## Group effects EMA [Two-Stage / GS Designs]

Hi VStus & ElMaestro!

This is really funny, we had 2 last days discussions with Helmut regarding Group effect during the workshop

Yes, in case of just adding a Group you do not see any changes (Fixed: sequence, period, treatment, group, subject(sequence))
But in case of Period %in% Group the situation is not the same!!

a little code for discussion:
# the original code is from this perfect paper: # http://link.springer.com/article/10.1208/s12248-014-9661-0 Analyse222BE <- function (data, alpha=0.05, Group = FALSE) {     data$Subj <- factor(data$Subj) # Subject   data$Per <- factor(data$Per)  # Period   data$Seq <- factor(data$Seq)  # Sequence   data$Trt <- factor(data$Trt)  # Treatment   # be explicite   ow <- options()   options(contrasts=c("contr.treatment","contr.poly"))     if(!Group) {     muddle <- lm(log(Var)~Trt+Per+Seq+Subj, data=data)   }  else {     muddle <- lm(log(Var)~Trt+Per+Seq+Subj+                           Group+Per:Group, data=data)   }   # in the standard contrasts option "contr.treatment"   # the coefficient TrtT is the difference T-R since TrtR is set to zero   lnPE     <- coef(muddle)["TrtT"]   lnCI     <- confint(muddle,c("TrtT"), level=1-2*alpha)   typeI    <- anova(muddle)   names(typeI)   <- "Pr(>F)"   # no need for the next   mse      <- summary(muddle)$sigma^2 # another possibility: #mse <- typeI["Residuals","Mean Sq] #df <- df.residual(muddle) # back transformation to the original domain CV <- 100*sqrt(exp(mse)-1) PE <- exp(lnPE) CI <- exp(lnCI) # output cat(sep,"\n") options(digits=8) cat("Type I sum of squares: ") print(typeI) cat("\nBack-transformed PE and ",100*(1-2*alpha)) cat("% confidence interval\n") cat("CV (%) ..................................:", formatC(CV, format="f", digits=2),"\n") cat("Point estimate (GMR).(%).................:", formatC(100*PE, format="f", digits=2),"\n") cat("Lower confidence limit.(%)...............:", formatC(100*CI, format="f", digits=2) ,"\n") cat("Upper confidence limit.(%)...............:", formatC(100*CI,format="f", digits=2) ,"\n") cat(sep,"\n\n") #reset options options(ow) } data <- read.delim("https://static-content.springer.com/esm/art%3A10.1208%2Fs12248-014-9661-0/MediaObjects/12248_2014_9661_MOESM1_ESM.txt") Group1 <- subset(data, Subj <= 9) Group1$Group <- 1 Group2 <- subset(data, Subj > 9) Group2\$Group <- 2 data<-rbind(Group1, Group2) Analyse222BE(data, alpha=0.05, Group = FALSE) Analyse222BE(data, alpha=0.05, Group = TRUE)

> Analyse222BE(data, alpha=0.05, Group = FALSE) _______________________________________________________________________________ _______________________________________________________________________________ Type I sum of squares: Analysis of Variance Table Response: log(Var)           Df  Sum Sq   Mean Sq  F value     Pr(>F)    Trt        1 0.02285 0.0228494  3.57254   0.076998 .  Per        1 0.04535 0.0453497  7.09049   0.017019 *  Seq        1 0.21836 0.2183553 34.14018 2.4964e-05 *** Subj      16 4.24539 0.2653366 41.48578 5.2285e-10 *** Residuals 16 0.10233 0.0063958                        --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Back-transformed PE and  90% confidence interval CV (%) ..................................: 8.01 Point estimate (GMR).(%).................: 95.09 Lower confidence limit.(%)...............: 90.76 Upper confidence limit.(%)...............: 99.62 _______________________________________________________________________________ > Analyse222BE(data, alpha=0.05, Group = TRUE) _______________________________________________________________________________ _______________________________________________________________________________ Type I sum of squares: Analysis of Variance Table Response: log(Var)           Df  Sum Sq   Mean Sq  F value     Pr(>F)    Trt        1 0.02285 0.0228494  3.42473   0.084021 .  Per        1 0.04535 0.0453497  6.79711   0.019816 *  Seq        1 0.21836 0.2183553 32.72757 4.0497e-05 *** Subj      16 4.24539 0.2653366 39.76923 2.1387e-09 *** Per:Group  1 0.00225 0.0022549  0.33797   0.569635    Residuals 15 0.10008 0.0066719                        --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Back-transformed PE and  90% confidence interval CV (%) ..................................: 8.18 Point estimate (GMR).(%).................: 94.92 Lower confidence limit.(%)...............: 90.47 Upper confidence limit.(%)...............: 99.59 _______________________________________________________________________________ 
Even PE differs!
What the heck?? Where am I wrong? I need to take some Schützomycin!
PS: I see now, the model with Period:Group is wrong

Kind regards,
Mittyri Ing. Helmut Schütz 