Package '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)

---

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

object

An object of class powerLongSurv

---