Consider a hypothetical clinical trial to treat interstitial cystitis (IC), a painful, chronic inflammatory condition of the bladder with no known cause that most commonly affects women. Two treatments will be compared: lidocaine alone (“lidocaine”) versus lidocaine plus a fictitious experimental drug called Mironel (“Mir+lido”). The design is balanced, randomized, doubleblind, and femaleonly. The primary outcome is a measure of overall improvement at week 4 of the study, measured on a sevenpoint Likert scale as shown in Table 75.34.
Table 75.34: SelfReport Improvement Scale
Compared to when I started 

this study, my condition is: 

Much worse 
–3 
Worse 
–2 
Slightly worse 
–1 
The same 
0 
Slightly better 
+1 
Better 
+2 
Much better 
+3 
The planned data analysis is a onesided WilcoxonMannWhitney test with where the alternative hypothesis represents greater improvement for “Mir+lido.”
You are asked to graphically assess the power of the planned trial for sample sizes between 100 and 250, assuming that the conditional outcome probabilities given treatment are equal to the values in Table 75.35.
Table 75.35: Conjectured Conditional Probabilities
Response 


Treatment 
–3 
–2 
–1 
0 
+1 
+2 
+3 
Lidocaine 
0.01 
0.04 
0.20 
0.50 
0.20 
0.04 
0.01 
Mir+lido 
0.01 
0.03 
0.15 
0.35 
0.30 
0.10 
0.06 
Use the following statements to compute the power at sample sizes of 100 and 250 and generate a power curve:
ods graphics on; proc power; twosamplewilcoxon vardist("lidocaine") = ordinal ((3 2 1 0 1 2 3) : (.01 .04 .20 .50 .20 .04 .01)) vardist("Mir+lido") = ordinal ((3 2 1 0 1 2 3) : (.01 .03 .15 .35 .30 .10 .06)) variables = "lidocaine"  "Mir+lido" sides = u ntotal = 100 250 power = .; plot step=10; run; ods graphics off;
The VARDIST= option is used to define the distribution for each treatment, and the VARIABLES= option specifies the distributions to compare. The SIDES=U option corresponds to the alternative hypothesis that the second distribution ("Mir+lido") is more favorable. The NTOTAL= option specifies the total sample sizes of interest, and the POWER= option with a missing value (.) identifies the parameter to solve for. The default GROUPWEIGHTS= and ALPHA= options specify a balanced design and significance level .
The STEP=10 option in the PLOT statement requests a point for each sample size increment of 10. The default values for the X=, MIN=, and MAX= plot options specify a sample size range of 100 to 250 (the same as in the analysis) for the X axis.
The tabular and graphical results are shown in Output 75.10.1 and Output 75.10.2, respectively.
Output 75.10.1: Power Values for WilcoxonMannWhitney Test
Fixed Scenario Elements  

Method  O'BrienCastelloe approximation 
Number of Sides  U 
Group 1 Variable  lidocaine 
Group 2 Variable  Mir+lido 
Pooled Number of Bins  7 
Alpha  0.05 
Group 1 Weight  1 
Group 2 Weight  1 
NBins per Group  1000 
Computed Power  

Index  N Total  Power 
1  100  0.651 
2  250  0.939 
The achieved power ranges from 0.651 to 0.939, increasing with sample size.