The SEQDESIGN Procedure

SAMPLESIZE Statement

SAMPLESIZE <MODEL= option> ;

If each observation in the data set provides one unit of information in a hypothesis testing such as a one-sample test for the mean, the SAMPLESIZE statement computes the required sample sizes for the sequential design specified in each DESIGN statement. However, for a survival analysis, an individual in the survival time data might provide only partial information because of censoring. For this hypothesis, the SAMPLESIZE statement computes the required numbers of events. With additional accrual information in a survival analysis, the sample sizes can also be computed.

Only one SAMPLESIZE statement can be specified. For each specified group sequential design, the SAMPLESIZE statement computes the required sample sizes or numbers of events. The SAMPLESIZE statement is not required if the SEQDESIGN procedure is used only to compare features among different designs. Table 80.4 lists the options available in the SAMPLESIZE statement.

Table 80.4 SAMPLESIZE Statement Options
Option	Description
Fixed-Sample Models
INPUTNOBS	Specifies the sample size for fixed-sample design
INPUTNEVENTS	Specifies the number of events for fixed-sample design
One-Sample Models
ONESAMPLEMEAN	Specifies the one-sample $\text{[math]}$ test for mean
ONESAMPLEFREQ	Specifies the one-sample test for binomial proportion
Two-Sample Models
TWOSAMPLEMEAN	Specifies the two-sample $\text{[math]}$ test for mean difference
TWOSAMPLEFREQ	Specifies the two-sample test for binomial proportions
TWOSAMPLESURVIVAL	specifies the log-rank test for two survival distributions
Regression Models
REG	Specifies the test for a regression parameter
LOGISTIC	Specifies the test for a logistic regression parameter
PHREG	Specifies the test for a proportional hazards regression parameter

The MODEL= option specifies the input sample size or number of events from a fixed-sample study, or it specifies a statistical model to compute the required sample size. The MODEL=INPUTNOBS option specifies the input sample size from a fixed-sample study of nonsurvival data, and the MODEL=INPUTNEVENTS option specifies the number of events from a fixed-sample study of survival data. The remaining MODEL= options specify the statistical models used to compute the required sample size. The default is MODEL=TWOSAMPLEMEAN, the two-sample $\text{[math]}$ test for the mean difference.

With the MODEL=INPUTNOBS or MODEL=INPUTNEVENTS option, the required sample size or number of events for the group sequential trial is computed by multiplying the input sample size or number of events by the ratio between the design information level and its corresponding fixed-sample information level. This ratio can be obtained by dividing the Max Information (Percent Fixed-Sample) in the "Design Information" table by $\text{[math]}$ . See the section Design Information for a description of the "Design Information" table.

Fixed-Sample Models

The following two options compute the required sample size or number of events for a group sequential trial by using the sample size or number of events for the fixed-sample design.

MODEL=INPUTNOBS < ( options ) >

specifies the sample size information for a fixed-sample design. The available options are as follows:

N= $\text{[math]}$
SAMPLE= ONE | TWO
WEIGHT= $\text{[math]}$
MATCHNOBS= YES | NO

The required N= $\text{[math]}$ option specifies the sample size $\text{[math]}$ for the fixed-sample design. The SAMPLE=ONE option specifies a one-sample test, and the SAMPLE=TWO option specifies a two-sample test. The default is SAMPLE=ONE.

With a two-sample test, the WEIGHT= option specifies the sample size allocation weights for the two groups. If $\text{[math]}$ is not specified, $\text{[math]}$ is used. The default is WEIGHT=1, equal allocation for the two groups. The derived fractional sample sizes are rounded up to integers, and the MATCHNOBS=YES option requests these integer sample sizes to match the sample size allocation.

See the section Input Sample Size for Fixed-Sample Design for a detailed description of the input sample size for the fixed-sample design in sample size computation.

MODEL=INPUTNEVENTS < ( options ) >

specifies the number of events $\text{[math]}$ for a fixed-sample survival test. The available options are as follows:

D= $\text{[math]}$
SAMPLE= ONE | TWO

The required D= $\text{[math]}$ option specifies the fixed-sample number of events $\text{[math]}$ . The SAMPLE=ONE option specifies a one-sample test, and the SAMPLE=TWO option specifies a two-sample test. The default is SAMPLE=ONE.

In order to derive the sample size, addition options are needed. The available options for the sample size computation are as follows:

HAZARD= $\text{[math]}$
MEDSURVTIME= $\text{[math]}$
WEIGHT= $\text{[math]}$
ACCRATE= $\text{[math]}$
ACCTIME= $\text{[math]}$
FOLTIME= $\text{[math]}$
TOTALTIME= $\text{[math]}$

The hazard rates are needed for the sample size computation. For a one-sample test, the HAZARD= $\text{[math]}$ option specifies the hazard rate $\text{[math]}$ explicitly, and the MEDSURVTIME= $\text{[math]}$ option specifies the hazard rate implicitly through the median survival time $\text{[math]}$ . Similarly, for a two-sample test, the HAZARD= $\text{[math]}$ $\text{[math]}$ option specifies the hazard rates $\text{[math]}$ and $\text{[math]}$ for groups A and B explicitly, and the MEDSURVTIME= $\text{[math]}$ $\text{[math]}$ option specifies hazard rates for groups A and B implicitly through the median survival times $\text{[math]}$ and $\text{[math]}$ . Also, for a two-sample test, $\text{[math]}$ if $\text{[math]}$ is not specified and $\text{[math]}$ if $\text{[math]}$ is not specified.

With a two-sample test, the WEIGHT= option specifies the sample size allocation weights for the two groups. If $\text{[math]}$ is not specified, $\text{[math]}$ is used. The default is WEIGHT=1.

Assuming that the hazard rates are constant and the individual accrual is uniform in the accrual time $\text{[math]}$ with a constant accrual rate $\text{[math]}$ , the sample size and study time can be derived.

The ACCRATE= option specifies the constant accrual rate $\text{[math]}$ , and the ACCTIME= and FOLTIME= options specify the accrual time $\text{[math]}$ and follow-up time $\text{[math]}$ , respectively. The TOTALTIME= option specifies the total study time, $\text{[math]}$ .

If the ACCRATE= option is specified, then one of the ACCTIME=, FOLTIME, and TOTALTIME options is required for the sample size computation. Otherwise, two of the ACCTIME=, FOLTIME, and TOTALTIME options are required to compute the accrual rate and sample size.

See the section Input Number of Events for Fixed-Sample Design for a detailed description of the input number of events for the fixed-sample design in sample size computation.

One-Sample Models

The following two options compute the required sample size for a one-sample group sequential test.

MODEL=ONESAMPLEMEAN < ( options ) >

specifies the one-sample $\text{[math]}$ test for mean. The available options are as follows:

MEAN= $\text{[math]}$
STDDEV= $\text{[math]}$

The MEAN= option specifies the alternative reference $\text{[math]}$ and is required if the alternative reference is not specified or derived in the procedure. If the MEAN=option is not specified, the specified or derived alternative reference is used.

The STDDEV= option specifies the standard deviation $\text{[math]}$ . The default is STDDEV=1. See the section Test for a Normal Mean for a detailed description of the one-sample $\text{[math]}$ test for mean.

Note that the one-sample $\text{[math]}$ test for mean also includes the paired difference in two-treatment comparison (Jennison and Turnbull 2000, pp. 51–52), where $\text{[math]}$ is the mean of differences within pairs under the alternative hypothesis and $\text{[math]}$ is the standard deviation for the mean of differences within pairs.

MODEL=ONESAMPLEFREQ < ( options ) >

specifies the one-sample test for binomial proportion with the null hypothesis $\text{[math]}$ and the alternative hypothesis $\text{[math]}$ , where $\text{[math]}$ and $\text{[math]}$ . The available options are as follows:

NULLPROP= $\text{[math]}$
PROP= $\text{[math]}$
REF= NULLPROP | PROP

The NULLPROP= and PROP= options specify the proportions under the null and alternative hypotheses, respectively. The default for the null reference is NULLPROP=0.5. The PROP= option is required if the alternative reference is not specified or derived in the procedure. If the PROP= option is not specified, the specified or derived alternative reference $\text{[math]}$ is used to compute the alternative reference $\text{[math]}$ .

The REF= option specifies the hypothesis under which the proportion is used in the sample size computation. The REF=NULLPROP option uses the null hypothesis, and the REF=PROP option uses the alternative hypothesis to compute the sample size. The default is REF=PROP. See the section Test for a Binomial Proportion for a detailed description of the one-sample tests for proportion.

Two-Sample Models

The following three options compute the required sample size or number of events for a two-sample group sequential trial.

MODEL=TWOSAMPLEMEAN < ( options ) >

specifies the two-sample $\text{[math]}$ test for mean difference. The available options are as follows:

MEANDIFF= $\text{[math]}$
STDDEV= $\text{[math]}$
WEIGHT= $\text{[math]}$
MATCHNOBS= YES | NO

The MEANDIFF= option specifies the alternative reference $\text{[math]}$ and is required if the alternative reference is not specified or derived in the procedure. If the MEANDIFF= option is not specified, the specified or derived alternative reference is used.

The STDDEV= option specifies the standard deviations $\text{[math]}$ and $\text{[math]}$ . If $\text{[math]}$ is not specified, $\text{[math]}$ . The default is STDDEV=1.

The WEIGHT= option specifies the sample size allocation weights for the two groups. If $\text{[math]}$ is not specified, $\text{[math]}$ is used. The default is WEIGHT=1, equal sample size for the two groups. The derived fractional sample sizes are rounded up to integers, and the MATCHNOBS=YES option requests these integer sample sizes to match the sample size allocation. The default is MATCHNOBS=NO.

See the section Test for the Difference between Two Normal Means for a detailed description of the two-sample $\text{[math]}$ test for mean difference.

MODEL=TWOSAMPLEFREQ < ( options ) >

specifies the two-sample test for binomial proportions. The available options are as follows:

NULLPROP= $\text{[math]}$
PROP= $\text{[math]}$
TEST= PROP | LOGOR | LOGRR
REF= NULLPROP | PROP | AVGNULLPROP | AVGPROP
WEIGHT= $\text{[math]}$
MATCHNOBS= YES | NO

The NULLPROP= option specifies proportions $\text{[math]}$ and $\text{[math]}$ in groups A and B, respectively, under the null hypothesis. If $\text{[math]}$ is not specified, $\text{[math]}$ . The default is NULLPROP= $\text{[math]}$ .

The PROP= option specifies proportion $\text{[math]}$ in group A under the alternative hypothesis. The proportion $\text{[math]}$ in group B under the alternative hypothesis is given by $\text{[math]}$ . The PROP= option is required if the alternative reference is not specified or derived in the procedure. If the PROP= option is not specified, the specified or derived alternative reference is used to compute $\text{[math]}$ , the proportion in group A under the alternative hypothesis.

The TEST= option specified the null hypothesis $\text{[math]}$ in the test. The TEST=PROP option uses the difference in proportions $\text{[math]}$ , the TEST=LOGOR option uses the log odds-ratio test $\text{[math]}$ , where

$\text{[math]}$

and the TEST=LOGRR option uses the log relative risk test with $\text{[math]}$ , where

$\text{[math]}$

The default is TEST=LOGOR.

The REF= option specifies the hypothesis under which the proportions are used in the sample size computation. The REF=NULLPROP option uses the null proportions $\text{[math]}$ and $\text{[math]}$ , the REF=PROP option uses the alternative proportions $\text{[math]}$ and $\text{[math]}$ , the REF=AVGNULLPROP option uses the average null proportion, and the REF=AVGPROP option uses the average alternative proportion. The default is REF=PROP.

The WEIGHT= option specifies the sample size allocation weights for the two groups. If $\text{[math]}$ is not specified, $\text{[math]}$ is used. The default is WEIGHT=1, equal sample size for the two groups. The derived fractional sample sizes are also rounded up to integers, and the MATCHNOBS=YES option requests that these integer sample sizes match the sample size allocation.

See the section Test for the Difference between Two Binomial Proportions, the section Test for Two Binomial Proportions with a Log Odds Ratio Statistic, and the section Test for Two Binomial Proportions with a Log Relative Risk Statistic for a detailed description of the two-sample tests for proportions.

MODEL=TWOSAMPLESURVIVAL < ( options ) >

MODEL=TWOSAMPLESURV < ( options ) >

specifies the log-rank test for two survival distributions with the null hypothesis $\text{[math]}$ , where the parameter $\text{[math]}$ , $\text{[math]}$ is the value of $\text{[math]}$ under the null hypothesis and the values $\text{[math]}$ and $\text{[math]}$ are the hazard rates for groups A and B, respectively.

The available options for the number of events are as follows:

NULLHAZARD= $\text{[math]}$
NULLMEDSURVTIME= $\text{[math]}$
HAZARD= $\text{[math]}$
MEDSURVTIME= $\text{[math]}$
HAZARDRATIO= $\text{[math]}$

The NULLHAZARD= option specifies hazard rates $\text{[math]}$ and $\text{[math]}$ for groups A and B, respectively, under the null hypothesis. If $\text{[math]}$ is not specified, $\text{[math]}$ . The NULLMEDSURVTIME= option specifies the median survival times $\text{[math]}$ and $\text{[math]}$ under the null hypothesis. If $\text{[math]}$ is not specified, $\text{[math]}$ . If both NULLHAZARD= and NULLMEDSURVTIME= option are not specified, NULLHAZARD= $\text{[math]}$ , which corresponds to NULLMEDSURVTIME= $\text{[math]}$ , is used.

The hazard rate for group B under the alternative hypothesis $\text{[math]}$ , as the hazard rate under the null hypothesis. The HAZARD=, MEDSURVTIME=, and HAZARDRATIO= options specify the group A hazard rate $\text{[math]}$ , the group A median survival time $\text{[math]}$ , and the hazard ratio $\text{[math]}$ , respectively, under the alternative hypothesis. The HAZARD=, MEDSURVTIME=, or HAZARDRATIO= option is required if the alternative reference is not specified or derived in the procedure. If these three options are not specified, the specified or derived alternative reference $\text{[math]}$ is used to compute $\text{[math]}$ from the equation:

$\text{[math]}$

In order to derive the sample size, additional options are needed. The available options for the sample size computation are as follows:

REF= NULLHAZARD | HAZARD
WEIGHT= $\text{[math]}$
ACCRATE= $\text{[math]}$
ACCTIME= $\text{[math]}$
FOLTIME= $\text{[math]}$
TOTALTIME= $\text{[math]}$

The REF= option specifies the hypothesis under which the hazard is used in the sample size computation. The REF=NULLHAZARD option uses the null hypothesis, and the REF=HAZARD option uses the alternative hypothesis. The default is REF=HAZARD.

With the available maximum information, the number of events can be derived for the specified hypothesis. Assuming that the hazard rates are constant and the individual accrual is uniform in the accrual time $\text{[math]}$ with a constant accrual rate $\text{[math]}$ , the sample size and study time can be derived.

If the ACCRATE= option is specified, then one of the ACCTIME=, FOLTIME=, and TOTALTIME= options is required for the sample size computation. Otherwise, two of the ACCTIME=, FOLTIME=, and TOTALTIME= options are required to compute the accrual rate and sample size.

See the section Test for Two Survival Distributions with a Log-Rank Test for a detailed description of the two-sample log-rank test for survival data.

Regression Models

The following three options compute the required sample size or number of events for group sequential tests on a regression parameter.

MODEL=REG < ( options ) >

specifies the $\text{[math]}$ test for a normal regression parameter. The available options are as follows:

BETA= $\text{[math]}$
VARIANCE= $\text{[math]}$
XVARIANCE= $\text{[math]}$
XRSQUARE= $\text{[math]}$

The BETA= option specifies the alternative reference $\text{[math]}$ and is required if the alternative reference is not specified or derived in the procedure. If the BETA= option is not specified, $\text{[math]}$ , the specified or derived alternative reference.

The VARIANCE= and XVARIANCE= options specify the variances for the response variable Y and covariate X, respectively. The defaults are VARIANCE=1 and XVARIANCE=1. For a model with more than one covariate, the XRSQUARE= option can be used to derive the variance of X after adjusting for other covariates. The default is XRSQUARE=0.

See the section Test for a Parameter in the Regression Model for a detailed description of the $\text{[math]}$ test for the regression parameter.

MODEL=LOGISTIC < ( options ) >

specifies the $\text{[math]}$ test for a logistic regression parameter. The available options are as follows:

BETA= $\text{[math]}$
PROP= $\text{[math]}$
XVARIANCE= $\text{[math]}$
XRSQUARE= $\text{[math]}$

The PROP= option specifies the proportion of the binary response variable Y. The default is PROP= $\text{[math]}$ . The XVARIANCE= option specifies the variance of the covariate X. The default is XVARIANCE=1. For a model with more than one covariate, the XRSQUARE= option can be used to derive the variance of X after adjusting for other covariates. The default is XRSQUARE=0.

See the section Test for a Parameter in the Logistic Regression Model for a detailed description of the $\text{[math]}$ test for the logistic regression parameter.

MODEL=PHREG < ( options ) >

specifies the $\text{[math]}$ test for a proportional hazards regression parameter. The available options for the number of events are as follows:

BETA= $\text{[math]}$
XVARIANCE= $\text{[math]}$
XRSQUARE= $\text{[math]}$

The XVARIANCE= option specifies the variance of the covariate X. The default is XVARIANCE=1. For a model with more than one covariate, the XRSQUARE= option can be used to derive the variance of X after adjusting for other covariates. The default is XRSQUARE=0.

In order to derive the sample size, additional options are needed. The available options for the sample size computation are as follows:

HAZARD= $\text{[math]}$
MEDSURVTIME= $\text{[math]}$
ACCRATE= $\text{[math]}$
ACCTIME= $\text{[math]}$
FOLTIME= $\text{[math]}$
TOTALTIME= $\text{[math]}$

The hazard rate is required for the sample size computation. The HAZARD= $\text{[math]}$ option specifies the hazard rate $\text{[math]}$ explicitly, and the MEDSURVTIME= $\text{[math]}$ option specifies the hazard rate implicitly through the median survival time $\text{[math]}$ .

The ACCRATE= option specifies the constant accrual rate $\text{[math]}$ , the ACCTIME= option specifies the accrual time $\text{[math]}$ , and the FOLTIME= option specifies the follow-up time $\text{[math]}$ . The TOTALTIME= option specifies the total study time, $\text{[math]}$ .

See the section Test for a Parameter in the Proportional Hazards Regression Model for a detailed description of the $\text{[math]}$ test for the proportional hazards regression parameter.