help stpower cox dialog: stpower cox
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Title
[ST] stpower cox -- Sample size, power, and effect size for the Cox
proportional hazards model
Syntax
Sample-size determination
stpower cox [coef] [, options]
Power determination
stpower cox [coef], n(numlist) [options]
Effect-size determination
stpower cox, n(numlist) {power(numlist) | beta(numlist)} [options]
where coef is the regression coefficient (effect size) of a covariate of
interest, in a Cox proportional hazards model, desired to be detected
by a test with a prespecified power. coef may be specified either as
one number or as a list of values (see numlist) enclosed in
parentheses.
options description
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Main
* alpha(numlist) significance level; default is alpha(0.05)
* power(numlist) power; default is power(0.8)
* beta(numlist) probability of type II error; default is
beta(0.2)
* n(numlist) sample size; required to compute power or
effect size
* hratio(numlist) hazard ratio (effect size) associated with
a one-unit increase in covariate of
interest; default is hratio(0.5)
onesided one-sided test; default is two sided
sd(#) standard deviation of covariate of
interest; default is sd(0.5)
r2(#) squared coefficient of multiple correlation
with other covariates; default is r2(0)
failprob(#) overall probability of an event (failure)
of interest; default is failprob(1),
meaning no censoring
wdprob(#) the proportion of subjects anticipated to
withdraw from the study; default is
wdprob(0)
parallel treat number lists in starred options as
parallel (do not enumerate all possible
combinations of values) when multiple
values per option are specified
Reporting
hr report hazard ratio, not coefficient
table display results in a table with default
columns
columns(colnames) display results in a table with specified
colnames columns
notitle suppress table title
nolegend suppress table legend
colwidth(# [# ...]) column widths; default is colwidth(9)
separator(#) draw a horizontal separator line every #
lines; default is separator(0) meaning no
separator lines
saving(filename[, replace]) save the table data to filename; use
replace to overwrite existing filename
+ noheader suppress table header; seldom used
+ continue draw a continuation border in the table
output; seldom used
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* Starred options may be specified either as one number or as a list of
values (see numlist).
+ noheader and continue are not shown in the dialog box.
colnames description
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alpha significance level
power power
beta type II error probability
n total number of subjects
e total number of events (failures)
hr hazard ratio
coef coefficient (log hazard-ratio)
sd standard deviation
r2 squared multiple-correlation coefficient
pr overall probability of an event (failure)
w proportion of withdrawals
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By default, the following colnames are displayed:
power, n, e, sd, and alpha are always displayed;
coef is displayed, unless the hr option is specified, in which case
hr is displayed;
pr if overall probability of an event (failprob()) is specified;
r2 if squared multiple-correlation coefficient (r2()) is specified;
and
w if withdrawal proportion (wdprob()) is specified.
Menu
Statistics > Survival analysis > Power and sample size > Cox proportional
hazards model
Description
stpower cox estimates required sample size, power, and effect size for
survival analyses that use Cox proportional hazards (PH) models. It also
reports the number of events (failures) required to be observed in a
study. The estimates of sample size or power are obtained for the test
of the effect of one covariate, x1 (binary or continuous), on time to
failure adjusted for other predictors, x2,...,xp, in a PH model. The
command provides options to account for possible correlation between a
covariate of interest and other predictors and for withdrawal of subjects
from the study. Optionally, the minimal effect size (minimal detectable
difference in a regression coefficient, beta_1, or hazard ratio) may be
obtained for given sample size and power.
You can use stpower cox to
o calculate required number of events and sample size when you know
power and effect size expressed as a hazard ratio or a
coefficient (log hazard-ratio),
o calculate power when you know sample size (number of events) and
effect size expressed as a hazard ratio or a coefficient (log
hazard-ratio), and
o calculate effect size and display it as a coefficient (log
hazard-ratio) or a hazard ratio when you know sample size (number
of events) and power.
stpower cox's input parameter, coef, is the value beta_1a of the
regression coefficient, beta_1, of a covariate of interest, x1, from a
Cox PH model, which is desired to be detected by a test with prespecified
power.
Options
+------+
----+ Main +-------------------------------------------------------------
alpha(numlist) sets the significance level of the test. The default is
alpha(0.05).
power(numlist) sets the power of the test. The default is power(0.8).
If beta() is specified, this value is set to be 1-beta(). Only one
of power() or beta() may be specified.
beta(numlist) sets the probability of a type II error of the test. The
default is beta(0.2). If power() is specified, this value is set to
be 1-power(). Only one of beta() or power() may be specified.
n(numlist) specifies the number of subjects in the study to be used to
compute the power of the test or the minimal effect size (minimal
detectable value of the regression coefficient, beta_1, or hazard
ratio) if power() or beta() is also specified.
hratio(numlist) specifies the hazard ratio associated with a one-unit
increase in the covariate of interest, x1, when other covariates are
held constant. The default is hratio(0.5). This value defines the
minimal clinically significant effect of a covariate on the response
to be detected by a test with a certain power, specified in power(),
in a Cox PH model. If coef is specified, hratio() is not allowed and
the hazard ratio is instead computed as exp(coef).
onesided indicates a one-sided test. The default is two sided.
sd(#) specifies the standard deviation of the covariate of interest, x1.
The default is sd(0.5).
r2(#) specifies the squared multiple-correlation coefficient between x1
and other predictors x2, ..., xp in a Cox PH model. The default is
r2(0), meaning that x1 is independent of other covariates. This
option defines the proportion of variance explained by the regression
of x1 on x2, ..., xp (see [R] regress).
failprob(#) specifies the overall probability of a subject failing (or
experiencing an event of interest, or not being censored) in the
study. The default is failprob(1), meaning that all subjects
experience an event (or fail) in the study; that is, no censoring of
subjects occurs.
wdprob(#) specifies the proportion of subjects anticipated to withdraw
from a study. The default is wdprob(0). wdprob() may not be
combined with n().
parallel reports results sequentially (in parallel) over the list of
numbers supplied to options allowing numlist. By default, results
are computed over all combinations of the number lists in the
following order of nesting: alpha(), hratio() or list of coefficients
coef, power() or beta(), and n(). This option requires that options
with multiple values each contain the same number of elements.
+-----------+
----+ Reporting +--------------------------------------------------------
hr specifies that the hazard ratio be displayed rather than the
regression coefficient. This option affects how results are
displayed and not how they are estimated.
table displays results in a tabular format and is implied if any number
list contains more than one element. This option is useful if you
are producing results one case at a time and wish to construct your
own custom table by using a forvalues loop.
columns(colnames) specifies results in a table with specified colnames
columns. The order of columns in the output table is the same as the
order of colnames specified in columns(). Column names in columns()
must be space-separated.
notitle prevents the table title from displaying.
nolegend prevents the table legend from displaying and column headers
from being marked.
colwidth(# [# ...]) specifies column widths. The default is 9 for all
columns. The number of specified values may not exceed the number of
columns in the table. A missing value (.) may be specified for any
column to indicate the default width (9). If fewer widths are
specified than the number of columns in the table, the last width
specified is used for the remaining columns.
separator(#) specifies how often separator lines should be drawn between
rows of the table. The default is separator(0), meaning that no
separator lines should be displayed.
saving(filename[, replace]) creates a Stata data file (.dta file)
containing the table values with variable names corresponding to the
displayed colnames. replace indicates that filename be overwritten,
if it exists. saving() is appropriate only with tabular output.
The following options are available with stpower cox but are not shown in
the dialog box:
noheader prevents the table header from displaying. This option is
useful when the command is issued repeatedly, such as within a loop.
noheader implies notitle.
continue draws a continuation border at the bottom of the table. This
option is useful when the command is issued repeatedly within a loop.
Short introduction to stpower cox
The argument coef or option hratio() may be used to specify the effect
size desired to be detected by a test. If argument coef is omitted, then
the value of the log of the hazard ratio specified in the hratio() option
or the log of the default hazard-ratio value of 0.5 is used to compute
beta_1a. If argument coef is specified, then hratio() is not allowed and
the hazard ratio is computed as exp(coef).
If power determination is desired, then sample size n() must be
specified. Otherwise, sample-size determination is assumed with
power(0.8) (or, equivalently, beta(0.2)). The default setting for power
or, alternatively, the probability of a type II error, a failure to
reject the null hypothesis when the alternative hypothesis is true, may
be changed by using power() or beta(), respectively. If both n() and
power() (or beta()) are specified, the value of the regression
coefficient, beta_1a (or hazard ratio if the hr option is specified),
which can be detected by a test with requested power() for fixed sample
size n(), is computed.
The default probability of a type I error, a rejection of the null
hypothesis when the hypothesis is true, of a test is 0.05 but may be
changed by using the alpha() option. One-sided tests may be requested by
using onesided. By default, no censoring, no correlation between x1 and
other predictors, and no withdrawal of subjects from the study are
assumed. This may be changed by specifying failprob(), r2(), and
wdprob(), respectively.
Optionally, the results may be displayed in a table using table or
columns() as demonstrated in Examples below and in [ST] stpower. For
examples on how to plot a power curve, see Examples below, [ST] stpower,
and example 7 in [ST] stpower logrank.
Remarks on the method used in stpower cox
stpower cox implements the method of Hsieh and Lavori (2000) for the
sample-size and power computation, which reduces to the method of
Schoenfeld (1983) for a binary covariate. The sample size is related to
the power of a test through the number of events observed in the study;
that is, for a fixed number of events the power of a test is independent
of the sample size. As a result, the sample size is estimated as the
number of events divided by the overall probability of a subject failing
in a study. See Methods and formulas in [ST] stpower cox for the
formulas used in the computation.
Examples
Compute number of failures required to detect a 0.5 reduction in the
hazard for a binary covariate of interest with standard deviation 0.5,
using a one-sided 5% Wald test with a power of 80%
. stpower cox, onesided
Compute required sample size to detect a log hazard-ratio of -1 for a
covariate of interest with standard deviation 0.3, assuming only 85% of
subjects survive until the end of the study
. stpower cox -1, sd(0.3) failprob(0.85)
Compute power of the test just described for a sample size of 150,
assuming the covariate of interest is correlated with other covariates
with R2 = 0.3
. stpower cox -1, n(150) sd(0.3) failprob(0.8) r2(0.3)
Determine minimal detectable value of the coefficient (log hazard-ratio)
for the variable in the previous example with 90% power for a sample size
of 150
. stpower cox, n(150) power(0.9) sd(0.3) failprob(0.8) r2(0.3)
Obtain sample sizes for a range of hazard ratios and powers
. stpower cox, hratio(0.1(0.2)0.9) power(0.8 0.9) hr
Saved results
stpower cox saves the following in r():
Scalars
r(N) total number of subjects
r(E) total number of events (failures)
r(power) power of test
r(alpha) significance level of test
r(hratio) hazard ratio
r(onesided) 1 if one-sided test, 0 otherwise
r(sd) standard deviation
r(Pr_E) probability of an event (failure) (if specified)
r(r2) squared multiple correlation (if specified)
r(w) proportion of withdrawals (if specified)
Macros
r(metric) displayed metric (log-hazard or hazard)
References
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.
Schoenfeld, D. A. 1983. Sample-size formula for the proportional-hazards
regression model. Biometrics 39: 499-503.
Also see
Manual: [ST] stpower cox
Help: [ST] stpower, [ST] stpower logrank, [ST] stpower exponential,
[R] sampsi, [ST] stcox, [ST] glossary
