DySS (version 1.0)

monitor_long_md: 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
)

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.

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.

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)

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)