sim.nonpara: Multi-Stage Nonparametric Procedure

In unkyunglee/HDChangePoint: Estimating disease onset from change points of markers measured with error

Description

Multi-Stage Nonparametric Procedure

Usage

sim.nonpara(
  n = 80,
  model = "arctan",
  dist = "normal",
  k1 = 10,
  k2 = 10,
  num.interp = 50,
  newl = 50,
  eps.sd = 0.05,
  mean.diff = 1,
  tolerance = 0.009,
  itermax = 20,
  iter = 0,
  time.length = 20,
  dat = outdat
)

Arguments

n	number of sample size.
model	a character string for a nonlinear model: "logist" or "arctan".
dist	a character string for the distribution of within-subject error term in the longitudinal model. Default is "normal".
k1	a parameter for the dimension of the basis functions in order to represent the monotone increasing and convex smooth function.
k2	a parameter for the dimension of the basis functions in order to represent the monotone increasing and concave smooth function.
num.interp	number of pseudo-data points, which are unifromly generated within the observed data points.
newl	a length of time points (log transformed ages) at which predictors are required for each individual longitudinal trajectory.
eps.sd	a true scale parameter of the within-subject error term in the longitudinal model.
mean.diff	an initial tolerence for the convergence criterion. Default is 1.
tolerance	a parameter for the tolerence for the convergence criterion. Default is 0.009.
itermax	a parameter for the maximum number of iterations in the multi-stage nonparametric algorithm. Default is 50.
iter	initial number of iteration in the multi-stage nonparametric algorithm. The default is 0.
time.length	a length of time points for each individual longitudinal trajectory graph to be plotted, should be less than newl.
dat	a data frame of the generated data set.

Value

A list of the simulation results includes

• true_za n-length of the true individual inflection points vector.

• zstar0a n-length of the estimated initial individual inflection points vector.

• zstara n-length of the estimated individual inflection points vector.

• indvidual.Taa n-length of estimated individual inflection points vector after all trajectories were shifted by their inflection points.

• newlogSa newl-length of the new time points vector at which predictors are required for all subjects.

• tms.preda newl-length of the predcited longitudinal trajectory corresponding newlogS from all subjects' longitudinal data.

• tms.se.preda newl-length of the estimated standard errors for tms.pred.

• global.Testimated inflection point on the shifted time points for all subjects.

• est.sigma.epsian estimated scale parameter of the within-subject error in the longitudinal model.

• ind.b.sda n-length of the boostrap standard deviations vector of zstar, where each component is the bootstrap standard deviaion of the estimated inflection point for each subject.

• ind.est.cpA n x 2 95% bootstrap confidence intervals matrix for zstar, i.e., each row has the lower bound and the upper bound of the 95% bootstrap confidence intervals for each individual's estimated inflection point.

• est.beta0estimated intercept parameter of the log-normal model for the inflection point.

• str.beta0estimated standard error of est.beta0.

• est.betaa (p-1)-length of estimated coefficient vector of subject specific covariates in the log-normal model for the inflection point.

• str.betaa (p-1)-length of vector with the estimated standard errors of est.beta.

• est.sigma.eian estimated scale parameter of the random error in the log-normal model for the inflection point.

• xx.timeA time.length x n time points matrix, where each column is a subset of the each column of newdlogS, i.e., the individual time points at which estimated numerical derivatives are required for each subject.

• ind.org.tmsA time.length x n true longitudinal trajectories matrix, where each column is the true individual longitudinal trajectory at each column of xx.time for each subject.

• ind.est.tmsA time.length x n estimated longitudinal trajectories matrix, where each column is the subset of ind.predict.tms, i.e., estimated individual longitudinal trajectory at each column of xx.time for each subject.

• trueD1A time.length x n numerically estimated first derivatives matrix of ind.org.tms, where each column is the numerically estimated first derivative of each column of ind.org.tms at each column of xx.time for each subject.

• trueD2A time.length x n numerically estimated second derivatives matrix of ind.org.tms, where each column is the numerically estimated second derivative of each column of ind.org.tms at each column of xx.time for each subject.

• predD1A time.length x n numerically estimated first derivatives matrix of ind.est.tms, where each column is the numerically estimated first derivative of each column of ind.est.tms at each column of xx.time for each subject.

• predD2A time.length x n numerically estimated second derivatives matrix of ind.est.tms, where each column is the numerically estimated second derivative of each column of ind.est.tms at each column of xx.time for each subject.

• iternumber of interations until convergence.

• mean.diffestimated convergence criterion, which is less than a tolerance if the algorithm convergences.

Examples

library(HDChangePoint)
# How to Generate Simulated Data using mydata() #
n=80; model="logist"; p=2; bb0=0.5;bb=0.1; x.sd=0.3; v1=8; v2=10;
dist="normal"; eps.sd=0.05;u.sd=0.05;

## Specify parameters for the multi-stage nonparametric procedure
num.interp=45;newl=45; k1=20; k2=20; tolerance=0.009; iter=0; time.length=20;

set.seed(22)
## Data generation under the logistic model
outdat<-mydata(n=n, model=model, p=p, bb0=bb0, bb=bb, x.sd=x.sd,
dist=dist,v1=v1, v2=v2, eps.sd=eps.sd, u.sd=u.sd) #

## Multi-stage nonparametric estimation
results<-sim.nonpara(n=n, model=model, dist=dist, k1=k1, k2=k2,
num.interp=num.interp, newl=newl, eps.sd=eps.sd, mean.diff=1, tolerance=tolerance,
itermax=50, iter=iter, time.length=time.length, dat=outdat)

unkyunglee/HDChangePoint documentation built on Nov. 27, 2021, 2:57 p.m.