Group sequential method subjecting to non-normality

Question

In the context of group sequential methods(GSM) for a clinical trial with two treatment arms, it is usually assumed that data follows normal distribution $N(\mu,\sigma^2)$. Then GSM such as Pocock's test and O'Brien and Fleming test can be applied to the problem.

My question is that if data does not follow normality assumption, what kind of test should one use ? Since in reality many data are from skewed distributions,e.g., exponential, chi-square or lognormal, violation of normality should often be seen. Then in this case what method should we use to do group sequential test? Any reference or material would be appreciated.

thank you.

Answer 1

A key thing to realize is that in the assumptions of many sequential methods, it's not an assumption that the data is normal, but rather that the statistic is normal.

This is a much more reasonable assumption. As you stated, most analysts rarely see normally distributed data. However, it is quite common that the statistic of interest approaches a normal distribution as the sample size becomes reasonably large.

As a simple example, suppose you are comparing means between two different groups. The data itself may be non-normal, but the central limit theorem states that that the estimated means will be approximately normal for large samples.