nSurvival {gsDesign}R Documentation

3.3: Time-to-event sample size calculation (Lachin-Foulkes)

Description

nSurvival() is used to calculate the sample size for a clinical trial with a time-to-event endpoint. The Lachin and Foulkes (1986) method is used.

Usage

nSurvival(lambda.0, lambda.1, Ts, Tr, eta = 0, rand.ratio = 1,
      alpha = 0.05, beta = 0.10, sided = 2, approx = FALSE,
      type = c("rr", "rd"), entry = c("unif", "expo"), gamma = NA)

Arguments

lambda.0, lambda.1 event hazard rate for placebo and treatment group respectively.
eta equal dropout hazard rate for both groups.
rand.ratio randomization ratio between placebo and treatment group. Default is balanced design, i.e., randomization ratio is 1.
Ts maximum study duration.
Tr accrual (recruitment) duration.
alpha type I error rate. Default is 0.05 since 2-sided testing is default.
beta type II error rate. Default is 0.10 (90% power).
sided one or two-sided test? Default is two-sided test.
approx logical. If TRUE, the approximation sample size formula for risk difference is used.
type type of sample size calculation: risk ratio (“rr”) or risk difference (“rd”).
entry patient entry type: uniform entry ("unif") or exponential entry ("expo").
gamma rate parameter for exponential entry. NA if entry type is "unif" (uniform). A non-zero value is supplied if entry type is "expo" (exponential).

Details

nSurvival produces the number of subjects and events for a set of pre-specified trial parameters, such as accrual duration and follow-up period. The calculation is based on Lachin and Foulkes method and can be used for risk ratio or risk difference. The function also consider non-uniform entry as well as uniform entry.

If the logical approx is TRUE, the variance under alternative hypothesis is used to replace the variance under null hypothesis.

For non-uniform entry. a non-zero value of gamma for exponential entry must be supplied. For positive gamma, the entry distribution is convex, whereas for negative gamma, the entry distribution is concave.

Value

nSurvival produces a list with the following component returned:

Method As input.
Entry As input.
Sample.size Number of subjects.
Num.events Number of events.
Hazard.p, Hazard.t hazard rate for placebo and treatment group. As input.
Dropout as input.
Frac.p, Frac.t randomization proportion for placebo and treatment. As input.
Gamma as input.
Alpha as input.
Beta as input.
Sided as input.
Study.dura Study duration.
Accrual Accrual period.

Author(s)

Shanhong Guan shanhong_guan@merck.com

References

Lachin JM and Foulkes MA (1986), Evaluation of Sample Size and Power for Analyses of Survival with Allowance for Nonuniform Patient Entry, Losses to Follow-Up, Noncompliance, and Stratification. Biometrics, 42, 507-519.

Examples


# consider a trial with 
# 2 year maximum follow-up
# 6 month uniform enrollment
# Treatment/placebo hazards = 0.1/0.2 per 1 person-year
# drop out hazard 0.1 per 1 person-year
# alpha = 0.05 (two-sided)
# power = 0.9 (default beta=.1)

ss <- nSurvival(lambda.0=.2 , lambda.1=.1, eta = .1, Ts = 2, Tr = .5,
                sided=1, alpha=.025)

#  symmetric, 2-sided design with O'Brien-Fleming-like boundaries
#  sample size is computed based on a fixed design requiring n=100
        x<-gsDesign(k = 5, test.type = 2)
        x
# boundary plot
        plot(x)
# power plot
        plot(x, plottype = 2)
# total sample size
   ceiling(x$n.I[x$k] * ss$Sample.size)
# number of events at analyses
   ceiling(ss$Num.events * x$n.I)

[Package gsDesign version 2.0-5 Index]