The POWER Procedure

TWOSAMPLEFREQ Statement

Subsections:

Summary of Options
Dictionary of Options
Restrictions on Option Combinations
Option Groups for Common Analyses

TWOSAMPLEFREQ <options>;

The TWOSAMPLEFREQ statement performs power and sample size analyses for tests of two independent proportions. The Farrington-Manning score, Pearson’s chi-square, Fisher’s exact, and likelihood ratio chi-square tests are supported.

Summary of Options

Table 89.21 summarizes the options available in the TWOSAMPLEFREQ statement.

Table 89.21: TWOSAMPLEFREQ Statement Options

Option	Description
Define analysis
TEST=	Specifies the statistical analysis
Specify analysis information
ALPHA=	Specifies the significance level
NULLODDSRATIO=	Specifies the null odds ratio
NULLPROPORTIONDIFF=	Specifies the null proportion difference
NULLRELATIVERISK=	Specifies the null relative risk
SIDES=	Specifies the number of sides and the direction of the statistical test or confidence interval
Specify effects
GROUPPROPORTIONS=	Specifies the two independent proportions, $p_1$ and $p_2$
ODDSRATIO=	Specifies the odds ratio $\left[p_2/(1-p_2)\right] / \left[p_1/(1-p_1) \right]$
PROPORTIONDIFF=	Specifies the proportion difference $p_2 - p_1$
REFPROPORTION=	Specifies the reference proportion $p_1$
RELATIVERISK=	Specifies the relative risk $p_2 / p_1$
Specify sample size and allocation
GROUPNS=	Specifies the two group sample sizes
GROUPWEIGHTS=	Specifies the sample size allocation weights for the two groups
NFRACTIONAL	Enables fractional input and output for sample sizes
NPERGROUP=	Specifies the common sample size per group
NTOTAL=	Specifies the sample size
Specify power
POWER=	Specifies the desired power of the test
Control ordering in output
OUTPUTORDER=	Controls the output order of parameters

Table 89.22 summarizes the valid result parameters for different analyses in the TWOSAMPLEFREQ statement.

Table 89.22: Summary of Result Parameters in the TWOSAMPLEFREQ Statement

Analyses	Solve For	Syntax
TEST= FISHER	Power	POWER= .
	Sample size	NTOTAL= .
		NPERGROUP= .
TEST= FM	Power	POWER= .
	Sample size	NTOTAL= .
		NPERGROUP= .
TEST= FM_RR	Power	POWER= .
	Sample size	NTOTAL= .
		NPERGROUP= .
TEST= LRCHI	Power	POWER= .
	Sample size	NTOTAL= .
		NPERGROUP= .
TEST= PCHI	Power	POWER= .
	Sample size	NTOTAL= .
		NPERGROUP= .

Dictionary of Options

ALPHA=number-list

specifies the level of significance of the statistical test. The default is 0.05, which corresponds to the usual 0.05 $\times$ 100% = 5% level of significance. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

GROUPPROPORTIONS=grouped-number-list GPROPORTIONS=grouped-number-list GROUPPS=grouped-number-list GPS=grouped-number-list

specifies the two independent proportions, $p_1$ and $p_2$ . For information about specifying the grouped-number-list, see the section Specifying Value Lists in Analysis Statements.

GROUPNS=grouped-number-list GNS=grouped-number-list

specifies the two group sample sizes. For information about specifying the grouped-number-list, see the section Specifying Value Lists in Analysis Statements.

GROUPWEIGHTS=grouped-number-list GWEIGHTS=grouped-number-list

specifies the sample size allocation weights for the two groups. This option controls how the total sample size is divided between the two groups. Each pair of values for the two groups represents relative allocation weights. Additionally, if the NFRACTIONAL option is not used, the total sample size is restricted to be equal to a multiple of the sum of the two group weights (so that the resulting design has an integer sample size for each group while adhering exactly to the group allocation weights). Values must be integers unless the NFRACTIONAL option is used. The default value is (1 1), a balanced design with a weight of 1 for each group. For information about specifying the grouped-number-list, see the section Specifying Value Lists in Analysis Statements.

NFRACTIONAL NFRAC

enables fractional input and output for sample sizes. See the section Sample Size Adjustment Options for information about the ramifications of the presence (and absence) of the NFRACTIONAL option.

NPERGROUP=number-list NPERG=number-list

specifies the common sample size per group or requests a solution for the common sample size per group by specifying a missing value (NPERGROUP= .). Use of this option implicitly specifies a balanced design. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

NTOTAL=number-list

specifies the sample size or requests a solution for the sample size by specifying a missing value (NTOTAL= .). For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

NULLODDSRATIO=number-list NULLOR=number-list

specifies the null odds ratio. You can specify this option only if you also specify the ODDSRATIO= and TEST= PCHI options. The NULLODDSRATIO= option is inconsistent with TEST= PCHI, which tests the proportion difference rather than the odds ratio, and its value is converted internally to a NULLPROPORTIONDIFF value by fixing the reference proportion. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements. By default, NULLOR=1.

NULLPROPORTIONDIFF=number-list NULLPDIFF=number-list

specifies the null proportion difference. You can specify this option only if you also specify the GROUPPROPORTIONS= or PROPORTIONDIFF= option and the TEST= FM or TEST= PCHI option. If you are using a nondefault null value, then TEST= FM is recommended. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements. By default, NULLPDIFF=0.

NULLRELATIVERISK=number-list NULLRR=number-list

specifies the null relative risk. You can specify this option only if you also specify the GROUPPROPORTIONS= or RELATIVERISK= option and the TEST= FM_RR or TEST= PCHI option. If you are using a nondefault null value, then TEST= FM_RR is recommended. The NULLRELATIVERISK= option is inconsistent with TEST= PCHI, which tests the proportion difference rather than the relative risk, and its value is converted internally to a NULLPROPORTIONDIFF value by fixing the reference proportion. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements. By default, NULLRR=1.

ODDSRATIO=number-list OR=number-list

specifies the odds ratio $\left[p_2/(1-p_2)\right] / \left[p_1/(1-p_1) \right]$ . For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

OUTPUTORDER=INTERNAL | REVERSE | SYNTAX

controls how the input and default analysis parameters are ordered in the output. OUTPUTORDER= INTERNAL (the default) arranges the parameters in the output according to the following order of their corresponding options:

SIDES=
NULLPROPORTIONDIFF=
NULLODDSRATIO=
NULLRELATIVERISK=
ALPHA=
GROUPPROPORTIONS=
REFPROPORTION=
PROPORTIONDIFF=
ODDSRATIO=
RELATIVERISK=
GROUPWEIGHTS=
NTOTAL=
NPERGROUP=
GROUPNS=
POWER=

The OUTPUTORDER= SYNTAX option arranges the parameters in the output in the same order in which their corresponding options are specified in the TWOSAMPLEFREQ statement. The OUTPUTORDER= REVERSE option arranges the parameters in the output in the reverse of the order in which their corresponding options are specified in the TWOSAMPLEFREQ statement.

POWER=number-list

specifies the desired power of the test or requests a solution for the power by specifying a missing value (POWER= .). The power is expressed as a probability, a number between 0 and 1, rather than as a percentage. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

PROPORTIONDIFF=number-list PDIFF=number-list

specifies the proportion difference $p_2 - p_1$ . For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

REFPROPORTION=number-list REFP=number-list

specifies the reference proportion $p_1$ . For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

RELATIVERISK=number-list RR=number-list

specifies the relative risk $p_2 / p_1$ . For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

SIDES=keyword-list

specifies the number of sides (or tails) and the direction of the statistical test or confidence interval. For information about specifying the keyword-list, see the section Specifying Value Lists in Analysis Statements. You can specify the following keywords:

1: specifies a one-sided test, with the alternative hypothesis in the same direction as the effect.
2: specifies a two-sided test.
U: specifies an upper one-sided test, with the alternative hypothesis indicating an effect greater than the null value.
L: specifies a lower one-sided test, with the alternative hypothesis indicating an effect less than the null value.

If the effect size is zero, then SIDES= 1 is not permitted; instead, specify the direction of the test explicitly in this case with either SIDES= L or SIDES= U. By default, SIDES=2.

TEST=FISHER | FM | FM_RR | LRCHI | PCHI

specifies the statistical analysis. You can specify the following values:

FISHER: specifies Fisher’s exact test.
FM: specifies the score test of Farrington and Manning (1990) for proportion difference.
FM_RR: specifies the score test of Farrington and Manning (1990) for relative risk.
LRCHI: specifies the likelihood ratio chi-square test.
PCHI: specifies Pearson’s chi-square test for proportion difference.

If you are using a nondefault null value for a noninferiority or superiority test, then TEST= FM or TEST= FM_RR is the most appropriate choice. In the absence of any nondefault null values, the default is TEST=PCHI. If you specify at least one nonzero null difference by using the NULLPROPORTIONDIFF= option, then the default is TEST=FM. If you specify at least one null relative risk not equal to 1 by using the NULLRR= option, then the default is TEST=FM_RR. For information about the power and sample size computational methods and formulas, see the section Analyses in the TWOSAMPLEFREQ Statement.

Restrictions on Option Combinations

To specify the proportions, choose one of the following parameterizations:

individual proportions (by using the GROUPPROPORTIONS= option)
difference between proportions and reference proportion (by using the PROPORTIONDIFF= and REFPROPORTION= options)
odds ratio and reference proportion (by using the ODDSRATIO= and REFPROPORTION= options)
relative risk and reference proportion (by using the RELATIVERISK= and REFPROPORTION= options)

To specify the sample size and allocation, choose one of the following parameterizations:

sample size per group in a balanced design (by using the NPERGROUP= option)
total sample size and allocation weights (by using the NTOTAL= and GROUPWEIGHTS= options)
individual group sample sizes (by using the GROUPNS= option)

Option Groups for Common Analyses

This section summarizes the syntax for the common analyses that are supported in the TWOSAMPLEFREQ statement.

Pearson Chi-Square Test for Two Proportions

You can use the NPERGROUP= option in a balanced design and express effects in terms of the individual proportions, as in the following statements. Default values for the SIDES= and ALPHA= options specify a two-sided test with a significance level of 0.05.

proc power;
   twosamplefreq test=pchi
      groupproportions = (.15 .25)
      nullproportiondiff = .03
      npergroup = 50
      power = .;
run;

You can also specify an unbalanced design by using the NTOTAL= and GROUPWEIGHTS= options and express effects in terms of the odds ratio. The default value of the NULLODDSRATIO= option specifies a test of no effect.

proc power;
   twosamplefreq test=pchi
      oddsratio = 2.5
      refproportion = 0.3
      groupweights = (1 2)
      ntotal = .
      power = 0.8;
run;

You can also specify sample sizes with the GROUPNS= option and express effects in terms of relative risks. The default value of the NULLRELATIVERISK= option specifies a test of no effect.

proc power;
   twosamplefreq test=pchi
      relativerisk = 1.5
      refproportion = 0.2
      groupns = 40 | 60
      power = .;
run;

You can also express effects in terms of the proportion difference. The default value of the NULLPROPORTIONDIFF= option specifies a test of no effect, and the default value of the GROUPWEIGHTS= option specifies a balanced design.

proc power;
   twosamplefreq test=pchi
      proportiondiff = 0.15
      refproportion = 0.4
      ntotal = 100
      power = .;
run;

Farrington-Manning Score Test for Proportion Difference

The following statements demonstrate a sample size computation for the Farrington-Manning score test for the difference of two independent proportions:

proc power;
   twosamplefreq test=fm
      proportiondiff = 0.06
      refproportion = 0.32
      nullproportiondiff = -0.02
      sides = u
      ntotal = .
      power = 0.85;
run;

Farrington-Manning Score Test for Relative Risk

The following statements demonstrate a sample size computation for the Farrington-Manning score test for the relative risk of two independent proportions:

proc power;
   twosamplefreq test=fm_rr
      relativerisk = 1.1
      refproportion = 0.32
      nullrelativerisk = 0.95
      sides = u
      ntotal = .
      power = 0.9;
run;

Fisher’s Exact Conditional Test for Two Proportions

The following statements demonstrate a power computation for Fisher’s exact conditional test for two proportions. Default values for the SIDES= and ALPHA= options specify a two-sided test with a significance level of 0.05.

proc power;
   twosamplefreq test=fisher
      groupproportions = (.35 .15)
      npergroup = 50
      power = .;
run;

Likelihood Ratio Chi-Square Test for Two Proportions

The following statements demonstrate a sample size computation for the likelihood ratio chi-square test for two proportions. Default values for the SIDES= and ALPHA= options specify a two-sided test with a significance level of 0.05.

proc power;
   twosamplefreq test=lrchi
      oddsratio = 2
      refproportion = 0.4
      npergroup = .
      power = 0.9;
run;