The SEQDESIGN Procedure

SAMPLESIZE Statement

  • SAMPLESIZE <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 each sequential design that is specified in a 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.

You can specify the following option:

MODEL <( CEILADJDESIGN=INCLUDE | EXCLUDE )> = model-request

specifies the input sample size or number of events from a fixed-sample study or specifies a statistical model to compute the required sample size. Table 4 summarizes the types of model-request that you can specify, and the subsections that follow Table 4 provide more information about the model-request for each type of model.

You can also specify one of the following values for the optional CEILADJDESIGN= suboption:

EXCLUDE

does not create a ceiling-adjusted design.

INCLUDE

creates a ceiling-adjusted design that corresponds to integer-valued sample sizes at the stages for nonsurvival data, and to integer-valued times or sample sizes at the stages for survival data.

Because the information levels in the adjusted design are different from the levels in the original design, the Type I and Type II error levels cannot be maintained simultaneously. If BOUNDARYKEY=BOTH or BOUNDARYKEY=NONE in the DESIGN statement, then the Type I error level is maintained. Otherwise, the BOUNDARYKEY= option selects the type of error level to be maintained.

The CEILADJDESIGN=INCLUDE option adds the ceiling-adjusted design information in the design information table, and creates a ceiling-adjusted boundary information table. See Example 110.2 for an illustration of the CEILADJDESIGN=INCLUDE option for nonsurvival data and Example 110.14 for an illustration of the option for survival data.

Other tables that are associated with the adjusted design, such as error-spending information, are not displayed in the SEQDESIGN procedure, but you can easily generate them from this adjusted-boundary information table in the companion SEQTEST procedure. See Example 110.2 for an illustration of this usage.

By default, CEILADJDESIGN=EXCLUDE.

Table 4 summarizes the types of model-request that you can specify.

Table 4: MODEL= Option

Option Description
Fixed-Sample Models
INPUTNOBS Specifies the sample size for a fixed-sample design
INPUTNEVENTS Specifies the number of events for a fixed-sample design
One-Sample Models
ONESAMPLEMEAN Specifies the one-sample Z test for the mean
ONESAMPLEFREQ Specifies the one-sample test for the binomial proportion
Two-Sample Models
TWOSAMPLEMEAN Specifies the two-sample Z test for the 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=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 that are used to compute the required sample size. The default is MODEL=TWOSAMPLEMEAN, the two-sample Z test for the mean difference.

When MODEL=INPUTNOBS or MODEL=INPUTNEVENTS, 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 of the design information level to 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 100. For a description of the "Design Information" table, see the section Design Information.

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 input sample size from a fixed-sample study of nonsurvival data. The available options are as follows:

  • N=n

  • SAMPLE=ONE  |  TWO

  • WEIGHT=w Subscript a   < w Subscript b >

  • MATCHNOBS=YES  |  NO

The required N=n option specifies the sample size n 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 w Subscript b is not specified, w Subscript b Baseline equals 1 is used. The default is WEIGHT=1, which results in 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.

For more information about the input sample size for the fixed-sample design in sample size computation, see the section Input Sample Size for Fixed-Sample Design.

MODEL=INPUTNEVENTS ( D=d   < options > )

specifies the number of events from a fixed-sample study of survival data. The required D=d option specifies the fixed-sample number of events d. To derive the sample size, you need to specify additional options from the following list:

  • ACCNOBS=n Subscript a

  • ACCRATE=r Subscript a

  • ACCRUAL=UNIFORM  |  EXP(PARM=gamma 0)

  • ACCTIME=upper T Subscript a

  • CEILING=TIME  |  N

  • FOLTIME=upper T Subscript f

  • HAZARD=h Subscript a <   h Subscript b >

  • LOSS=NONE  |  EXP(HAZARD=tau  |  MEDLOSSTIME=t Subscript tau )

  • MEDSURVTIME=t Subscript a <   t Subscript b >

  • SAMPLE=ONE  |  TWO

  • TOTALTIME=T

  • WEIGHT=w Subscript a   < w Subscript b >

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 w Subscript b is not specified, w Subscript b=1 is used. The default is WEIGHT=1.

For a one-sample test, the HAZARD= h Subscript a option specifies the hazard rate h Subscript a explicitly, and the MEDSURVTIME=t Subscript a option specifies the hazard rate implicitly through the median survival time t Subscript a. Similarly, for a two-sample test, the HAZARD= h Subscript a Baseline h Subscript b option specifies the hazard rates h Subscript a and h Subscript b for groups A and B explicitly, and the MEDSURVTIME=t Subscript a Baseline t Subscript b option specifies hazard rates for groups A and B implicitly through the median survival times t Subscript a and t Subscript b. Also, for a two-sample test, h Subscript b Baseline equals h Subscript a if h Subscript b is not specified and t Subscript b Baseline equals t Subscript a if t Subscript b is not specified.

The ACCRUAL= option specifies the method for individual accrual. The ACCRUAL=UNIFORM option (which is the default) specifies that the individual accrual is uniform in the accrual time upper T Subscript a with a constant accrual rate r Subscript a, and the ACCRUAL=EXP(PARM=gamma 0) option specifies that the individual accrual is truncated exponential with a scaled power parameter gamma 0, where gamma 0 greater-than-or-equal-to negative 10 and gamma 0 not-equals 0. With a scaled parameter gamma 0, the power parameter for the truncated exponential with the accrual time upper T Subscript a is given by gamma equals gamma 0 slash upper T Subscript a.

The ACCTIME= and FOLTIME= options specify the accrual time upper T Subscript a and follow-up time upper T Subscript f, respectively. The TOTALTIME= option specifies the total study time, upper T equals upper T Subscript a Baseline plus upper T Subscript f.

The ACCRATE= option specifies the constant accrual rate r Subscript a. If you specify the ACCRATE= option, then you must also specify one of the ACCTIME=, FOLTIME=, and TOTALTIME= options for the sample size computation. Otherwise, you must specify two of the ACCTIME=, FOLTIME=, and TOTALTIME= options to compute the accrual rate and sample size.

The ACCNOBS= option specifies the total number of individuals in the study. If you specify the ACCNOBS= option, then you must also specify one of the ACCTIME=, FOLTIME=, and TOTALTIME= options for the sample size computation. Otherwise, you must specify two of the ACCTIME=, FOLTIME=, and TOTALTIME= options to compute the accrual rate and sample size.

The CEILING= option specifies the additional sample size information to be displayed in the "Number of Events (D) and Sample Sizes (N)" table. The CEILING=TIME option (which is the default) displays additional information that includes ceiling times at the stages, and the CEILING=N option displays additional information that includes ceiling sample sizes at the stages. When you specify the SAMPLE=TWO option along with the CEILING=N option, the ceiling sample sizes at each stage are derived to match the sample size allocation weights for the two groups.

The LOSS= option specifies the individual loss to follow-up in the sample size computation. The LOSS=NONE option (which is the default) specifies no loss to follow-up, and the LOSS=EXP option specifies exponential loss function. The HAZARD=tau suboption specifies the exponential loss hazard rate tau, and the MEDLOSSTIME=t Subscript tau suboption specifies the exponential loss hazard rate through the median loss times t Subscript tau.

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

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 Z test for mean. The available options are as follows:

  • MEAN= mu 1

  • STDDEV= sigma

The MEAN= option specifies the alternative reference mu 1 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 sigma. The default is STDDEV=1. See the section Test for a Normal Mean for a detailed description of the one-sample Z test for mean.

Note that the one-sample Z test for mean also includes the paired difference in two-treatment comparison (Jennison and Turnbull 2000, pp. 51–52), where mu 1 is the mean of differences within pairs under the alternative hypothesis and sigma 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 upper H 0 colon theta equals 0 and the alternative hypothesis upper H 1 colon theta equals theta 1, where theta equals p minus p 0 and theta 1 equals p 1 minus p 0. The available options are as follows:

  • NULLPROP= p 0

  • PROP= p 1

  • 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 theta 1 is used to compute the alternative reference p 1 equals p 0 plus theta 1.

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 Z test for mean difference. The available options are as follows:

  • MEANDIFF= theta 1

  • STDDEV= sigma Subscript a Baseline less-than sigma Subscript b Baseline greater-than

  • WEIGHT= w Subscript a Baseline less-than w Subscript b Baseline greater-than

  • MATCHNOBS= YES  |  NO

The MEANDIFF= option specifies the alternative reference theta 1 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 sigma Subscript a and sigma Subscript b. If sigma Subscript b is not specified, sigma Subscript b Baseline equals sigma Subscript a. The default is STDDEV=1.

The WEIGHT= option specifies the sample size allocation weights for the two groups. If w Subscript b is not specified, w Subscript b Baseline equals 1 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 Z test for mean difference.

MODEL=TWOSAMPLEFREQ < ( options ) >

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

  • NULLPROP= p Subscript 0 a Baseline less-than p Subscript 0 b Baseline greater-than

  • PROP= p Subscript 1 a

  • TEST= PROP | LOGOR | LOGRR

  • REF= NULLPROP | PROP | AVGNULLPROP | AVGPROP

  • WEIGHT= w Subscript a Baseline less-than w Subscript b Baseline greater-than

  • MATCHNOBS= YES  |  NO

The NULLPROP= option specifies proportions p Subscript a Baseline equals p Subscript 0 a and p Subscript b Baseline equals p Subscript 0 b in groups A and B, respectively, under the null hypothesis. If p Subscript 0 b is not specified, p Subscript 0 b Baseline equals p Subscript 0 a. The default is NULLPROP=0.5.

The PROP= option specifies proportion p Subscript a Baseline equals p Subscript 1 a in group A under the alternative hypothesis. The proportion p Subscript 1 b in group B under the alternative hypothesis is given by p Subscript 1 b Baseline equals p Subscript 0 b. 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 p Subscript 1 a, the proportion in group A under the alternative hypothesis.

The TEST= option specified the null hypothesis upper H 0 colon theta equals 0 in the test. The TEST=PROP option uses the difference in proportions theta equals left-parenthesis p Subscript a Baseline minus p Subscript b Baseline right-parenthesis minus left-parenthesis p Subscript 0 a Baseline minus p Subscript 0 b Baseline right-parenthesis, the TEST=LOGOR option uses the log odds-ratio test theta equals delta minus delta 0, where

delta equals normal l normal o normal g left-parenthesis StartFraction p Subscript a Baseline left-parenthesis 1 minus p Subscript b Baseline right-parenthesis Over p Subscript b Baseline left-parenthesis 1 minus p Subscript a Baseline right-parenthesis EndFraction right-parenthesis delta 0 equals normal l normal o normal g left-parenthesis StartFraction p Subscript 0 a Baseline left-parenthesis 1 minus p Subscript 0 b Baseline right-parenthesis Over p Subscript 0 b Baseline left-parenthesis 1 minus p Subscript 0 a Baseline right-parenthesis EndFraction right-parenthesis

and the TEST=LOGRR option uses the log relative risk test with theta equals delta minus delta 0, where

delta equals normal l normal o normal g left-parenthesis StartFraction p Subscript a Baseline Over p Subscript b Baseline EndFraction right-parenthesis delta 0 equals normal l normal o normal g left-parenthesis StartFraction p Subscript 0 a Baseline Over p Subscript 0 b Baseline EndFraction right-parenthesis

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 p Subscript 0 a and p Subscript 0 b, the REF=PROP option uses the alternative proportions p Subscript 1 a and p Subscript 1 b, 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 w Subscript b is not specified, w Subscript b Baseline equals 1 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 upper H 0 colon theta equals delta minus delta 0 equals 0, where the parameter delta equals minus normal l normal o normal g left-parenthesis h Subscript a Baseline slash h Subscript b Baseline right-parenthesis, delta 0 is the value of delta under the null hypothesis and the values h Subscript a and h Subscript b are the constant hazard rates for groups A and B, respectively.

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

  • NULLHAZARD= h Subscript 0 a Baseline less-than h Subscript 0 b Baseline greater-than

  • NULLMEDSURVTIME= t Subscript 0 a Baseline less-than t Subscript 0 b Baseline greater-than

  • HAZARD= h Subscript 1 a

  • HAZARDRATIO= lamda 1

  • MEDSURVTIME= t Subscript 1 a

The NULLHAZARD= option specifies hazard rates h Subscript a Baseline equals h Subscript 0 a and h Subscript b Baseline equals h Subscript 0 b for groups A and B, respectively, under the null hypothesis. If h Subscript 0 b is not specified, h Subscript 0 b Baseline equals h Subscript 0 a. The NULLMEDSURVTIME= option specifies the median survival times t Subscript a Baseline equals t Subscript 0 a and t Subscript b Baseline equals t Subscript 0 b under the null hypothesis. If t Subscript 0 b is not specified, t Subscript 0 b Baseline equals t Subscript 0 a. If both NULLHAZARD= and NULLMEDSURVTIME= option are not specified, NULLHAZARD=0.06931, which corresponds to NULLMEDSURVTIME=10, is used.

The hazard rate for group B under the alternative hypothesis, h Subscript 1 b, is identical to the hazard rate under the null hypothesis, h Subscript 0 b. The HAZARD=, MEDSURVTIME=, and HAZARDRATIO= options specify the group A hazard rate h Subscript 1 a, the group A median survival time t Subscript 1 a, and the hazard ratio lamda 1 equals h Subscript 1 a Baseline slash h Subscript 1 b, 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 theta 1 is used to compute h Subscript 1 a from the equation:

theta 1 equals minus normal l normal o normal g left-parenthesis StartFraction h Subscript 1 a Baseline Over h Subscript 1 b Baseline EndFraction right-parenthesis minus left-parenthesis minus normal l normal o normal g left-parenthesis StartFraction h Subscript 0 a Baseline Over h Subscript 0 b Baseline EndFraction right-parenthesis right-parenthesis equals minus normal l normal o normal g left-parenthesis StartFraction h Subscript 1 a Baseline Over h Subscript 0 a Baseline EndFraction right-parenthesis

To derive the sample size, you need to specify additional options from the following list:

  • ACCNOBS=n Subscript a

  • ACCRATE=r Subscript a

  • ACCRUAL=UNIFORM  |  EXP(PARM=gamma 0)

  • ACCTIME=upper T Subscript a

  • CEILING=TIME  |  N

  • FOLTIME=upper T Subscript f

  • LOSS=NONE  |  EXP(HAZARD=tau  |  MEDLOSSTIME=t Subscript tau)

  • REF=NULLHAZARD | HAZARD

  • TOTALTIME=T

  • WEIGHT=w Subscript a   < w Subscript b >

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 w Subscript b is not specified, w Subscript b Baseline equals 1 is used. The default is WEIGHT=1, equal sample size for the two groups.

The ACCRUAL= option specifies the method for individual accrual. The ACCRUAL=UNIFORM option (which is the default) specifies that the individual accrual is uniform in the accrual time upper T Subscript a with a constant accrual rate r Subscript a, and the ACCRUAL=EXP(PARM=gamma 0) option specifies that the individual accrual is truncated exponential with a scaled power parameter gamma 0, where gamma 0 greater-than-or-equal-to negative 10 and gamma 0 not-equals 0. With a scaled parameter gamma 0, the power parameter for the truncated exponential with the accrual time upper T Subscript a is given by gamma equals gamma 0 slash upper T Subscript a.

The ACCTIME= and FOLTIME= options specify the accrual time upper T Subscript a and follow-up time upper T Subscript f, respectively. The TOTALTIME= option specifies the total study time, upper T equals upper T Subscript a Baseline plus upper T Subscript f.

The ACCRATE= option specifies the constant accrual rate r Subscript a. If you specify the ACCRATE= option, then you must also specify one of the ACCTIME=, FOLTIME=, and TOTALTIME= options for the sample size computation. Otherwise, you must specify two of the ACCTIME=, FOLTIME=, and TOTALTIME= options to compute the accrual rate and sample size.

The ACCNOBS= option specifies the total number of individuals in the study. If you specify the ACCNOBS= option, then you must also specify one of the ACCTIME=, FOLTIME=, and TOTALTIME= options for the sample size computation. Otherwise, you must specify two of the ACCTIME=, FOLTIME=, and TOTALTIME= options to compute the accrual rate and sample size.

The CEILING= option specifies the additional sample size information to be displayed in the "Number of Events (D) and Sample Sizes (N)" table. The CEILING=TIME option (which is the default) displays additional information that includes ceiling times at the stages, and the CEILING=N option displays additional information that includes ceiling sample sizes at the stages. When you specify CEILING=N, the ceiling sample sizes at each stage are derived to match the sample size allocation weights for the two groups.

The LOSS= option specifies the individual loss to follow-up in the sample size computation. The LOSS=NONE option (which is the default) specifies no loss to follow-up, and the LOSS=EXP option specifies exponential loss function. The HAZARD=tau suboption specifies the exponential loss hazard rate tau, and the MEDLOSSTIME=t Subscript tau suboption specifies the exponential loss hazard rate through the median loss times t Subscript tau.

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 Z test for a normal regression parameter. The available options are as follows:

  • BETA= beta 1

  • VARIANCE= sigma Subscript y Superscript 2

  • XVARIANCE= sigma Subscript x Superscript 2

  • XRSQUARE= r Subscript x Superscript 2

The BETA= option specifies the alternative reference beta 1 and is required if the alternative reference is not specified or derived in the procedure. If the BETA= option is not specified, beta 1 equals theta 1, 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 Z test for the regression parameter.

MODEL=LOGISTIC < ( options ) >

specifies the Z test for a logistic regression parameter. The available options are as follows:

  • BETA= beta 1

  • PROP= p

  • XVARIANCE= sigma Subscript x Superscript 2

  • XRSQUARE= r Subscript x Superscript 2

The BETA= option specifies the alternative reference beta 1 and is required if the alternative reference is not specified or derived in the procedure. If the BETA= option is not specified, beta 1 equals theta 1, the specified or derived alternative reference.

The PROP= option specifies the proportion of the binary response variable Y. The default is PROP=0.5. 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 Z test for the logistic regression parameter.

MODEL=PHREG < ( options ) >

specifies the Z test for a proportional hazards regression parameter. The available options for the number of events are as follows:

  • BETA= beta 1

  • XVARIANCE= sigma Subscript x Superscript 2

  • XRSQUARE= r Subscript x Superscript 2

The BETA= option specifies the alternative reference beta 1 and is required if the alternative reference is not specified or derived in the procedure. If the BETA= option is not specified, beta 1 equals theta 1, 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.

To derive the sample size, you need to specify additional options from the following list:

  • ACCNOBS=n Subscript a

  • ACCRATE=r Subscript a

  • ACCRUAL=UNIFORM  |  EXP(PARM=gamma 0)

  • ACCTIME=upper T Subscript a

  • CEILING=TIME  |  N

  • FOLTIME=upper T Subscript f

  • HAZARD=h Subscript a

  • LOSS=NONE  |  EXP(HAZARD=tau  |  MEDLOSSTIME=t Subscript tau)

  • MEDSURVTIME=t Subscript a

  • TOTALTIME=T

The hazard rate is required for the sample size computation. The HAZARD= h Subscript a option specifies the hazard rate h Subscript a explicitly, and the MEDSURVTIME=t Subscript a option specifies the hazard rate implicitly through the median survival time t Subscript a.

The ACCRUAL= option specifies the method for individual accrual. The ACCRUAL=UNIFORM option (which is the default) specifies that the individual accrual is uniform in the accrual time upper T Subscript a with a constant accrual rate r Subscript a, and the ACCRUAL=EXP(PARM=gamma 0) option specifies that the individual accrual is truncated exponential with a scaled power parameter gamma 0, where gamma 0 greater-than-or-equal-to negative 10 and gamma 0 not-equals 0. With a scaled parameter gamma 0, the power parameter for the truncated exponential with the accrual time upper T Subscript a is given by gamma equals gamma 0 slash upper T Subscript a.

The ACCTIME= and FOLTIME= options specify the accrual time upper T Subscript a and follow-up time upper T Subscript f, respectively. The TOTALTIME= option specifies the total study time, upper T equals upper T Subscript a Baseline plus upper T Subscript f.

The ACCRATE= option specifies the constant accrual rate r Subscript a. If you specify the ACCRATE= option, then you must also specify one of the ACCTIME=, FOLTIME=, and TOTALTIME= options for the sample size computation. Otherwise, you must specify two of the ACCTIME=, FOLTIME=, and TOTALTIME= options to compute the accrual rate and sample size.

The ACCNOBS= option specifies the total number of individuals in the study. If you specify the ACCNOBS= option, then you must also specify one of the ACCTIME=, FOLTIME=, and TOTALTIME= options for the sample size computation. Otherwise, you must specify two of the ACCTIME=, FOLTIME=, and TOTALTIME= options to compute the accrual rate and sample size.

The CEILING= option specifies the additional sample size information to be displayed in the "Number of Events (D) and Sample Sizes (N)" table. The CEILING=TIME option (which is the default) displays additional information that includes ceiling times at the stages, and the CEILING=N option displays additional information that includes ceiling sample sizes at the stages.

The LOSS= option specifies the individual loss to follow-up in the sample size computation. The LOSS=NONE option (which is the default) specifies no loss to follow-up, and the LOSS=EXP option specifies exponential loss function. The HAZARD=tau suboption specifies the exponential loss hazard rate tau, and the MEDLOSSTIME=t Subscript tau suboption specifies the exponential loss hazard rate through the median loss times t Subscript tau.

For a detailed description of the Z test for the proportional hazards regression parameter, see the section Test for a Parameter in the Proportional Hazards Regression Model.

Last updated: December 09, 2022