main.arctan.nlme: Parametric nonlinear mixed effects model (NLME) approach:...

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

Description

Parametric nonlinear mixed effects model (NLME) approach: When true data are generated by the arctangent model, the parametric NLME procedure is performed under the correct arctangent model.

Usage

main.arctan.nlme(
  n = 80,
  model = "arctan",
  dat = outdat,
  num.boot = 1000,
  time.length = 20,
  true.gam1 = 2.45/pi,
  true.gam3 = pi/1.1,
  para1 = 0.8,
  para2 = 0.2,
  para3 = 0.2,
  para4 = 2.8,
  para5 = 1.5,
  eps.sd = 0.05,
  dist = "normal"
)

Arguments

n	number of sample size.
model	a character string for a nonlinear model: "logist" or "arctan".
dat	a data frame of the generated data set.
num.boot	number of bootsrap replicates.
time.length	number of data points at which predictors are required for each individual longitudinal trajectory. This time point for graphs to be plotted.
true.gam1	a true scale parameter for gam1 in the arctangent model, see arctanf().
true.gam3	a true parameter for gam3, which determines steepness of the arctangent model, see arctanf().
para1	an initial parameter for gam1, which is used for the parametric nonlinear mixed effects model (NLME) approach.
para2	an initial intercept parameter for the inflection point gam2, which is used for the parametric nonlinear mixed effects model (NLME) approach.
para3	an initial (p-1)-length of coefficient vector of subject specific covariates for the inflection point gam2, which is used for the parametric nonlinear mixed effects model (NLME) approach.
para4	an initial parameter for gam3, which is used for the parametric nonlinear mixed effects model (NLME) approach.
para5	an initial vertical shift parameter for gam4, which is used for the parametric nonlinear mixed effects model (NLME) approach.
eps.sd	a true scale parameter of the within-subject error term in the longitudinal model.
dist	a character string for the distribution of within-subject error term in the longitudinal model. Default is "normal".

Value

A list of

• est.gam1estimated fixed effect parameter for gam1 in the arctangent function, see arctanf().

• est.betathe (p-1)-length of estimated coefficient vector of subjec-specific covariates in the log-normal model for inflection points.

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

• est.gam3estimated fixed effect parameter for gam3 in the arctangent function, see arctanf().

• est.gam4estimated fixed effect parameter for gam4 in the arctangent function, see arctanf().

• est.str.gam1estimated standard error of gam1.

• est.str.betathe (p-1)-length of estimated standard errors of the coefficient vector of subject-specific covariates in the log-normal model for inflection points.

• est.str.beta0estimated standard errors of the intercept of the log-normal model for inflection points.

• est.str.gam3estimated standard error of gam3.

• est.str.gam4estimated standard error of gam4.

• cp.lower.gam1estimated lower bound of the 95% confidence interval for gam1.

• cp.upper.gam1estimated upper bound of the 95% confidence interval for gam1.

• cp.lower.beta0estimated lower bound of the 95% confidence interval for beta0, which is the intercept of the log-normal model for inflection points.

• cp.upper.beta0estimated upper bound of the 95% confidence interval for beta0, which is the intercept of the log-normal model for inflection points.

• cp.lower.betaestimated lower bound of the 95% confidence interval for beta, which is the (p-1)-length of the coefficient vector of subject specific covariates in the log-normal model for inflection points.

• cp.upper.betaestimated upper bound of the 95% confidence interval for beta, which is the (p-1)-length of the coefficient vector of subject specific covariates in the log-normal model for inflection points.

• cp.lower.gam3estimated lower bound of the 95% confidence interval for gam3.

• cp.upper.gam3estimated upper bound of the 95% confidence interval for gam3.

• cp.lower.gam4estimated lower bound of the 95% confidence interval for gam4.

• cp.upper.gam4estimated upper bound of the 95% confidence interval for gam4.

• est.rand.efestimated random effects in the log normal model for the inflection points.

• est.logTthe n-length of the estimated inflection points vector, where each element is the individual estimated inflection point.

• true.logTthe n-length of the true inflection points vector, where each element is the true individual inflection point.

• new.pred.dataa time.length x 5 x n array of data set to generate boostrap estimates, which includes ID, log scaled ages, subject specfici covariates, true longitudinal trajectories and estimated longitudinal trajectories for each subject.

• true.first.deriva time.length x n array of the first derivatives of the true longitudinal trajectories, where each column is the first derivatives of the true longitudinal responses corresponding subject-specific log scaled ages in new.pred.data for each subject.

• true.second.deriva time.length x n array of the second derivatives of the true longitudinal trajectories, where each column is the second derivatives of the true longitudinal responses corresponding subject-specific log scaled ages in new.pred.data for each subject.

• est.first.deriva time.length x n array of the estiamted first derivatives of longitudinal trajectories, where each column is the estimated second derivatives of longitudinal responses corresponding subject-specific log scaled ages in new.pred.data for each subject.

• est.second.deriva time.length x n array of the estiamted second derivatives of longitudinal trajectories, where each column is the estimated second derivatives of longitudinal responses corresponding subject-specific log scaled ages in new.pred.data for each subject.

• boot.est.logTa n x num.boot array of the bootstrap estimated inflection points, where each row is a num.boot-length of boostrap estimates of the inflection point for each subject.

• ind.sdthe n-length of the estimated boostrap standard deviations, where each element is the estimated standard deviation of the bootstrap estimates for each subject (each row of boot.est.logT).

• cp.boota n x 2 array of the 95% bootstrap confidence intervals, where each row has the lower bound and the upper bound of the 95% confidence interval for the individual inflection point (i.e., 25th and 97.5th percentiles of the increasing ordered boostrap estimates for each row of boot.est.logT).

Examples

library(HDChangePoint)
## Specify parameters to generate true data
n=80;
model="arctan";
p=2;
bb0=2;
bb=0.1;
x.sd=0.3;
v1=5;
v2=7;
dist="normal";
eps.sd=0.05;
u.sd=0.05;

## generate data with seed number
set.seed(22)
outdat<-mydata(n=n, model=model, p=p, bb0=bb0, bb=bb, x.sd=x.sd,
v1=v1, v2=v2, dist=dist, eps.sd=eps.sd, u.sd=u.sd)

## Specify parameters for the parametric NLME procedure
num.boot=1000;
true.gam1=2.45/pi;
true.gam3=pi/1.1;
time.length=45;
eps.sd=0.05;
dist="normal";
para1=6.5;
para2=6.3;
para3=0;
para4=2.8;
para5=1.5;

## Do parametric NLME estimation
results<-main.arctan.nlme(n=n, model=model, dat=outdat, num.boot=num.boot, time.length=time.length,
true.gam1=true.gam1, true.gam3=true.gam3, para1=para1, para2=para2, para3=para3,
para4=para4, para5=para5, eps.sd=eps.sd, dist=dist)

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