## No random effects in ANOVA [General Sta­tis­tics]

Hi Abhimanyu,

❝ Generally we mention this sentence in Bio-equivalence protocol "ANOVA model will include Sequence, Formulation and Period as fixed effects and Subject (Sequence) as a random effect. Sequence effect will be tested using Subject (Sequence) as error term."

❝ Why we take "Subject (Sequence) as a random effect??"

Simple:

Because you copypasted this part from one protocol to the other and it is also mentioned in most (all?) guidelines.

Seriously:
• There are no random effects in ANOVA. In SAS-lingo: When you use PROC GLM and have a RANDOM statement it just changes how residual errors are used in calculating the F-value.
If you want to have subjects as a true random effect (i.e., required by the FDA and Health Cana­da) you have to use PROC MIXED instead.
• The nested structure subject(sequence) leads to an over-specificed model, contradics the law of parsimony, and is just silly.
• Such a nesting is superfluous, since in BE subjects are uniquely coded. If, say, subject 1 is allocated to a given sequence there is not yet ‘another’ subject 1 allocated to another sequence. Randomization is not like Schrö­din­ger’s cat. Hence, the nested term in the guidelines is an insult to the mind. This explains the many lines in PROC GML given with ‘.’ and in Phoenix WinNonlin as ‘not estimable’.
• The simple model sequence, subject, period, treatment gives identi­cal (‼) estimates of the residual variance and the treatment effect and hence, its confidence interval.
Whether subjects should be treated as a fixed or random effect is almost a philosophical question. In the strict sense:
1. If you specify subjects as a fixed effect in the model, you make a statement about the subjects in the study.
2. If you specify them as a random effect, you make a statement about the population of other subjects.
At the end of the day you extrapolate results of the study to the population of patients.
Some statisticians (including ones of the FDA, Health Canada, China’s CDE, and myself) think that (b) is the correct way. Others (of the EMA, …) prefer (a). If the study is balanced and complete (i.e., no missing periods) the outcome is identical.

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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