## No ANOVA by lme() – lengthy reply [🇷 for BE/BA]

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") <- "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

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") <- "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?   Ing. Helmut Schütz 