SurvGSD (version 1.0.0)

SSize.FixAlter: Maximum sample size for a group sequential test under a generalized gamma survival distribution or a log-logistic survival distribution.

Description

A function obtains maximum sample sizes and associated expected values for a group sequential design under a generalized gamma survival distribution or a log-logistic survival distribution for a given dropout censoring distribution.

Usage

SSize.FixAlter(t, R, T, FUN.C, para0, para1 = NULL, haz.r, rho = 0,
  eta = 1, theta = 0, px = 0.5, spf = 1, alpha = 0.05, power = 0.8)

Arguments

t

the interim analysis time (vector).

R

the recuritment duration.

T

the study duration.

FUN.C

the cumulative distribution function of dropout censoring. FUN.C = function(y) punif(y,0,h) for a uniform dropout censoring U(0,h); FUN.C = function(y) rep(0,length(y)) for assuming no dropout censoring.

para0

c(q0,mu0,sigma0), parameters of an assumed generalized gamma distribution for the control arm. A character string q0="LLG" indiactes an assumed log-logistic survival distribution \(F_0(y;\xi,\zeta)=1/(1+(y/\xi)^{-\zeta})\) for the control arm, where \(\xi\) = mu0 and \(\zeta\) = sigma0.

para1

c(q1,mu1,sigma1), parameters of an assumed generalized gamma distribution for the treatment arm. A character string q1="LLG" indiactes an assumed log-logistic survival distribution \(F_1(y;\xi,\zeta)=1/(1+(y/\xi)^{-\zeta})\) for the treatment arm, where \(\xi\) = mu1 and \(\zeta\) = sigma1.

haz.r

the hazard ratio of the treatment arm to the control arm (numeric or function).

rho

the power in the weight of the Harrington-Fleming statistic. \(\rho=0\) for the logrank test; \(\rho=1\) for the Wilcoxon test.

eta, theta

parameters of the entry distribution with \(\eta \ge -\theta/R\) and \(\eta >0\) (\(\theta=0\) for the Uniform dropout censoring).

px

the proportion of patients assigned to the treatment arm. The default is px = 0.5 indicating 1:1 allocation.

spf

1 = O<U+2019>Brien-Fleming-type; 2 = Pocock-type alpha-spending function. The default is spf = 1.

alpha

the type I error. The default is alpha = 0.05.

power

A desired value of the power. The default is power = 0.8.

Value

MaxSize

the maximum sample size.

ExpSize

the expected sample size.

ExpEvent

the expected number of events.

A.power

actual achieved power.

Info.fractions

information fractions at times of all the interim analyses.

boundary

the monitoring boundary values of the standardized Harrington-Fleming statistic at all the interim analyses.

References

Hsu, C.-H., Chen, C.-H, Hsu, K.-N. and Lu, Y.-H. (2018). A useful design utilizing the information fraction in a group sequential clinical trial with censored survival data. To appear in Biometrics.

Azzalini, A. and Genz, A. (2015). The R package `mnormt': The multivariate normal and 't' distributions (version 1.5-3). URL http://azzalini.stat.unipd.it/SW/Pkg-mnormt.

Casper, C. and Perez, O. A. (2014). The R package `ldbounds': Lan-DeMets method for group sequential boundaries (version 1.1-1). URL https://cran.r-project.org/web/packages/ldbounds/index.html.

Jackson, C., Metcalfe, P. and Amdahl, J. (2017). The R package `flexsurv': Flexible Parametric Survival and Multi-State Models (version 1.1). URL https://github.com/chjackson/flexsurv-dev.

Examples

# NOT RUN {
# Assume an exponential (log-logistic) survival distribution
# with q0=sigma0=1, mu0=0.367 (xi0=1, zeta0=1.75) for the control arm,
# a uniform patient entry (eta=1,theta=0) and a uniform dropout censoring distribution Unif(0,h)
# having a 15% censoring probability (lfu=0.15) for a study with R=2, T=3 and the interim
# analysis time at t=1,1.5,2,2.5.

# To obtain the required h for the uniform dropout censoring distribution.
Find.h(lfu=0.15, R=2, T=3, q=1, mu=0.367, sigma=1, eta=1, theta=0) ## exponential
Find.h(lfu=0.15, R=2, T=3, q="LLG", mu=1, sigma=1.75, eta=1, theta=0) ## log-logistic

# To obtain the maximum sample size for testing a treatment difference of a hazard ratio of 2/3
# with a type-I error of 0.05 and a power of 0.8.
SSize.FixAlter(t=c(1,1.5,2,2.5), R=2, T=3, FUN.C=function(y) punif(y,0,7.018),
para0=c(1,0.367,1), para1=NULL, haz.r=2/3, rho=0, eta=1, theta=0) # exponential
SSize.FixAlter(t=c(1,1.5,2,2.5), R=2, T=3, FUN.C=function(y) punif(y,0,7.211),
para0=c("LLG",1,1.75), para1=NULL, haz.r=2/3, rho=0, eta=1, theta=0) # log-logistic

# To obtain the maximum sample size for testing H_0:F_0=F_1 with a type-I error of 0.05
# and a power of 0.8, where F_1 is an exponential (log-logistic) distribution
# with the parameter para1=c(1,0.772,1) (para1=c("LLG",1.5,1.75)).
SSize.FixAlter(t=c(1,1.5,2,2.5), R=2, T=3, FUN.C=function(y) punif(y,0,7.018),
para0=c(1,0.367,1), para1=c(1,0.772,1), haz.r=NULL, rho=0, eta=1, theta=0) # exponential
SSize.FixAlter(t=c(1,1.5,2,2.5), R=2, T=3, FUN.C=function(y) punif(y,0,7.211),
para0=c("LLG",1,1.75), para1=c("LLG",1.5,1.75), haz.r=NULL, rho=0, eta=1, theta=0) # log-logistic

# }