powerLongSurv: 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 $H_{0} : β = 0 and H_{1 A} : β > 0$ or $H_{0} : β = 0 and H_{1 B} : β < 0$ with Type I error $α$ . The choice of the alternative is determined by the sign of $β$ . Negative values for $β$ indicate that the alternative hypothesis is $H_{1 B}$ , while $β \geq 0$ indicates that it is $H_{1 A}$ .

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-8)

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

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.

Author

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

Maintainer: Shannon T. Holloway <sthollow@ncsu.edu>

Details

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

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

Examples

Run this code

## 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)

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