The SEQDESIGN Procedure 
SAMPLESIZE Statement 
If each observation in the data set provides one unit of information in a hypothesis testing such as a onesample 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 78.4 lists the options available in the SAMPLESIZE statement.
Option 
Description 

FixedSample Models 

INPUTNOBS 
Specifies the sample size for fixedsample design 
INPUTNEVENTS 
Specifies the number of events for fixedsample design 
OneSample Models 

ONESAMPLEMEAN 
Specifies the onesample test for mean 
ONESAMPLEFREQ 
Specifies the onesample test for binomial proportion 
TwoSample Models 

TWOSAMPLEMEAN 
Specifies the twosample test for mean difference 
TWOSAMPLEFREQ 
Specifies the twosample test for binomial proportions 
TWOSAMPLESURVIVAL 
specifies the logrank 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 fixedsample study, or it specifies a statistical model to compute the required sample size. The MODEL=INPUTNOBS option specifies the input sample size from a fixedsample study of nonsurvival data, and the MODEL=INPUTNEVENTS option specifies the number of events from a fixedsample 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 twosample 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 fixedsample information level. This ratio can be obtained by dividing the Max Information (Percent FixedSample) in the "Design Information" table by . See the section Design Information for a description of the "Design Information" table.
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 fixedsample design.
specifies the sample size information for a fixedsample design. The available options are as follows:
N=
SAMPLE= ONE  TWO
WEIGHT=
MATCHNOBS= YES  NO
The required N= option specifies the sample size for the fixedsample design. The SAMPLE=ONE option specifies a onesample test, and the SAMPLE=TWO option specifies a twosample test. The default is SAMPLE=ONE.
With a twosample test, the WEIGHT= option specifies the sample size allocation weights for the two groups. If is not specified, 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 FixedSample Design for a detailed description of the input sample size for the fixedsample design in sample size computation.
specifies the number of events for a fixedsample survival test. The available options are as follows:
D=
SAMPLE= ONE  TWO
The required D= option specifies the fixedsample number of events . The SAMPLE=ONE option specifies a onesample test, and the SAMPLE=TWO option specifies a twosample 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=
MEDSURVTIME=
WEIGHT=
ACCRATE=
ACCTIME=
FOLTIME=
TOTALTIME=
The hazard rates are needed for the sample size computation. For a onesample test, the HAZARD= option specifies the hazard rate explicitly, and the MEDSURVTIME= option specifies the hazard rate implicitly through the median survival time . Similarly, for a twosample test, the HAZARD= option specifies the hazard rates and for groups A and B explicitly, and the MEDSURVTIME= option specifies hazard rates for groups A and B implicitly through the median survival times and . Also, for a twosample test, if is not specified and if is not specified.
With a twosample test, the WEIGHT= option specifies the sample size allocation weights for the two groups. If is not specified, is used. The default is WEIGHT=1.
Assuming that the hazard rates are constant and the individual accrual is uniform in the accrual time with a constant accrual rate , the sample size and study time can be derived.
The ACCRATE= option specifies the constant accrual rate , and the ACCTIME= and FOLTIME= options specify the accrual time and followup time , respectively. The TOTALTIME= option specifies the total study time, .
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 FixedSample Design for a detailed description of the input number of events for the fixedsample design in sample size computation.
The following two options compute the required sample size for a onesample group sequential test.
specifies the onesample test for mean. The available options are as follows:
MEAN=
STDDEV=
The MEAN= option specifies the alternative reference 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 . The default is STDDEV=1. See the section Test for a Normal Mean for a detailed description of the onesample test for mean.
Note that the onesample test for mean also includes the paired difference in twotreatment comparison (Jennison and Turnbull 2000, pp. 51–52), where is the mean of differences within pairs under the alternative hypothesis and is the standard deviation for the mean of differences within pairs.
specifies the onesample test for binomial proportion with the null hypothesis and the alternative hypothesis , where and . The available options are as follows:
NULLPROP=
PROP=
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 is used to compute the alternative reference .
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 onesample tests for proportion.
The following three options compute the required sample size or number of events for a twosample group sequential trial.
specifies the twosample test for mean difference. The available options are as follows:
MEANDIFF=
STDDEV=
WEIGHT=
MATCHNOBS= YES  NO
The MEANDIFF= option specifies the alternative reference 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 and . If is not specified, . The default is STDDEV=1.
The WEIGHT= option specifies the sample size allocation weights for the two groups. If is not specified, 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 twosample test for mean difference.
specifies the twosample test for binomial proportions. The available options are as follows:
NULLPROP=
PROP=
TEST= PROP  LOGOR  LOGRR
REF= NULLPROP  PROP  AVGNULLPROP  AVGPROP
WEIGHT=
MATCHNOBS= YES  NO
The NULLPROP= option specifies proportions and in groups A and B, respectively, under the null hypothesis. If is not specified, . The default is NULLPROP=.
The PROP= option specifies proportion in group A under the alternative hypothesis. The proportion in group B under the alternative hypothesis is given by . 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 , the proportion in group A under the alternative hypothesis.
The TEST= option specified the null hypothesis in the test. The TEST=PROP option uses the difference in proportions , the TEST=LOGOR option uses the log oddsratio test , where
and the TEST=LOGRR option uses the log relative risk test with , where
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 and , the REF=PROP option uses the alternative proportions and , 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 is not specified, 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 twosample tests for proportions.
specifies the logrank test for two survival distributions with the null hypothesis , where the parameter , is the value of under the null hypothesis and the values and are the hazard rates for groups A and B, respectively.
The available options for the number of events are as follows:
NULLHAZARD=
NULLMEDSURVTIME=
HAZARD=
MEDSURVTIME=
HAZARDRATIO=
The NULLHAZARD= option specifies hazard rates and for groups A and B, respectively, under the null hypothesis. If is not specified, . The NULLMEDSURVTIME= option specifies the median survival times and under the null hypothesis. If is not specified, . If both NULLHAZARD= and NULLMEDSURVTIME= option are not specified, NULLHAZARD=, which corresponds to NULLMEDSURVTIME=, is used.
The hazard rate for group B under the alternative hypothesis , as the hazard rate under the null hypothesis. The HAZARD=, MEDSURVTIME=, and HAZARDRATIO= options specify the group A hazard rate , the group A median survival time , and the hazard ratio , 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 is used to compute from the equation:
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=
ACCRATE=
ACCTIME=
FOLTIME=
TOTALTIME=
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.
The WEIGHT= option specifies the sample size allocation weights for the two groups. If is not specified, is used. The default is WEIGHT=1, equal sample size for the two groups.
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 with a constant accrual rate , the sample size and study time can be derived.
The ACCRATE= option specifies the constant accrual rate , and the ACCTIME= and FOLTIME= options specify the accrual time and followup time , respectively. The TOTALTIME= option specifies the total study time, .
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 LogRank Test for a detailed description of the twosample logrank test for survival data.
The following three options compute the required sample size or number of events for group sequential tests on a regression parameter.
specifies the test for a normal regression parameter. The available options are as follows:
BETA=
VARIANCE=
XVARIANCE=
XRSQUARE=
The BETA= option specifies the alternative reference and is required if the alternative reference is not specified or derived in the procedure. If the BETA= option is not specified, , 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 test for the regression parameter.
specifies the test for a logistic regression parameter. The available options are as follows:
BETA=
PROP=
XVARIANCE=
XRSQUARE=
The BETA= option specifies the alternative reference and is required if the alternative reference is not specified or derived in the procedure. If the BETA= option is not specified, , the specified or derived alternative reference.
The PROP= option specifies the proportion of the binary response variable Y. The default is PROP=. 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 test for the logistic regression parameter.
specifies the test for a proportional hazards regression parameter. The available options for the number of events are as follows:
BETA=
XVARIANCE=
XRSQUARE=
The BETA= option specifies the alternative reference and is required if the alternative reference is not specified or derived in the procedure. If the BETA= option is not specified, , the specified or derived alternative reference.
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=
MEDSURVTIME=
ACCRATE=
ACCTIME=
FOLTIME=
TOTALTIME=
The hazard rate is required for the sample size computation. The HAZARD= option specifies the hazard rate explicitly, and the MEDSURVTIME= option specifies the hazard rate implicitly through the median survival time .
Assuming that the hazard rates are constant and the individual accrual is uniform in the accrual time with a constant accrual rate , the sample size and study time can be derived.
The ACCRATE= option specifies the constant accrual rate , the ACCTIME= option specifies the accrual time , and the FOLTIME= option specifies the followup time . The TOTALTIME= option specifies the total study time, .
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 a Parameter in the Proportional Hazards Regression Model for a detailed description of the test for the proportional hazards regression parameter.
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