime=rep(1,nrow(data_example_long_1d$time_matrix_IC)),
  design_interval=data_example_long_1d$design_interval,
  n_time_units=data_example_long_1d$n_time_units,
  ATS_nominal=200,CL_lower=0,CL_upper=5)