sampleSizeSurvival: Compute sample size for a survival endpoint

In felix-hof/biostatUZH: Misc Tools of the Department of Biostatistics, EBPI, University of Zurich

Compute sample size for a survival endpoint

Description

Calculates two of the following quantities if one of them is given: Sample size, required number of events and power. The distribution of survival times is assumed to be either non-parametric given a Kaplan-Meier estimate or following an exponential or Weibull model given rate parameters or scale and shape parameters, respectively. The same time unit should be used for the survival times, the accrual period and the follow-up period.

Usage

sampleSizeSurvival(
  HR,
  a.length,
  f.length,
  sig.level = 0.05,
  power = NULL,
  n = NULL,
  n.events = NULL,
  alloc.ratio = 1,
  drop.rate = 0,
  non.inf.margin = 0,
  dist = c("exponential", "weibull", "non-parametric"),
  lambda = NULL,
  shape = NULL,
  survfit.ref = NULL,
  alternative = c("two.sided", "one.sided"),
  method = c("exact", "approx")
)

Arguments

HR	Hazard ratio of experimental group vs. control group.
a.length	Length of accrual period.
f.length	Length of follow-up period.
sig.level	Significance level.
power	Desired power.
n	Required sample size.
n.events	Required total number of events.
alloc.ratio	Allocation ratio: Ratio of the number of patients in the experimental group divided by the number of patients in the control group.
drop.rate	Drop-out rate.
non.inf.margin	Non-inferiority margin.
dist	Distributional assumption for survival times. Either "exponential", "weibull" or "non-parametric". Default is "exponential".
lambda	The rate parameter in the exponential distribution and the scale parameter in the Weibull distribution.
shape	The shape parameter of the Weibull distribution
survfit.ref	The survfit object, i.e. the Kaplan-Meier estimate of survival in the control group.
alternative	Either "one.sided" or "two.sided" depending on whether the alternative hypothesis is one- or two-sided.
method	Either "exact" or "approx", indicating whether the integral for the probability of event is solved by integration the function or approximated. If a non-parametric approach is chosen only the approximate approach is available.

Value

A list with the entries

n	Required total sample size.
HR	Hazard ratio of experimental group vs. control group.
power	Power of the study.
sig.level	Significance level.
alternative	Indicates whether the the alternative hypothesis is one- or two-sided.
distribution	Distributional assumption for survival times. Either "exponential" for exponential, "weibull" or "non-parametric".
PrEvent	Probability that a patient will experience the event during the study.
Events	Required total number of events.

Author(s)

Uriah Daugaard and Leonhard Held
[e-mail]

References

Collett, D. (2015). Modelling Survival Data in Medical Research. New York: Chapman and Hall/CRC.

Schoenfeld, D.A. (1983). Sample-Size Formula for the Proportional-Hazards Regression Model. Biometrics, 39, 499–503.

See Also

The function sampleSizeSurvival depends on survEvents and PrEvent.

Examples

## survival of females in lung cancer data
data(lung, package = "survival")
lung.female <- subset(lung, sex == 2)
survObj <- Surv(time = lung.female$time, event=lung.female$status == 2,
                type='right')
fit <- survfit(survObj ~ 1)
## exponential model
exp.reg <- survreg(survObj~1, dist = "exponential")
## Weibull model
weib.reg <- survreg(survObj~1, dist = "weibull")

## estimate the sample size with 5 different approaches

## Non-parametric
sampleSizeSurvival(HR = 0.65, power = 0.9, a.length = 400,
                   f.length = 400, dist = "non-parametric", survfit.ref = fit,
                   alloc.ratio = 1, method = "approx")

## Exponential, approximate
exp.lambda <- 1/exp(coef(exp.reg))
sampleSizeSurvival(HR = 0.65, power = 0.90, a.length = 400,
                   f.length = 400, dist = "exponential",
                   lambda = exp.lambda,
                   alloc.ratio = 1, method = "approx")

## Exponential, exact
sampleSizeSurvival(HR = 0.65, power = 0.90, a.length = 400,
                   f.length = 400, dist = "exponential",
                   lambda = exp.lambda,
                   alloc.ratio = 1, method = "exact")

weib.scale <- unname(exp(coef(weib.reg)))
weib.shape <- unname(1/weib.reg$scale)
## Weibull, approximate
sampleSizeSurvival(HR = 0.65, power = 0.90, a.length = 400,
                   f.length = 400, dist = "weibull", lambda = weib.scale,
                   alloc.ratio = 1, shape = weib.shape,
                   method = "approx")

## Weibull, exact
sampleSizeSurvival(HR = 0.65, power = 0.90, a.length = 400,
                   f.length = 400, dist = "weibull", lambda = weib.scale,
                   alloc.ratio = 1, shape = weib.shape,
                   method = "exact")

felix-hof/biostatUZH documentation built on Sept. 27, 2024, 1:48 p.m.