Bioequivalence and Bioavailability Forum

Helmut,

Thank you very much for answer!!! It was very complete!!!

please, look the ANOVA table results that was generate by proposed code (no changes were made with the sequence effect):

❝ attr(TypeIII, "heading")[1] <- "Type III Analysis of Variance Table\n"

❝ MSdenom <- TypeIII["sequence:subject", "Mean Sq"]

❝ df2 <- TypeIII["sequence:subject", "Df"]

❝ fvalue <- TypeIII["sequence", "Mean Sq"] / MSdenom

❝ df1 <- TypeIII["sequence", "Df"]

❝ TypeIII["sequence", 4] <- fvalue

❝ TypeIII["sequence", 5] <- pf(fvalue, df1, df2, lower.tail = FALSE)

❝ print(TypeIII, digits = 6, signif.stars = FALSE)

❝

❝ Analysis of Variance Table

❝

❝ Response: log(PK)

❝                   Df   Sum Sq Mean Sq F value   Pr(>F)

❝ Sequence           1   1.3253 1.32531 2.44067 0.120391

❝ Period             3   3.5824 1.19413 2.19909 0.090673

❝ Treatment          1   2.7923 2.79228 5.14222 0.024818

❝ Sequence:Subject  48 233.6721 4.86817 8.96514  < 2e-16

❝ Residuals        146  79.2796 0.54301

So I made a small modification in your code:

Fit_1 <- lm(log(Cmax) ~ Sequence + Subject%in%Sequence + Period + Treatment , data=Cmax)
Type_I<-anova(Fit_1)
Type_III       <- Type_I # use what we have
attr(Type_III, "heading")[1] <- "Type III Analysis of Variance Table\n"
MSdenom       <- Type_III[4, "Mean Sq"]
df2           <- Type_III[4, "Df"]
fvalue        <- Type_III[1, "Mean Sq"] / MSdenom
df1           <- Type_III[1, "Df"]
Type_III["Sequence", 4] <- fvalue
Type_III["Sequence", 5] <- pf(fvalue, df1, df2, lower.tail = FALSE)
print(Type_III, digits = 6, signif.stars = TRUE)


And here, the new results

#########################################################################
Type III Analysis of Variance Table

Response: log(Cmax)
                  Df   Sum Sq Mean Sq F value   Pr(>F)   
Sequence           1   1.3253 1.32531 0.27224 0.604233   
Period             3   3.5824 1.19413 2.19909 0.090673 . 
Treatment          1   2.7923 2.79228 5.14222 0.024818 * 
Sequence:Subject  48 233.6721 4.86817 8.96514  < 2e-16 ***
Residuals        146  79.2796 0.54301                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

One last doubt: How can we include at function lme() a term for carryover first-order effect (keeping the sequence effect in the model)? We have many DF for estimate this effect, so I presume that it can be estimated to replicate designs as this our example!!! How and how many columns should we have in the dataset to estimate the first-order carryover effect?

This test can be useful when we are working with auto-inducers drugs (I read your article and I like very much).


At Phoenix WinNonlin this can be make creating two collumns named "Carry" and "Over". The collumn "Carry" is composed by 0 (if data of period 1) or 1 (if data period 2,3,4 ...). You should define "Carry" as covariate and "Over" as Classification. The collumn "Over" indicates which treatment was administered in the previous period. The fixed model: Sequence+Treatment+Period+Carry*over. The specification for random effects that I use is the same oriented by FDA for replicate design (Repeted specification=Period, Variance Bloking Variable=Subject, Group=Treatment (Type=Variance components), Random effects model=Treatment, Variance blocking Variables=Subject (Type=Banded No-Diagonal Factor Analytic f=2)

How would be this parametrization at function lme at R software?