Power calculation in joint modeling of longitudinal and survival data - k-th Order Trajectories and Unknown Sigma

Description

Compute the power in joint modeling of longitudinal and survival data when the variance-covariance matrix Sigma_Theta is unknown and the trajectories are order k.

The function computes power for a one-sided test, either

H_0: \beta = 0 \quad \mbox{ and } \quad H_{1A}: \beta > 0

or

H_0: \beta = 0 \quad \mbox{ and } \quad H_{1B}: \beta < 0

with Type I error \alpha. The choice of the alternative is determined by the sign of \beta. Negative values for \beta indicate that the alternative hypothesis is H_{1B}, while \beta \ge 0 indicates that it is H_{1A}.

It creates a powerLongSurv object.

Usage

powerLongSurv(
  N,
  nevents,
  tmedian,
  meantf,
  p,
  t,
  SigmaTheta,
  sigmae_2,
  ordtraj,
  beta = 0,
  alpha = 0.05,
  tol = 1.5e-08
)

Arguments

Details

The function powerLongSurv is used to calculate the power in joint modeling of longitudinal and survival data.

Value

An object of S4 class powerLongSurv, which has the following 12 components

Author(s)

Emil A. Cornea, Liddy M. Chen, Bahjat F. Qaqish, Haitao Chu, and Joseph G. Ibrahim

References

L. M. Chen, J. G. Ibrahim, and H. Chu. Sample size and power determination in joint modeling of longitudinal and survival data. Statist. Med. 2011, 30 2295-2309

See Also

powerLongSurv-class, show-methods

Examples

 ## Example 1.
 ## **********
 ## Input elements of Sigma_theta in forumula 4.6;
 SigmaTheta <- matrix(c(1.2,0.0,0.0,0.0,0.7,0.0,0.0,0.0,0.8),nrow=3,ncol=3)
 
 N        <-  200; # Total sample size;
 nevents  <-  140; # Number of events;
 tmedian  <-  0.7; # median survival;
 meantf   <-  1.4; # mean follow-up time;
 beta     <-  0.2; # Effect of the trajectory;
 alpha    <-  0.05;# Type-I Error (2-sided);
 sigmae_2 <-  0.09; # measurement error;
 
 ## schedule of measurement;
 t <- c(0.4, 0.8, 1.2, 1.6, 2) ; # maximum 2 year follow-up;
 
 ## Input estimated proportion subjects with 2,3,4,5,6 measurements;
 ## This is \xi in formula 4.6;
 ## The data is obtained from the simulated data for the calculation in table 2;
 p <- c(0.3, 0.4, 0.15, 0.1, 0.05);
 
 ## Input the order of trajectories
 ordtraj <- 1 ## linear trajectories
 
 ## Call function
 ## Linear Trajectories
 pLSl <- powerLongSurv(N, nevents, tmedian, meantf, p, t, SigmaTheta,
                       sigmae_2, ordtraj, beta, alpha=0.05)
 pLSl
 show(pLSl)
 unclass(pLSl)
 
 ## Constant Trajectories
 powerLongSurv(N, nevents, tmedian, meantf, p, t, SigmaTheta, sigmae_2,
               ordtraj=0, beta, alpha=0.05)
 
 ## Quadratic Trajectories
 powerLongSurv(N, nevents, tmedian, meantf, p, t, SigmaTheta, sigmae_2,
               ordtraj=2, beta, alpha=0.05)
 
 ## ***************************************************************************
 
 ## Example 2.
 ## **********
 ## Input elements of Sigma_theta in forumula 4.6;
 SigmaTheta <- matrix(c(1.2,0.0,0.0,0.0,0.7,0.0,0.0,0.0,0.8),nrow=3,ncol=3)
 
 N        <-  200; # Total sample size;
 nevents  <-  140; # Number of events;
 tmedian  <-  0.7; # median survival;
 meantf   <-  1.4; # mean follow-up time;
 beta     <-  0.2; # Effect of the trajectory;
 alpha    <-  0.05;# Type-I Error (2-sided);
 sigmae_2 <-  0.09; # measurement error;
 
 ## schedule of measurement;
 t <- c(0.4, 0.8, 1.2, 1.6);
 
 ## Input estimated proportion subjects with 2,3,4,5,6 measurements;
 ## This is \xi in formula 4.6;
 ## The data is obtained from the simulated data for the calculation in table 2;
 p <- c(0.3, 0.4, 0.2, 0.1);
 
 ## Input the order of trajectories
 ordtraj <- 2 ## quadratic trajectories
 
 ## Call function
 ## Quadratic Trajectories
 pLSq <- powerLongSurv(N,nevents,tmedian,meantf,p,t,SigmaTheta,sigmae_2,ordtraj,beta, alpha = 0.05)
 pLSq
 show(pLSq)
 unclass(pLSq)
 
 ## Constant Trajectories
 powerLongSurv(N, nevents, tmedian, meantf, p, t, SigmaTheta, sigmae_2,
               ordtraj=0, beta, alpha=0.05)
 
 ## Linear Trajectories
 powerLongSurv(N, nevents, tmedian, meantf, p, t, SigmaTheta, sigmae_2,
               ordtraj=1, beta, alpha=0.05)

Class "powerLongSurv"

Description

Class of objects like the output of function "powerLongSurv()".

Slots

title

Object of class "character"

subtitle

Object of class "character"

t

Object of class "vector"

p

Object of class "vector"

N

Object of class "integer"

nevents

Object of class "integer"

censr

Object of class "numeric"

tmedian

Object of class "numeric"

meantf

Object of class "numeric"

SigmaTheta

Object of class "matrix"

ordtraj

Object of class "integer"

BSigma

Object of class "matrix"

beta

Object of class "numeric"

alpha

Object of class "numeric"

power

Object of class "numeric"

Objects from the Class

Objects can be created by calls of the form new("powerLongSurv", ...).

Author(s)

Emil A. Cornea, Liddy M. Chen, Bahjat F. Qaqish, Haitao Chu, and Joseph G. Ibrahim

See Also

powerLongSurv, show-methods

Examples

showClass("powerLongSurv")

Methods for Function show

Description

Methods for function show

Usage

## S4 method for signature 'powerLongSurv'
show(object)

Arguments