Proc Power in SAS 9.1

Outline

• Sample size and power calculations

• Customizing plots of power function

• ODS Tables

Statistical analysis covered in the power procedure

• t tests for means • equivalence tests for means • confidence intervals for means • tests of binomial proportions • multiple regression • tests of correlation and partial correlation • one-way analysis of variance • rank tests for comparing two survival curves

Syntax

PROC POWER < options > ; MULTREG < options > ; ONECORR < options > ; ONESAMPLEFREQ < options > ; ONESAMPLEMEANS < options > ; ONEWAYANOVA < options > ; PAIREDFREQ < options > ; PAIREDMEANS < options > ; TWOSAMPLEFREQ < options > ; TWOSAMPLEMEANS < options > ; TWOSAMPLESURVIVAL < options > ; PLOT < plot-options > < / graph-options > ;

Twosamplemeans statement

Twosamplemeans <options>; Performing power and sample size analyses for two-

independent-sample versions of pooled and unpooled t-tests, equivalence tests and confidence interval precision.

<options>: design, data analysis method, variability,

type I Error, effect size, power , sample size.

Two sample independent mean

**missing value identifies a parameter as result parameter;

Proc power; twosamplemeans test=diff dist=normal meandiff = 3 3.5 4 stddev= 8 to 9 by 0.5 groupweights = (1 2) power = 0.8 ntotal = .; plot y=power min=0.5 max=0.99;

Two-sample t Test for Mean Difference

Computed N Total

Index Mean

Diff Std Dev

Actual Power

N Total

1 3.0 8.0 0.803 255

2 3.0 8.5 0.803 288

3 3.0 9.0 0.801 321

4 3.5 8.0 0.805 189

5 3.5 8.5 0.805 213

6 3.5 9.0 0.803 237

7 4.0 8.0 0.802 144

8 4.0 8.5 0.801 162

9 4.0 9.0 0.805 183

Fixed Scenario Elements

Distribution Normal

Method Exact

Group 1 Weight 1

Group 2 Weight 2

Nominal Power 0.8

Number of Sides 2

Null Difference 0

Alpha 0.05

Two sample independent mean

Proc power; twosamplemeans meandiff = 3 3.5 4 stddev=8 to 9 by 0.5 groupweights=(1 2) power = . ntotal = 249; plot x=n min=150 max=400;run;

Two-sample t Test Fixed Scenario Elements

Distribution Normal

Method Exact

Group 1 Weight 1

Group 2 Weight 2

Total Sample Size 249

Number of Sides 2

Null Difference 0

Alpha 0.05

Computed Power

Index Mean

Diff Std Dev Power

1 3.0 8.0 0.794

2 3.0 8.5 0.744

3 3.0 9.0 0.695

4 3.5 8.0 0.900

5 3.5 8.5 0.862

6 3.5 9.0 0.822

7 4.0 8.0 0.959

8 4.0 8.5 0.937

9 4.0 9.0 0.909

Twosamplefreq statement

Twosamplefreq <options>;

Do power and sample size analyses for tests of two independent proportions. Pearson’s chi-square, Fisher’s exact, and likelihood ratio chi-square tests are supported.

Fisher’s Exact Test

Proc power; Twosamplefreq test=fisher Proportiondiff = 0.10 to 0.15 by 0.01 Refproportion = 0.20 npergroup= . Power = 0.85; plot y=power min=0.5 max=0.99;Run;

Fisher's Exact Conditional Test for Two Proportions

Fixed Scenario Elements

Distribution Exact conditional

Method Walters normal approximation

Reference (Group 1) Proportion 0.2

Nominal Power 0.85

Number of Sides 2

Alpha 0.05

Computed N Per Group

Index Proportion

Diff Actual Power

N Per Group

1 0.10 0.850 354

2 0.11 0.851 298

3 0.12 0.851 254

4 0.13 0.851 220

5 0.14 0.852 193

6 0.15 0.851 170

Twosamplesurvival Statement

Twosamplesurvival <options>;

Power and sample size analyses for comparing two survival curves by the log-rank, Gehan, and Tarone-Ware rank tests.

Survival analysis

proc power; twosamplesurvival test = logrank groupmedsurtimes = (16 22) accrualtime = 6 totaltime = 18 groupns = 40 | 60 power = . ;run;

Log-Rank Test for Two Survival Curves

Fixed Scenario Elements

Method Lakatos normal approximation

Form of Survival Curve 1 Exponential

Form of Survival Curve 2 Exponential

Accrual Time 6

Total Time 18

Group 1 Median Survival Time 16

Group 2 Median Survival Time 22

Group 1 Sample Size 40

Group 2 Sample Size 60

Number of Sides 2

Number of Time Sub-Intervals 12

Group 1 Loss Exponential Hazard 0

Group 2 Loss Exponential Hazard 0

Alpha 0.05

Computed Power

Power

0.178

Customizing Plots

Adding reference lines

Axis Options in Plot statement:• XOPTS: specify plot characteristics pertaining to

the x-axis. - REF=number-list : specifies locations for reference

lines extending from the x-axis across the entire plotting region.

-CROSSREF=YES or NO: specifies whether the reference lines defined by REF should be crossed with a reference line on y-axis that indicates the solution point on the curve.

• YOPTS

Adding reference lines

*add reference lines to highlight power=0.8 and power=0.9;

Proc power plotonly;

twosamplemeans

meandiff = 3 4

stddev=8 9

power = .

ntotal = 100;

plot x=n min=20 max=500 yopts=(ref=0.8 0.9);

run;

plot x=n min=20 max=500 yopts=(ref=0.8 0.9)

yopts=(ref=0.8 0.9 crossref=yes)

yopts=(ref=0.9) xopts=(ref=100 crossref=yes)

Linking plot features to parameters

Vary (feature <by parameter-list>... Feature <by parameter-list>

Specify how plot features should be linked to

Varying analysis parameters.

Available features are color, linestyle, panel and symbol.

Linking plot features to parameters

Proc power plotonly; twosamplemeans meandiff = 3 4 stddev=8 9 power = 0.9 ntotal = .; plot y=power min=0.5 max=0.95;run;

vary (linestyle by meandiff, symbol by stddev)

vary (symbol by meandiff, color by stddev);

Choosing Legend Styles using“Key” option

Proc power plotonly;

twosamplemeans

meandiff = 3 4

stddev=8 9

power = 0.9

ntotal = .;

plot y=power min=0.5 max=0.95 key = bycurve;

run;

key = byfeature

key = byfeature (pos=inset)

key = bycurve

key = bycurve (numbers=off pos=inset)

key = oncurves

ODS Tables

ODS tables

• FixedElements: including all single-value

Analysis parameters

• Output: showing all input and computed analysis parameters, error descriptions

• PlotContent: data contained in plots including analysis and parameters and indices identifying plot features

ODS path names

• The ODS path names are created as follows.

- Power.<analysis statement name>.FixedElements

- Power.<analysis statement name>.Output

- Power.<analysis statement name>.PlotContent