The SEQTEST Procedure

PROC SEQTEST Statement

Subsections:

Table Output Options
Graphics Output Options

The PROC SEQTEST statement invokes the SEQTEST procedure. Table 90.1 summarizes the options available in the PROC SEQTEST statement.

Table 90.1: Summary of PROC SEQTEST Options

Option	Description
Input Data Sets
BOUNDARY=	Specifies the data set for boundary information
DATA=	Specifies the data set for parameter estimates and information levels
PARMS=	Specifies the data set for parameter estimates and standard errors
Boundaries
BETABOUNDARY=	Specifies whether the $\beta$ boundary is used in the computation
	of the Type I error level $\alpha$
BETAOVERLAP=	Checks for overlapping of the lower and upper $\beta$ boundaries
	at the current and subsequent interim stages in a two-sided design
BOUNDARYKEY=	Specifies the boundary key to maintain Type I and II error probability levels
BOUNDARYSCALE=	Specifies the boundary scale
ERRSPENDADJ=	Specifies error spending methods for boundary adjustments
ERRSPENDMIN=	Specifies minimum error spending values for the boundaries
INFOADJ=	Specifies whether information levels at future interim stages should be
	adjusted
NSTAGES=	Specifies the number of stages
Test Statistics
DATA( INFOVAR= )	Specifies the information variable in the DATA= data set
DATA( TESTVAR= )	Specifies the test variable in the DATA= data set
PARMS( INFOVAR= )	Specifies the information variable in the PARMS= data set
PARMS( TESTVAR= )	Specifies the test variable in the PARMS= data set
p-Values and Confidence Intervals
CIALPHA=	Specifies the significance levels for the confidence interval
CITYPE=	Specifies the types of confidence interval
ORDER=	Specifies the ordering of the sample space used to derive
	the p-values and confidence limits
Table Output
CONDPOWER	Displays conditional powers
ERRSPEND	Displays the cumulative error spending at each stage
PREDPOWER	Displays the predictive powers
PSS	Displays the powers and expected sample sizes
RCI	Displays the repeated confidence intervals
STOPPROB	Displays the expected cumulative stopping probabilities
Graphics Output
PLOTS=ASN	Displays the expected sample numbers plot
PLOTS=CONDPOWER	Displays the conditional powers plot
PLOTS=ERRSPEND	Displays the error spending plot
PLOTS=POWER	Displays the powers plot
PLOTS=RCI	Displays the repeated confidence intervals plot
PLOTS=TEST	Displays the boundary plot with test statistics

The BOUNDARY= option provides the information for the design and is required in the PROC SEQTEST statement. By default, the SEQTEST procedure displays tables of design information and test information. If ODS Graphics is enabled, the procedure also displays a sequential test plot.

The following options can be used in the PROC SEQTEST statement. They are listed in alphabetical order.

BETABOUNDARY=BINDING | NONBINDING

specifies whether the $\beta$ boundary is used in the computation of the Type I error level $\alpha$ . The BETABOUNDARY=BINDING option computes the Type I error probability with the $\beta$ (acceptance) boundary, and the BETABOUNDARY=NONBINDING suboption computes the Type I error probability without the $\beta$ boundary (Zhu, Ni, and Yao, 2011, pp. 132–133). For a detailed description of nonbinding acceptance boundary, see the section "Acceptance ( $\bbeta$ ) Boundary" in Chapter 89: The SEQDESIGN Procedure. The default is BETABOUNDARY=BINDING.

BETAOVERLAP=ADJUST | NOADJUST OVERLAP=ADJUST | NOADJUST

specifies whether to check for overlapping of the lower and upper $\beta$ boundaries for the two corresponding one-sided tests at the current and subsequent interim stages. This option applies to two-sided designs with early stopping to accept $H_0$ , or to either accept or reject $H_0$ . This type of overlapping might result from a small $\beta$ spending at an interim stage. When you specify BETAOVERLAP=ADJUST, the procedure checks for this type of overlapping at the current and subsequent interim stages. If such overlapping is found, the $\beta$ boundaries for the two-sided design at that stage are set to missing, and the $\beta$ spending values at subsequent stages are adjusted, as described in the section Boundary Adjustments for Overlapping Lower and Upper beta Boundaries.

You can specify BETAOVERLAP=NOADJUST to request that no adjustment be made. The default is BETAOVERLAP=ADJUST.

BOUNDARY=SAS-data-set

names the required SAS data set that contains the design boundary information. At stage 1, the data set is usually created from the "Boundary Information" table created by the SEQDESIGN procedure. At each subsequent stage, the data set is usually created from the "Test Information" table created by the SEQTEST procedure at the previous stage. The data set includes the variables _Scale_ for the boundary scale, _Stop_ for the stopping criterion, and _ALT_ for the type of alternative hypothesis. It also includes _Stage_ for the stage number, Info_Prop for the information proportion, and a set of the boundary variables from Bound_LA, Bound_LB, Bound_UB, and Bound_UA for boundary values at each stage.

The data set might also include _Info_ for the actual information level, NObs for the number of observation, and Events for the number of events required at each stage.

BOUNDARYKEY=ALPHA | BETA | BOTH

specifies the boundary key to be maintained in the boundary adjustments. The BOUNDARYKEY=ALPHA option maintains the Type I $\alpha$ level and derives the Type II error probability, and the BOUNDARYKEY=BETA option maintains the Type II $\beta$ level and derives the Type I error probability. The BOUNDARYKEY=BOTH option maintains both $\alpha$ and $\beta$ levels simultaneously by deriving a new maximum information. The default is BOUNDARYKEY=ALPHA.

specifies the boundary scale to be displayed in the output boundary table and plot. The BOUNDARYSCALE=MLE, BOUNDARYSCALE=SCORE, BOUNDARYSCALE=STDZ, and BOUNDARYSCALE=PVALUE options correspond to the boundary with the maximum likelihood estimator scale, score statistic scale, standardized normal Z scale, and p-value scale, respectively. The default is BOUNDARYSCALE=STDZ.

With the BOUNDARYSCALE=MLE or BOUNDARYSCALE=SCORE option, either the MAXINFO= option must be specified or the _Info_ variable must be in the BOUNDARY= data set to provide the necessary information level at each stage to derive the boundary values. Usually, these values are obtained from analysis output in SAS procedures.

Note that for a two-sided design, the p-value scale displays the one-sided fixed-sample p-value under the null hypothesis with a lower alternative hypothesis.

CIALPHA= $\alpha$ <( <LOWER= $\alpha _ l$ > <UPPER= $\alpha _ u$ > )>

specifies the significance levels for the confidence interval, where $0<\alpha <1$ , $0<\alpha _{l}<0.5$ , and $0<\alpha _{u}<0.5$ . The default is CIALPHA= 0.05.

For a lower confidence interval (CITYPE=LOWER), the CIALPHA= $\alpha$ option produces a $(1-\alpha )$ lower confidence interval. For an upper confidence interval (CITYPE=UPPER), the CIALPHA= $\alpha$ option produces a $(1-\alpha )$ upper confidence interval. The LOWER= and UPPER= suboptions are applicable only for a two-sided confidence interval (CITYPE=TWOSIDED). The LOWER= suboption specifies the lower significance level $\alpha _{l}$ and the upper significance level $\alpha _{u} = 1 - \alpha _{l}$ . The UPPER= suboption specifies the upper significance level $\alpha _{u}$ and the lower significance level $\alpha _{l} = 1 - \alpha _{u}$ . If both LOWER= and UPPER= suboptions are not specified, $\alpha _{l}= \alpha _{u}= \alpha /2$ . The significance levels $\alpha _{l}$ and $\alpha _{u}$ are then used for the $(1-\alpha _{l})$ lower confidence limit and $(1-\alpha _{u})$ upper confidence limit, respectively.

CITYPE=LOWER | UPPER | TWOSIDED

specifies the type of confidence interval. The CITYPE=LOWER, CITYPE=UPPER, and CITYPE=TWOSIDED options correspond to the lower confidence interval, upper confidence interval, and two-sided confidence interval, respectively. The default is CITYPE=LOWER for the design with an upper alternative, CITYPE=UPPER for the design with a lower alternative, and CITYPE=TWOSIDED for the design with a two-sided alternative.

DATA <( TESTVAR=variable | INFOVAR=variable )>=SAS-data-set

names the SAS data set that contains the test statistic and its associated information level for the stage. The SAS-data-set includes the stage variable _Stage_. You can also specify the following options within parentheses after the DATA keyword:

TESTVAR=variable

identifies the test variable in the SAS-data-set. If you specify this option, the data set also includes the scale variable _Scale_ for the test statistic. Usually, these test variable values are obtained from analysis output in SAS procedures.

INFOVAR=variable

identifies the information variable in the SAS-data-set to either identify or derive the information levels. If you specify this option, the following information variables apply:

_Info_ uses _Info_ for the information levels.
Events uses Events for the numbers of events to derive the information levels.
NObs uses NObs for the numbers of observations to derive the information levels.
None uses the information levels in the BOUNDARY= data set.

If you do not specify the INFOVAR= option, PROC SEQTEST uses _Info_ (if it exists) in the SAS-data-set for the information levels. Otherwise, the procedure uses NObs to derive information levels from the numbers of observation or uses Events to derive information levels from the numbers of events. If these variables are not in the SAS-data-set, the information levels in the BOUNDARY= data set are used. See Example 90.4 for an illustration of the INFOVAR=NObs option.

ERRSPENDADJ=method ERRSPENDADJ(boundary)=method BOUNDARYADJ=method BOUNDARYADJ(boundary)=method

specifies methods to compute the error spending values at the current and future interim stages for the boundaries. This option is applicable only if the observed information level at the current stage does not match the value provided in the BOUNDARY= data set. These error spending values are then used to derive the updated boundary values. The default is ERRSPENDADJ=ERRLINE. Note that the information levels at future interim stages are determined by the INFOADJ= option.

The following options specify available error spending methods for boundary adjustment:

NONE: specifies that the cumulative error spending at each interim stage not be changed, even if the corresponding information level has been changed.
ERRLINE: specifies the linear interpolation method for the adjustment.
ERRFUNCGAMMA < ( GAMMA= $\gamma$ ) >: specifies the gamma function method for the adjustment. The GAMMA= suboption specifies the $\gamma$ parameter in the function, where $\gamma \leq 3$ . The default is GAMMA=–2.
ERRFUNCOBF: specifies the approximate O’Brien-Fleming cumulative error spending function for the adjustment.
ERRFUNCPOC: specifies the approximate Pocock cumulative error spending function for the adjustment.
ERRFUNCPOW < ( RHO= $\rho$ ) >: specifies the power function method for the adjustment. The RHO= suboption specifies the power parameter $\rho$ in the function, where $\rho \geq 0.25$ . The default is RHO=2.

See the section Boundary Adjustments for Information Levels for a detailed description of the available error spending methods for boundary adjustment in the SEQTEST procedure.

If an error spending method for boundary adjustments is used for all boundaries in a group sequential test, you can use the ERRSPENDADJ=method option to specify the method. Otherwise, you can use the following ERRSPENDADJ(boundary)=method options to specify different methods for the boundaries.

ERRSPENDADJ(ALPHA)=method ERRSPENDADJ(REJECT)=method BOUNDARYADJ(ALPHA)=method BOUNDARYADJ(REJECT)=method

specifies the adjustment method for the $\alpha$ (rejection) boundary of a one-sided design or the lower and upper $\alpha$ boundaries of a two-sided design.

ERRSPENDADJ(LOWERALPHA)=method ERRSPENDADJ(LOWERREJECT)=method BOUNDARYADJ(LOWERALPHA)=method BOUNDARYADJ(LOWERREJECT)=method

specifies the adjustment method for the lower $\alpha$ boundary of a two-sided design.

ERRSPENDADJ(UPPERALPHA)=method ERRSPENDADJ(UPPERREJECT)=method BOUNDARYADJ(UPPERALPHA)=method BOUNDARYADJ(UPPERREJECT)=method

specifies the adjustment method for the upper $\alpha$ boundary of a two-sided design.

ERRSPENDADJ(BETA)=method ERRSPENDADJ(ACCEPT)=method BOUNDARYADJ(BETA)=method BOUNDARYADJ(ACCEPT)=method

specifies the adjustment method for the $\beta$ (acceptance) boundary of a one-sided design or the lower and upper $\beta$ boundaries of a two-sided design.

ERRSPENDADJ(LOWERBETA)=method ERRSPENDADJ(LOWERACCEPT)=method BOUNDARYADJ(LOWERBETA)=method BOUNDARYADJ(LOWERACCEPT)=method

specifies the adjustment method for the lower $\beta$ boundary of a two-sided design.

ERRSPENDADJ(UPPERBETA)=method ERRSPENDADJ(UPPERACCEPT)=method BOUNDARYADJ(UPPERBETA)=method BOUNDARYADJ(UPPERACCEPT)=method

specifies the adjustment method for the upper $\beta$ boundary of a two-sided design.

ERRSPENDMIN=numbers ERRSPENDMIN(boundary)=numbers

specifies the minimum error spending values at the current observed and future interim stages for the boundaries specified in the BOUNDARYKEY= option. The default is ERRSPENDMIN=0.

If a set of numbers is used for each boundary in the design, you can use the ERRSPENDMIN=numbers option. Otherwise, you can use the following ERRSPENDMIN(boundary)=numbers options to specify different sets of minimum error spending values for the boundaries. For a boundary, the error spending value at stage 1 is identical to its nominal p-value.

ERRSPENDMIN(ALPHA)=numbers ERRSPENDMIN(REJECT)=numbers: specifies the minimum error spending values for the $\alpha$ boundary of a one-sided design or the lower and upper $\alpha$ boundaries of a two-sided design.
ERRSPENDMIN(LOWERALPHA)=numbers ERRSPENDMIN(LOWERREJECT)=numbers: specifies the minimum error spending values for the lower $\alpha$ boundary of a two-sided design.
ERRSPENDMIN(UPPERALPHA)=numbers ERRSPENDMIN(UPPERREJECT)=numbers: specifies the minimum error spending values for the upper $\alpha$ boundary of a two-sided design.
ERRSPENDMIN(BETA)=numbers ERRSPENDMIN(ACCEPT)=numbers: specifies the minimum error spending values for the $\beta$ boundary of a one-sided design or the lower and upper $\beta$ boundaries of a two-sided design.
ERRSPENDMIN(LOWERBETA)=numbers ERRSPENDMIN(LOWERACCEPT)=numbers: specifies the minimum error spending values for the lower $\beta$ boundary of a two-sided design.
ERRSPENDMIN(UPPERBETA)=numbers ERRSPENDMIN(UPPERACCEPT)=numbers: specifies the minimum error spending values for the upper $\beta$ boundary of a two-sided design.

INFOADJ=NONE | PROP

specifies whether information levels at future interim stages are to be adjusted. If you specify INFOADJ=NONE, no adjustment is made, and the information levels are preserved at the levels provided in the BOUNDARY= data set. If you specify INFOADJ=PROP (which is the default), the information levels are adjusted proportionally from the levels provided in the BOUNDARY= data set. The section Information Level Adjustments at Future Stages describes how the adjustments are computed.

Note that if you specify BOUNDARYKEY=BOTH, the INFOADJ=NONE option is not applicable, and the INFOADJ=PROP option is used to adjusted the information levels at future stages proportionally from the levels provided in the BOUNDARY= data set to maintain both $\alpha$ and $\beta$ levels.

NSTAGES=number

specifies the number of stages for the clinical trial. The default is the number derived from the BOUNDARY= data set.

The specified NSTAGES= number might or might not be the same as the number derived in the BOUNDARY= data set. You can use the NSTAGES= option to set the next stage as the final stage to compute the conditional power, as described in the section Conditional Power Approach.

ORDER=LR | MLE | STAGEWISE

specifies the ordering of the sample space $(k, z)$ , where k is the stage number and z is the observed standardized Z statistic. The ordering is used to derive the p-values for the observed $(k, z)$ statistic and to create unbiased median estimate and confidence limits from the statistic. The ORDER=LR option specifies the LR ordering that compares the distances between observed standardized Z statistics and their corresponding hypothetical values, the ORDER=MLE option specifies the MLE ordering that compares values in the MLE scale, and the ORDER=STAGEWISE specifies the stagewise ordering that uses counterclockwise ordering around the continuation region. The default is ORDER=STAGEWISE. See the section Available Sample Space Orderings in a Sequential Test for a detailed description of these sample space orderings.

PARMS <( TESTVAR=variable | INFOVAR=variable )>=SAS-data-set

names the SAS data set that contains the parameter estimate and its associated standard error for the stage. The SAS-data-set includes the stage variable _Stage_. You can also specify the following options within parentheses after the PARMS keyword:

TESTVAR=variable

identifies the test variable in the SAS-data-set. If you specify this option, the SAS-data-set also includes the Parameter, Effect, Variable, or Parm variable that contains the variable. In addition, the SAS-data-set also includes the test statistic Estimate, the standard error of the estimate StdErr, and the test statistic scale variable _Scale_. Usually, these test variable values are obtained from analysis output in SAS procedures.

INFOVAR=variable

identifies the information variable in the SAS-data-set to either identify or derive the information levels. If you specify this option, the following information variables apply:

Events uses Events for the numbers of events to derive the information levels.
NObs uses NObs for the numbers of observations to derive the information levels.
None uses the information levels in the BOUNDARY= data set.
StdErr uses StdErr to derive the information levels.

If you do not specify the INFOVAR= option, PROC SEQTEST uses StdErr (if it exists) in the SAS-data-set to derive the information levels. Otherwise, the procedure uses NObs to derive information levels from the numbers of observation or uses Events to derive information levels from the numbers of events. If these variables are not in the SAS-data-set, the information levels in the BOUNDARY= data set are used.

Table Output Options

You can specify the following options in the PROC SEQTEST statement to display additional table output. They are listed in alphabetical order.

CONDPOWER <( options )>

displays conditional powers given the most recently observed statistic under specified hypothetical references.

You can specify the following options:

CREF= $c_1$ < $c_2$ …>

specifies the hypothetical references, where $c_{i} \geq 0$ . For a one-sided test, the powers are derived under the hypothetical references $\theta = \hat{\theta }$ and $\theta = c_{i} \theta _{1}$ , where $\hat{\theta }$ is the observed statistic, $\theta _{1}$ is the alternative reference, and $c_{i}$ are the values specified in the CREF= option. For a two-sided test, the powers are derived under hypothetical references $\theta = \hat{\theta }$ , $\theta = c_{i} \theta _{1l}$ , and $\theta = c_{i} \theta _{1u}$ , where $\theta _{1l}$ is the lower alternative reference and $\theta _{1u}$ is the upper alternative reference. The default is CREF= 0 0.5 1.0 1.5.

TYPE=ALLSTAGES | FINALSTAGE

specifies the probability to be computed for the conditional power. Two types of conditional power can be computed: TYPE=ALLSTAGES computes the conditional power as the total probability of rejecting the null hypothesis at all future stages given the observed statistic, and TYPE=FINALSTAGE computes the conditional power as the probability that the test statistic at the final stage would exceed the rejection critical value given the observed statistic. The default is TYPE=ALLSTAGES.

If interim stages exist between the current stage and the final stage, the conditional power that is computed when TYPE=FINALSTAGE is not the conditional probability to reject the null hypothesis $H_{0}$ . In this case, you can set the next stage as the final stage, and the resulting conditional power is the conditional probability to reject $H_{0}$ .

ERRSPEND

displays the error spending at each stage for each sequential boundary.

PREDPOWER

displays predictive powers given the most recently observed statistic. The predictive power is the posterior probability that the test statistic at the final stage would exceed the rejection critical value given the observed statistic and a prior distribution of the hypothetical reference. A noninformative prior is used in the procedure.

PSS <( CREF= $c_1$ < $c_2$ …> ) >

displays powers and expected sample sizes under various hypothetical references, where $c_{i} \geq 0$ .

For a one-sided design with the null reference $\theta _{0} = 0$ , the power and expected sample sizes under hypotheses $\theta = c_{i} \, \theta _{1}$ are displayed, where $\theta _{1}$ is the alternative reference and $c_{i}$ are the values specified in the CREF= option.

For a two-sided design, the power and expected sample sizes under hypotheses $\theta = c_{i} \theta _{1l}$ and $\theta = c_{i} \theta _{1u}$ are displayed, where $\theta _{1l}$ and $\theta _{1u}$ are the lower and upper alternative references, respectively. The default is CREF= 0 0.5 1.0 1.5.

Note that for a symmetric two-sided design, only the power and expected sample sizes under hypotheses $\theta = c_{i} \, \theta _{1u}$ are derived.

RCI

displays repeated confidence intervals for the parameter from the observed statistic at each stage. Repeated confidence intervals include both rejection and acceptance confidence intervals.

With the STOP=REJECT or STOP=BOTH option, rejection confidence limits can be derived, and the null hypothesis $H_{0}: \theta = 0$ is rejected if the lower rejection confidence limit is greater than 0 or the upper rejection confidence limit is less than 0.

With the STOP=ACCEPT or STOP=BOTH option, acceptance confidence limits can be derived, and the null hypothesis is accepted with alternative hypotheses $H_{1l}: \theta = \theta _{1l}$ and $H_{1u}: \theta = \theta _{1u}$ if the upper acceptance confidence limit is less than $\theta _{1u}$ and the lower acceptance confidence limit is greater than $\theta _{1l}$ .

STOPPROB <( CREF= $c_1$ < $c_2$ …> ) >

displays expected cumulative stopping probabilities under various hypothetical references, where $c_{i} \geq 0$ .

For a one-sided design, expected cumulative stopping probabilities at each stage under hypotheses $\theta = c_{i} \, \theta _1$ are displayed, where $\theta _1$ is the alternative reference and $c_{i}$ are the values specified in the CREF= option.

For a two-sided design, expected cumulative stopping probabilities at each stage under hypotheses $\theta = c_{i} \theta _{1l}$ and $\theta = c_{i} \theta _{1u}$ are displayed, where $\theta _{1l}$ and $\theta _{1u}$ are the lower and upper alternative references, respectively. Note that for a symmetric two-sided design, only expected cumulative stopping probabilities under hypotheses $\theta = c_{i} \, \theta _{1u}$ are derived. The default is CREF= 0 0.5 1.0 1.5.

Graphics Output Options

The following options can be used in the PROC SEQTEST statement to display plots with ODS Graphics. They are listed in alphabetical order.

PLOTS <( ONLY )> <= plot-request> PLOTS <( ONLY )> <= ( plot-request < …plot-request> ) >

specifies options that control the details of the plots. The default is PLOTS=TEST. The global plot option ONLY suppresses the default plots and displays only plots specifically requested.

ODS Graphics must be enabled before plots can be requested. For example:

ods graphics on;
proc seqtest Boundary=Bnd_LDL
             Parms(Testvar=Trt)=Parms_LDL1
             Plots=(test errspend);
run;
ods graphics off;

For more information about enabling and disabling ODS Graphics, see the section Enabling and Disabling ODS Graphics in Chapter 21: Statistical Graphics Using ODS.

The plot-request-options include the following.

ALL

produces all appropriate plots.

ASN <( CREF= $c_1$ < $c_2$ …> )>

displays a plot of the average sample numbers (expected sample sizes for nonsurvival data or expected number of events for survival data) under various hypothetical references, where $c_{i} \geq 0$ .

For a one-sided design, expected sample numbers under hypotheses $\theta = c_{i} \, \theta _1$ are displayed, where $\theta _1$ is the alternative reference and $c_{i}$ are the values specified in the CREF= option.

For a two-sided design, expected sample numbers under hypotheses $\theta = c_{i} \theta _{1l}$ and $\theta = c_{i} \theta _{1u}$ are displayed, where $\theta _{1l}$ and $\theta _{1u}$ are the lower and upper alternative references, respectively. Note that for a symmetric two-sided design, only the average sample numbers under hypotheses $\theta = c_{i} \, \theta _{1u}$ are derived. The default is CREF= 0 to 1.5 by 0.01.

CONDPOWER <( options )>

displays a plot of conditional powers given the most recently observed statistic under specified hypothetical references.

You can specify the following options:

CREF= $c_1$ < $c_2$ …>: specifies the hypothetical references, where $c_{i} \geq 0$ . For a one-sided test, the powers are derived under hypothetical references $\theta = \hat{\theta }$ and $\theta = c_{i} \theta _{1}$ , where $\hat{\theta }$ is the observed statistic, $\theta _{1}$ is the alternative reference, and $c_{i}$ are the values specified in the CREF= option. For a two-sided test, the powers are derived under hypothetical references $\theta = \hat{\theta }$ , $\theta = c_{i} \theta _{1l}$ , and $\theta = c_{i} \theta _{1u}$ , where $\theta _{1l}$ is the lower alternative reference and $\theta _{1u}$ is the upper alternative reference. The default is CREF= 0 to 1.5 by 0.01.
TYPE=ALLSTAGES | FINALSTAGE: specifies the probability to be computed for the conditional power. Two types of conditional power can be computed: TYPE=ALLSTAGES computes the conditional power as the total probability of rejecting the null hypothesis at all future stages given the observed statistic, and TYPE=FINALSTAGE computes the conditional power as the probability that the test statistic at the final stage would exceed the rejection critical value given the observed statistic. The default is TYPE=ALLSTAGES.

ERRSPEND <( HSCALE=INFO | STAGE ) >

displays a plot of the error spending for all sequential boundaries in the designs simultaneously. You can display the information level (HSCALE=INFO) or the stage number (HSCALE=STAGE) on the horizontal axis. With HSCALE=INFO, the information fractions are used in the plot. The default is HSCALE=STAGE.

NONE

suppresses all plots.

POWER <( CREF= $c_1$ < $c_2$ …> ) >

displays a plot of the power curves under various hypothetical references, where $c_{i} \geq 0$ .

For a one-sided design, powers under hypotheses $\theta = c_{i} \, \theta _1$ are displayed, where $\theta _1$ is the alternative reference and $c_{i}$ are the values specified in the CREF= option.

For a two-sided design, powers under hypotheses $\theta = c_{i} \theta _{1l}$ and $\theta = c_{i} \theta _{1u}$ are displayed, where $\theta _{1l}$ and $\theta _{1u}$ are the lower and upper alternative references, respectively. Note that for a symmetric two-sided design, only powers under hypotheses $\theta = c_{i} \, \theta _{1u}$ are derived. The default is CREF= 0 to 1.5 by 0.01.

RCI

displays a plot of repeated confidence intervals. Repeated confidence intervals include both rejection and acceptance confidence intervals.

With the STOP=REJECT or STOP=BOTH option, rejection confidence limits can be derived and the null hypothesis $H_{0}: \theta = 0$ is rejected if the lower rejection confidence limit is greater than 0 or the upper rejection confidence limit is less than 0.

With the STOP=ACCEPT or STOP=BOTH option, acceptance confidence limits can be derived and the null hypothesis is accepted with alternative hypotheses $H_{1l}: \theta = \theta _{1l}$ and $H_{1u}: \theta = \theta _{1u}$ if the upper acceptance confidence limit is less than $\theta _{1u}$ and the lower acceptance confidence limit is greater than $\theta _{1l}$ .

TEST <( HSCALE=INFO | SAMPLESIZE ) >

displays a plot of the sequential boundaries and test variables. Either the information level (HSCALE=INFO) or the sample size (HSCALE=SAMPLESIZE) is displayed on the horizontal axis. The HSCALE=SAMPLESIZE option is applicable only if the sample size information is available in both the input BOUNDARY= data set and input DATA= data set. The stage number for each stage is displayed inside the plot. The default is HSCALE=INFO.