help stpower dialogs: stpower cox
stpower logrank
stpower exponential
-------------------------------------------------------------------------------
Title
[ST] stpower -- Sample-size, power, and effect-size determination for
survival analysis
Syntax
Sample-size determination
stpower cox [...] [, ...]
stpower logrank [...] [, ...]
stpower exponential [...] [, ...]
Power determination
stpower cox [...], n(numlist) [...]
stpower logrank [...], n(numlist) [...]
stpower exponential [...], n(numlist) [...]
Effect-size determination
stpower cox, n(numlist) {power(numlist) | beta(numlist)} [...]
stpower logrank [...], n(numlist) {power(numlist) | beta(numlist)}
[...]
See [ST] stpower cox, [ST] stpower logrank, and [ST] stpower exponential.
Description
stpower computes sample size and power for survival analysis comparing
two survivor functions using the log-rank test or the exponential test
(to be defined later), as well as for more general survival analysis
investigating the effect of a single covariate in a Cox proportional
hazards regression model, possibly in the presence of other covariates.
It provides the estimate of the number of events required to be observed
(or the expected number of events) in a study. The minimal effect size
(minimal detectable difference, expressed as the hazard ratio or the log
hazard-ratio) may also be obtained for the log-rank test and for the Wald
test on a single coefficient from the Cox model.
Introduction to stpower subcommands
stpower offers three subcommands: stpower cox, stpower logrank, and
stpower exponential.
stpower cox provides estimates of sample size, power, or the minimal
detectable value of the coefficient when an effect of a single
covariate on subject survival is to be explored using the Cox
proportional hazards regression. It is assumed that the effect is to
be tested using the partial likelihood from the Cox model (for
example, score or Wald test), on the coefficient of the covariate of
interest.
stpower logrank reports estimates of sample size, power, or minimal
detectable value of the hazard ratio in the case when the two
survivor functions are to be compared using the log-rank test. The
only requirement about the distribution of the survivor functions is
that the two survivor functions must satisfy the proportional-hazards
assumption.
stpower exponential reports estimates of sample size or power when
the disparity in the two exponential survivor functions is to be
tested using the exponential test, the parametric test which test
statistic is a function of the maximum likelihood estimators of the
two exponential hazard rates. In particular, we refer to
(exponential) hazard-difference test as the exponential test for the
difference between hazards, and the (exponential) log hazard ratio
test as the exponential test for the log of the hazard ratio or,
equivalently, for the difference between log hazards.
All subcommands share a common syntax. Sample-size determination with a
power of 80% or, equivalently, a probability of a type II error, a
failure to reject the null hypothesis when the alternative hypothesis is
true, of 20% is the default. Other values of power or type II error
probability may be supplied via options power() or beta(), respectively.
If power determination is desired, sample size n() must be specified. If
the minimal detectable difference is of interest, both sample size n()
and power() (or type II error probability beta()) must be specified.
For sample size and power computation the default effect size corresponds
to a value of the hazard ratio of 0.5 and may be changed by specifying
option hratio(). The hazard ratio is defined as a ratio of hazards of
the experimental group to the control group (or the less favorable of the
two groups). In addition, alternative ways of specifying the effect size
are available, and these are particular to each of the subcommands.
The default probability of a type I error, a rejection of the null
hypothesis when the null hypothesis is true, of a test is 0.05 but may
changed by using option alpha(). Results for one-sided tests may be
requested by using option onesided. In order to change the default
setting of equal-sized groups in stpower logrank and stpower exponential,
one of options p1() or nratio() must be specified.
By default, all subcommands assume a type I study, that is, perform
computations for uncensored data. Also see Theory and terminology in
[ST] stpower. The censoring information may be taken into account by
specifying the appropriate arguments or options. Refer to [ST] stpower
cox, [ST] stpower logrank, and [ST] stpower exponential for details.
All subcommands can report results in a table. Results may be tabulated
for varying values of input parameters; see examples below and section
Creating output tables in [ST] stpower. An example of how to produce a
power curve is given below; also see section Power curves in [ST] stpower
and section Power and effect-size determination in [ST] stpower logrank.
Remarks on the methods used in stpower subcommands
All sample-size formulas used by stpower rely on the proportional-hazards
assumption, that is, the assumption that the hazard ratio does not depend
on time. See the documentation entry of each subcommand for the
additional assumptions imposed by the methods it uses.
stpower cox adopts the method of Hsieh and Lavori (2000) to compute
sample size and power for the test of a covariate obtained after the
Cox model fit.
stpower logrank uses the approach of Freedman (1982) and Schoenfeld
(1981) for sample-size and power computation. The approach of
Schoenfeld (1983) is used to obtain the estimates in the presence of
uniform accrual.
stpower exponential implements methods of Lachin (1981); Lachin and
Foulkes (1986); George and Desu (1974); and Rubinstein, Gail, and
Santner (1981) for the two-sample test of exponential survivor
functions. The explicit sample-size formula for the last method was
given in Lakatos and Lan (1992).
Examples
Cox model
Compute sample size required to detect a coefficient of -1 on a covariate
of interest with a standard deviation of 0.5 using a two-sided 5% Wald
test with 80% power (the default)
. stpower cox -1
Compute power of the test just described for a sample of 50 observations
. stpower cox -1, n(50)
Compute minimal value of coefficient that can be detected with 95% power
for a sample size of 50, assuming the covariate of interest has a
standard devation of 0.5 (the default)
. stpower cox, power(0.95) n(50)
Log-rank test
Compute sample size required to test the disparity in two survivor
functions corresponding to a 50% reduction in the hazard of the
experimental group (a hazard ratio of 0.5), using the default two-sided
5% log-rank test with 80% power
. stpower logrank 0.6
Compute power of the test just described for a sample size of 300
. stpower logrank 0.6, n(300)
Compute minimal value of hazard ratio that can be detected with 80% power
and a sample size of 300 when the probability of surviving to the end of
the study is 0.6 for the control group
. stpower logrank 0.6, n(300) power(0.8)
Produce a power curve as a function of the hazard ratio for a sample size
of 100
. stpower logrank, hratio(0.01(0.01)0.99) n(100) saving(mypower)
. use mypower
. twoway line power hr, xtitle(hazard ratio) title("Power (n=100)")
Exponential test
Compute sample size required to test the disparity in two exponential
survivor functions corresponding to a reduction in the hazard rate of the
experimental group from 0.2 to 0.4, using the default two-sided 5%
exponential test with 80% power
. stpower exponential 0.2 0.4
Compute power of the test just described for a sample size of 100
. stpower exponential 0.2 0.4, n(100)
References
Freedman, L. S. 1982. Tables of the number of patients required in
clinical trials using the logrank test. Statistics in Medicine 1:
121-129.
George, S. L., and M. M. Desu. 1974. Planning the size and duration of a
clinical trial studying the time to some critical event. Journal of
Chronic Diseases 27: 15-24.
Hsieh, F. Y., and P. W. Lavori. 2000. Sample-size calculations for the
Cox proportional hazards regression model with nonbinary covariates.
Controlled Clinical Trials 21: 552-560.
Lachin, J. M. 1981. Introduction to sample size determination and power
analysis for clinical trials. Controlled Clinical Trials 2: 93-113.
Lachin, J. M., and M. A. Foulkes. 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.
Lakatos, E., and K. K. G. Lan. 1992. A comparison of sample size methods
for the logrank statistic. Statistics in Medicine 11: 179-191.
Rubinstein, L. V., M. H. Gail, and T. J. Santner. 1981. Planning the
duration of a comparative clinical trial with loss to follow-up and a
period of continued observation. Journal of Chronic Diseases 34:
469-479.
Schoenfeld, D. A. 1981. The asymptotic properties of nonparametric tests
for comparing survival distributions. Biometrika 68: 316-319.
------. 1983. Sample-size formula for the proportional-hazards
regression model. Biometrics 39: 499-503.
Also see
Manual: [ST] stpower
Help: [ST] stpower cox, [ST] stpower exponential, [ST] stpower
logrank, [R] sampsi, [ST] glossary
