The POWER Procedure

PAIREDFREQ Statement

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

PAIREDFREQ <options> ;

The PAIREDFREQ statement performs power and sample size analyses for McNemar’s test for paired proportions.

Summary of Options

Table 71.14 summarizes the options available in the PAIREDFREQ statement.

Table 71.14: PAIREDFREQ Statement Options

Option	Description
Define analysis
DIST=	Specifies the underlying distribution assumed for the test statistic
TEST=	Specifies the statistical analysis
Specify analysis information
ALPHA=	Specifies the significance level
NULLDISCPROPRATIO=	Specifies the null value of the ratio of discordant proportions
SIDES=	Specifies the number of sides and the direction of the statistical test or confidence interval
Specify effects
CORR=	Specifies the correlation $\phi$ between members of a pair
DISCPROPDIFF=	Specifies the discordant proportion difference $p_{01} - p_{10}$
DISCPROPORTIONS=	Specifies the two discordant proportions, $p_{10}$ and $p_{01}$
DISCPROPRATIO=	Specifies the ratio $p_{01} / p_{10}$
ODDSRATIO=	Specifies the odds ratio $\left[p_{\cdot 1}/(1-p_{\cdot 1})\right] /\left[p_{1 \cdot }/(1-p_{1 \cdot }) \right]$
PAIREDPROPORTIONS=	Specifies the two paired proportions, $p_{1 \cdot }$ and $p_{\cdot 1}$
PROPORTIONDIFF=	Specifies the proportion difference $p_{\cdot 1} - p_{1 \cdot }$
REFPROPORTION=	Specifies either the reference first proportion $p_{1 \cdot }$ or the reference discordant proportion $p_{10}$
RELATIVERISK=	Specifies the relative risk $p_{\cdot 1} / p_{1 \cdot }$
TOTALPROPDISC=	Specifies the discordant proportion sum, $p_{10} + p_{01}$
Specify sample size
NFRACTIONAL	Enables fractional input and output for sample sizes
NPAIRS=	Specifies the total number of proportion pairs
Specify power
POWER=	Specifies the desired power of the test
Choose computational method
METHOD=	Specifies the computational method
Control ordering in output
OUTPUTORDER=	Controls the output order of parameters

Table 71.15 summarizes the valid result parameters in the PAIREDFREQ statement.

Table 71.15: Summary of Result Parameters in the PAIREDFREQ Statement

Analyses	Solve For	Syntax
TEST=MCNEMAR METHOD=CONNOR	Power	POWER=.
	Sample size	NPAIRS=.
TEST=MCNEMAR METHOD=EXACT	Power	POWER=.
TEST=MCNEMAR METHOD=MIETTINEN	Power	POWER=.
	Sample size	NPAIRS=.

Dictionary of Options

ALPHA=number-list

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

CORR=number-list

specifies the correlation $\phi$ between members of a pair. See the section Specifying Value Lists in Analysis Statements for information about specifying the number-list.

DISCPROPORTIONS=grouped-number-list DISCPS=grouped-number-list

specifies the two discordant proportions, $p_{10}$ and $p_{01}$ . See the section Specifying Value Lists in Analysis Statements for information about specifying the grouped-number-list.

DISCPROPDIFF=number-list DISCPDIFF=number-list

specifies the difference $p_{01} - p_{10}$ between discordant proportions. See the section Specifying Value Lists in Analysis Statements for information about specifying the number-list.

DISCPROPRATIO=number-list DISCPRATIO=number-list

specifies the ratio $p_{01} / p_{10}$ of discordant proportions. See the section Specifying Value Lists in Analysis Statements for information about specifying the number-list.

DIST=EXACT_COND DIST=NORMAL

specifies the underlying distribution assumed for the test statistic. EXACT_COND corresponds to the exact conditional test, based on the exact binomial distribution of the two types of discordant pairs given the total number of discordant pairs. NORMAL corresponds to the conditional test based on the normal approximation to the binomial distribution of the two types of discordant pairs given the total number of discordant pairs. The default value is EXACT_COND.

METHOD=CONNOR METHOD=EXACT METHOD=MIETTINEN

specifies the computational method. METHOD=EXACT (the default) uses the exact binomial distributions of the total number of discordant pairs and the two types of discordant pairs. METHOD=CONNOR uses an approximation from Connor (1987), and METHOD=MIETTINEN uses an approximation from Miettinen (1968). The CONNOR and MIETTINEN methods are valid only for DIST=NORMAL.

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. This option cannot be used with METHOD=EXACT.

NPAIRS=number-list

specifies the total number of proportion pairs (concordant and discordant) or requests a solution for the number of pairs with a missing value (NPAIRS=.). See the section Specifying Value Lists in Analysis Statements for information about specifying the number-list.

NULLDISCPROPRATIO=number-list NULLDISCPRATIO=number-list NULLRATIO=number-list NULLR=number-list

specifies the null value of the ratio of discordant proportions. The default value is 1. See the section Specifying Value Lists in Analysis Statements for information about specifying the number-list.

ODDSRATIO=number-list OR=number-list

specifies the odds ratio $\left[p_{\cdot 1}/(1-p_{\cdot 1})\right] / \left[p_{1 \cdot }/(1-p_{1 \cdot }) \right]$ . See the section Specifying Value Lists in Analysis Statements for information about specifying the number-list.

OUTPUTORDER=INTERNAL OUTPUTORDER=REVERSE OUTPUTORDER=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=
NULLDISCPROPRATIO=
ALPHA=
PAIREDPROPORTIONS=
PROPORTIONDIFF=
ODDSRATIO=
RELATIVERISK=
CORR=
DISCPROPORTIONS=
DISCPROPDIFF=
TOTALPROPDISC=
REFPROPORTION=
DISCPROPRATIO=
NPAIRS=
POWER=

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

PAIREDPROPORTIONS=grouped-number-list PPROPORTIONS=grouped-number-list PAIREDPS=grouped-number-list PPS=grouped-number-list

specifies the two paired proportions, $p_{1 \cdot }$ and $p_{\cdot 1}$ . See the section Specifying Value Lists in Analysis Statements for information about specifying the grouped-number-list.

POWER=number-list

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

PROPORTIONDIFF=number-list PDIFF=number-list

specifies the proportion difference $p_{\cdot 1} - p_{1 \cdot }$ . See the section Specifying Value Lists in Analysis Statements for information about specifying the number-list.

REFPROPORTION=number-list REFP=number-list

specifies either the reference first proportion $p_{1 \cdot }$ (when used in conjunction with the PROPORTIONDIFF=, ODDSRATIO=, or RELATIVERISK= option) or the reference discordant proportion $p_{10}$ (when used in conjunction with the DISCPROPDIFF= or DISCPROPRATIO= option). See the section Specifying Value Lists in Analysis Statements for information about specifying the number-list.

RELATIVERISK=number-list RR=number-list

specifies the relative risk $p_{\cdot 1} / p_{1 \cdot }$ . See the section Specifying Value Lists in Analysis Statements for information about specifying the number-list.

SIDES=keyword-list

specifies the number of sides (or tails) and the direction of the statistical test or confidence interval. See the section Specifying Value Lists in Analysis Statements for information about specifying the keyword-list. Valid keywords and their interpretation are as follows:

1: one-sided with alternative hypothesis in same direction as effect
2: two-sided
U: upper one-sided with alternative greater than null value
L: lower one-sided with alternative less than 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. The default value is 2.

TEST=MCNEMAR

specifies the McNemar test of paired proportions. This is the default test option.

TOTALPROPDISC=number-list TOTALPDISC=number-list PDISC=number-list

specifies the sum of the two discordant proportions, $p_{10} + p_{01}$ . See the section Specifying Value Lists in Analysis Statements for information about specifying the number-list.

Restrictions on Option Combinations

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

discordant proportions (using the DISCPROPORTIONS= option)
difference and sum of discordant proportions (using the DISCPROPDIFF= and TOTALPROPDISC=options)
difference of discordant proportions and reference discordant proportion (using the DISCPROPDIFF= and REFPROPORTION= options)
ratio of discordant proportions and reference discordant proportion (using the DISCPROPRATIO= and REFPROPORTION= options)
ratio and sum of discordant proportions (using the DISCPROPRATIO= and TOTALPROPDISC=options)
paired proportions and correlation (using the PAIREDPROPORTIONS= and CORR= options)
proportion difference, reference proportion, and correlation (using the PROPORTIONDIFF=, REFPROPORTION=, and CORR= options)
odds ratio, reference proportion, and correlation (using the ODDSRATIO=, REFPROPORTION=, and CORR= options)
relative risk, reference proportion, and correlation (using the RELATIVERISK=, REFPROPORTION=, and CORR= options)

Option Groups for Common Analyses

This section summarizes the syntax for the common analyses supported in the PAIREDFREQ statement.

McNemar Exact Conditional Test

You can express effects in terms of the individual discordant proportions, as in the following statements. Default values for the TEST=, SIDES=, ALPHA=, and NULLDISCPROPRATIO= options specify a two-sided McNemar test for no effect with a significance level of 0.05.

proc power;
   pairedfreq dist=exact_cond
      discproportions = 0.15 | 0.45
      npairs = 80
      power = .;
run;

You can also express effects in terms of the difference and sum of discordant proportions:

proc power;
   pairedfreq dist=exact_cond
      discpropdiff = 0.3
      totalpropdisc = 0.6
      npairs = 80
      power = .;
run;

You can also express effects in terms of the difference of discordant proportions and the reference discordant proportion:

proc power;
   pairedfreq dist=exact_cond
      discpropdiff = 0.3
      refproportion = 0.15
      npairs = 80
      power = .;
run;

You can also express effects in terms of the ratio of discordant proportions and the denominator of the ratio:

proc power;
   pairedfreq dist=exact_cond
      discpropratio = 3
      refproportion = 0.15
      npairs = 80
      power = .;
run;

You can also express effects in terms of the ratio and sum of discordant proportions:

proc power;
   pairedfreq dist=exact_cond
      discpropratio = 3
      totalpropdisc = 0.6
      npairs = 80
      power = .;
run;

You can also express effects in terms of the paired proportions and correlation:

proc power;
   pairedfreq dist=exact_cond
      pairedproportions = 0.6 | 0.8
      corr = 0.4
      npairs = 45
      power = .;
run;

You can also express effects in terms of the proportion difference, reference proportion, and correlation:

proc power;
   pairedfreq dist=exact_cond
      proportiondiff = 0.2
      refproportion = 0.6
      corr = 0.4
      npairs = 45
      power = .;
run;

You can also express effects in terms of the odds ratio, reference proportion, and correlation:

proc power;
   pairedfreq dist=exact_cond
      oddsratio = 2.66667
      refproportion = 0.6
      corr = 0.4
      npairs = 45
      power = .;
run;

You can also express effects in terms of the relative risk, reference proportion, and correlation:

proc power;
   pairedfreq dist=exact_cond
      relativerisk = 1.33333
      refproportion = 0.6
      corr = 0.4
      npairs = 45
      power = .;
run;

McNemar Normal Approximation Test

The following statements demonstrate a sample size computation for the normal-approximate McNemar test. The default value for the METHOD= option specifies an exact sample size computation. Default values for the TEST=, SIDES=, ALPHA=, and NULLDISCPROPRATIO= options specify a two-sided McNemar test for no effect with a significance level of 0.05.

proc power;
   pairedfreq dist=normal method=connor
      discproportions = 0.15 | 0.45
      npairs = .
      power = .9;
run;