estimate_pattern_long_md function

Estimate the Regular Longitudinal Pattern of Multivariate Data

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.

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.

Returns

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.

Details

Estimate the Regular Longitudinal Pattern of Multivariate Data

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)

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).