## Studentized & standardized residuals [Outliers]

Hi UdayK,

❝ […] outlier test using Phoenix WinNonlin Software (Studentized residual method) and R-Software (code) in the Bioequivalence 2way cross design.

“Studentized residual” is an ambiguous term. There are two flavors:
1. Internally studentized (aka “standardized”), where
$$\widehat{\sigma}^2={1 \over n-m}\sum_{j=1}^n \widehat{\varepsilon\,}_j^{\,2}$$
2. Externally studentized, where
$$\widehat{\sigma}_{(i)}^2={1 \over n-m-1}\sum_{\begin{smallmatrix}j = 1\\j \ne i\end{smallmatrix}}^n \widehat{\varepsilon\,}_j^{\,2}$$
#1 is easily accessible in Phoenix WinNonlin (divide the raw residual by the standard error). Assess only the first period. The value of the other period has the same value but with the opposite sign and is therefore, not informative. No idea how to get #2 In WinNonlin. Ask at Certara’s forum.
Both are easily obtained in SAS, R,…

In R for the fixed effects model (untested!):

mod  <- lm(log(PK) ~ sequence + subject%in%sequence + period + treatment,                      data = yourdata) res1 <- rstandard(mod) # 1. Internally studentized (standardized) res2 <- rstudent(mod)  # 2. Externally studentized

Note that #2 is in general more restrictive than #1, i.e., it might be that you detect more outliers.

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

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