Power and Sample Size
Power and sample size analysis optimizes the resource usage and design of a study, improving chances of conclusive results with maximum efficiency. The standard statistical testing paradigm implicitly assumes that Type I errors (mistakenly concluding significance when there is no true effect) are more costly than Type II errors (missing a truly significant result). This may be appropriate for your situation, or the relative costs of the two types of error may be reversed. Power and sample size analysis can help you achieve your desired balance between Type I and Type II errors. With optimal designs and sample sizes, you can improve your chances of detecting effects that might otherwise have been ignored, save money and time, and perhaps minimize risks to subjects.
The SAS/STAT power and sample size procedures include the following:
 GLMPOWER Procedure — Performs prospective power and sample size analysis for linear models
 POWER Procedure — Performs prospective power and sample size analyses for a variety of statistical analyses
 SEQDESIGN Procedure — Designs interim analyses for group sequential clinical trials
 SEQTEST Procedure — Performs interim analyses for group sequential clinical trials
GLMPOWER Procedure
Power and sample size analysis optimizes the resource usage and design of a study, improving chances of conclusive results with
maximum efficiency. The GLMPOWER procedure performs prospective power and sample size analysis for linear models, with a variety of goals:
 determining the sample size required to get a significant result with adequate probability (power)
 characterizing the power of a study to detect a meaningful effect
 conducting whatif analyses to assess sensitivity of the power or required sample size to other factors
The following are highlights of the GLMPOWER procedure's features:
 statistical analyses that are covered include Type III F tests and contrasts of
fixed effects in univariate and multivariate linear models, optionally with covariates
 for multivariate models, you can choose from the following tests:
 Wilks' lambda
 HotellingLawley trace
 Pillai's trace
 for the univariate approach to repeated measures, you can choose from the following types of F tests:
 uncorrected
 GreenhouseGeisser
 HuynhFeldt
 Box conservative

 supports BY group processing, which enables you to obtain separate analyses for grouped observations
 creates a SAS data set that corresponds to any output table
 automatically creates graphs by using ODS Graphics

For further details, see
GLMPOWER Procedure
POWER Procedure
The POWER procedure performs prospective power and sample size analyses for a variety of goals, such as the following:
 provides analysis for the following:
 t tests, equivalence tests, and confidence intervals for means
 tests, equivalence tests, and confidence intervals for binomial proportions
 multiple regression
 tests of correlation and partial correlation
 oneway analysis of variance
 rank tests for comparing two survival curves
 logistic regression with binary response
 WilcoxonMannWhitney (ranksum) test
 Cox proportional hazards regression
 FarringtonManning noniferiority tests of relative risk

 determining the sample size required to get a significant result with adequate probability (power)
 characterizing the power of a study to detect a meaningful effect
 conducting whatif analyses to assess sensitivity of the power or required sample size to other factors
 creates a SAS data set that corresponds to any output table
 automatically creates graphs by using ODS Graphics

For further details, see
POWER Procedure
SEQDESIGN Procedure
The purpose of the SEQDESIGN procedure is to design interim analyses for group sequential clinical trials. A group sequential trial provides for interim analyses before the formal
completion of the trial while maintaining the specified overall Type I and Type II error probability levels.
The SEQDESIGN procedure assumes that the standardized test statistics for the null hypothesis at the stages have the joint canonical distribution with the information levels at the stages for
the parameter. This implies that these test statistics are normally distributed. If the test statistic is not normally distributed, then it is assumed that the test statistic is computed from a large
sample such that the statistic has an approximately normal distribution.
You can use the SEQDESIGN procedure to compute required sample sizes for commonly used hypothesis tests.
The applicable tests include tests for binomial proportions and the logrank test for
two survival distributions.
Output from the SEQDESIGN Procedure
In addition to computing the boundary values for a group sequential design, the SEQDESIGN procedure computes the following quantities:
 maximum sample size (as a percentage of the corresponding fixedsample size) if the trial does not stop at an interim stage
 average sample sizes (as a percentage of the corresponding fixedsample size) under various hypothetical references, including the null and alternative references
 stopping probabilities at each stage under various hypothetical references to indicate how likely it is that the trial will stop at that stage

 sample sizes required at each stage for the specified hypothesis test with nonsurvival data at each stage for the specified hypothesis test with survival data
 numbers of events required at each stage for the specified hypothesis test with survival data

You can create more than one design with multiple DESIGN statements in the SEQDESIGN procedure and then choose the design with the most desirable features.
Group Sequential Methods
For a group sequential design, there are two possible boundaries for a onesided test and four possible
boundaries for a twosided test. Each boundary consists of one boundary value (critical value)
for each stage. The SEQDESIGN procedure provides the following methods for computing the boundary values:
 fixed boundary shape methods, which derive boundaries with specified boundary shapes
 Whitehead methods, which adjust boundaries derived for continuous monitoring so that they apply to discrete monitoring


For further details, see
SEQDESIGN Procedure
SEQTEST Procedure
The purpose of the SEQTEST procedure is to perform interim analyses for group sequential clinical trials. A group sequential trial provides for interim analyses before the formal completion of
the trial while maintaining the specified overall Type I and Type II error probability levels.
Features of the SEQTEST Procedure
At each stage, the data are analyzed with a statistical procedure such as the
REG procedure, and a test statistic and its associated information level are computed. The
information level is the amount of information available about the unknown parameter. For a maximum likelihood statistic, the information level is the inverse of its variance.
You then use the SEQTEST procedure to compare the test statistic with the corresponding boundary values obtained with the SEQDESIGN procedure.
If the information levels do not match the information levels specified in the design, the SEQTEST procedure modifies the boundary values to adjust for new information levels.
At the end of a trial, the parameter estimate is computed. The median unbiased estimate, confidence limits,
and pvalue depend on the specified sample space ordering.
A sample space ordering specifies the ordering for test statistics resulting in the stopping of a trial.
That is, for all the statistics in the rejection region and in acceptance region, the SEQTEST procedure
provides three different sample space orderings: the stagewise ordering uses counterclockwise
ordering around the continuous region, the LR ordering uses the distance between
the observed Z statistic, z, and its hypothetical value, and the MLE ordering uses the observed maximum likelihood estimate.
Note that for some clinical trials, the information levels are derived from statistics based on individuals
specified in the design plan and might not reach the target information levels. Thus, instead of specifying
the number of individuals in the protocol, the information levels can be specified. You can then adjust
the sample sizes to achieve the information levels for the trial.
Output from the SEQTEST Procedure
In addition to the boundary values and test statistics for the group sequential trial,
the SEQTEST procedure also computes the following quantities:
 average sample sizes (as a percentage of the corresponding fixedsample size) under various hypothetical references, including the null and alternative references
 stopping probabilities at each stage under various hypothetical references to indicate how likely it is that the trial will stop at that stage
 conditional power given the most recently observed statistic under specified hypothetical references

 predictive power given the most recently observed statistic
 repeated confidence intervals for the parameter from the observed statistic at each stage
 parameter estimate, pvalue for hypothesis testing, and median and confidence limits for the parameter at the conclusion of a sequential trial

For further details, see
SEQTEST Procedure