Non Inferiority Testing

[isecase]

Hi there,

I am a pharmacy student, doing a non-inferiority test to compare the means of a newer medication to older medications. How would I go about doing this test in STATA? What would be the command? I've only taken one statistics course and we did not go over calculating non-inferiority tests, so I apologize if I am asking something that is very basic.

Thank you,

-Case

[Rich Goldstein]

in general, graphical solutions are better than tests for this type of trial; you might want to start with http://www.trialsjournal.com/content/12/1/106

[Joe Canner]

Strictly speaking, it's the same procedure as a superiority test, but instead of looking to see whether the null hypothesis of non-inferiority is rejected, you look to see if it is not rejected. However, as Rich suggests, this is not really a good idea, since the easiest way to not reject the null hypothesis is to have an insufficient sample size. Accordingly, what you need are confidence intervals around your treatment difference, along with some a priori definition of how low the lower bound of the confidence interval can go before the new treatment would be considered inferior. The paper Rich linked to shows how to illustrate this graphically, although all you really need are the confidence interval and the pre-determined lower bound. Keep in mind as well, that sample size is very important such that your confidence limits are sufficiently narrow (and hence not likely to pass the lower bound even if the two treatments are similar).

[isecase]

Thank you both for your input! I will look into that.

[Svend Juul]

Imagine that the lbw dataset is about a trial comparing the effect of two drugs, "nonsmoke" and "smoker", on the outcome bwt. A high value of bwt is desirable, and you want to test whether the effect of nonsmoke is better than, or at least not inferior to, smoke.

This can be done, for example, with ttest. If you want to exclude inferiority of nonsmoke with a probability of 95%, look at the lower 90% confidence limit for the difference; here it is 105.859. Being > 0 it excludes (with 95% probability) inferiority of nonsmoke.compared to smoker:

. webuse lbw.dta, clear
. ttest bwt , by(smoke) level(90)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [90% Conf. Interval]
---------+--------------------------------------------------------------------
nonsmoke |     115    3054.957     70.1625     752.409    2938.604    3171.309
  smoker |      74    2772.297    76.70106    659.8075    2644.514    2900.081
---------+--------------------------------------------------------------------
combined |     189    2944.286    53.02811     729.016     2856.63    3031.941
---------+--------------------------------------------------------------------
    diff |            282.6592    106.9544                 105.859    459.4595
------------------------------------------------------------------------------
    diff = mean(nonsmoke) - mean(smoker)                          t =   2.6428
Ho: diff = 0                                     degrees of freedom =      187
Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
Pr(T < t) = 0.9955         Pr(|T| > |t|) = 0.0089          Pr(T > t) = 0.0045

[Steve Samuels]

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