powerLongSurv {JMdesign}

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

N

numeric specifying the total sample size; minimum 20.

nevents

numeric specifying the number of events; at least 20 and at most N.

tmedian

numeric specifying the median survival time; positive

meantf

numeric specifying the mean follow-up time; positive and no greater than max(t).

p

numeric vector of estimated subject proportions with 2,3,... measurements, respectively, zero proportions allowed.

t

numeric vector of measurement times, distinct positive components; same length as p.

SigmaTheta

numeric matrix specifying the covariance matrix Sigma_Theta

sigmae_2

numeric specifying the measurement error; positive.

ordtraj

integer specifying the order of trajectories, must be less the order of Sigma_Theta

beta

numeric specifying the effect of the trajectory; default value 0.

alpha

numeric, strictly between 0.0 and 1.0, specifying the Type-I Error (2-sided), default value 0.05.

tol

numeric, For floating point objects x and y, if |x-y| <= tol, x==y. Passed to R function all.equal.

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

title

character string

subtitle

character string

t

numeric vector

p

numeric vector

N

integer

nevents

integer

censr

numeric

tmedian

numeric

meantf

numeric

SigmaTheta

numeric matrix

ordtraj

integer

BSigma

numeric matrix

beta

numeric

alpha

numeric

power

numeric

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)