Example of a 2x2 Crossover Design Equivalence Test
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You want to determine whether your generic antacid is equivalent to a name-brand antacid. Two groups of participants receive a 5-day course of one antacid, followed by a 2-week washout period, and then a 5-day course of the other antacid. You measure gastric pH on the last day of each treatment. Because lower pH values are more acidic, higher values mean the drug is more effective. You will consider the antacids equivalent if the test pH is within 10% of the reference pH.

Group 1 receives the generic antacid (the test treatment) followed by the name-brand antacid (the reference treatment). Group 2 receives the name-brand antacid followed by the generic antacid.

1    Open the worksheet STOMACHACID.MTW.

2    Choose Stat > Equivalence Tests > 2x2 Crossover Design.

3    Choose Data for two sequences are unstacked.

4    From Treatment order for sequence 1, choose Test, Reference.

5    In Sequence 1, Period 1, enter 'Group 1, Generic'. In Sequence 1, Period 2, enter 'Group 1, Brand'.

6    In Sequence 2, Period 1, enter 'Group 2, Brand'. In Sequence 2, Period 2, enter 'Group 2, Generic'.

7    From Hypothesis about, choose Test mean - reference mean.

8    From What do you want to determine, choose Lower limit < test mean - reference mean < upper limit.

9    In Lower limit, enter -0.1. In Upper limit, enter 0.1.

10  Check Multiply by reference mean.

11  Click Options.

12  In Label for reference treatment, type Brand, and in Label for test treatment, type Generic.

13  Click OK in each dialog box.

Session window output

Equivalence Test for 2x2 Crossover Design: Group 1, Generic, Group 1, Brand, Group 2, Brand, 

 

 

Method

 

Treatment order for subjects in sequence 1: Generic, Brand

Treatment order for subjects in sequence 2: Brand, Generic

Lower equivalence limit = -0.1 × sample reference mean = -0.42503

Upper equivalence limit = 0.1 × sample reference mean = 0.42503

 

 

Descriptive Statistics

 

                 Period 1         Period 2

Sequence  N    Mean    StDev    Mean    StDev

1         9  4.0911  0.68641  4.3144  0.63677

2         8  4.1862  0.74110  3.7675  0.65741

 

Within-subject standard deviation = 0.08825

 

 

Effects

 

              Effect        SE  DF  T-Value  P-Value         95% CI

Carryover    0.45181   0.64988  15  0.69521    0.498   (-0.93339, 1.8370)

Treatment   -0.32104  0.060641  15  -5.2941    0.000  (-0.45030, -0.19179)

Period     -0.097708  0.060641  15  -1.6112    0.128  (-0.22696, 0.031546)

 

 

Difference: Mean(Generic) - Mean(Brand)

 

Difference        SE      95% CI     Equivalence Interval

  -0.32104  0.060641  (-0.42735, 0)   (-0.42503, 0.42503)

 

CI is not within the equivalence interval. Cannot claim equivalence.

 

 

Test

 

Null hypothesis:         Difference ≤ -0.42503 or Difference ≥ 0.42503

Alternative hypothesis:  -0.42503 < Difference < 0.42503

α level:                 0.05

 

Null Hypothesis        DF  T-Value  P-Value

Difference ≤ -0.42503  15   1.7149    0.053

Difference ≥ 0.42503   15  -12.303    0.000

 

The greater of the two P-Values is 0.053. Cannot claim equivalence.

Graph window output

Interpreting the results

Note

You should not evaluate equivalence if either the carryover effect or the period effect is significant. If either effect is significant, then the equivalence results may be unreliable.

The p-value for the carryover effect (0.498) and the p-value for the period effect (0.128) are both greater than 0.05. Thus these effects are not significant at the 0.05 level.

The p-value for the treatment effect (0.000) is less than 0.05. Thus the treatment effect is significant at the 0.05 level. The significant treatment effect indicates that one antacid is better than the other at raising stomach pH. The generic antacid did not raise stomach pH as much as the brand-name antacid. The mean stomach pH after the generic antacid was approximately -0.321 less than the average pH after the brand-name antacid.

The difference table and the equivalence plot show that the confidence interval for the difference (-0.42735, 0) falls partly outside of the equivalence interval (-0.42503, 0.42503). Thus you cannot claim that the two antacids are equally effective at raising stomach pH.

The test table confirms that you cannot claim significance. The highest p-value is 0.053, which is greater than the a level of 0.05. Thus you cannot conclude that the two antacids are equally effective at raising stomach pH.