Re: [R] How to analyse simple study: Placebo-controlled (2 groups) repeated measurements (ANOVA, ANCOA???) Karl Knoblick wrote: > Hallo! >  > I have two groups (placebo/verum), every subject is measured at 5 times, the first time t0 is the baseline measurement, t1 to t4 are the measurements after applying the medication (placebo or verum). The question is, if there is a significant difference in the two groups and how large the differnce is (95% confidence intervals). >  > Let me give sample data > # Data > ID<-factor(rep(1:50,each=5)) # 50 subjects > GROUP<-factor(c(rep("Verum", 115), rep("Placebo", 135))) > TIME<-factor(rep(paste("t",0:4,sep=""), 50)) > set.seed(1234) > Y<-rnorm(250) > # to have an effect: > Y[GROUP=="Verum" & TIME=="t1"]<-Y[GROUP=="Verum" & TIME=="t1"] + 0.6  > Y[GROUP=="Verum" & TIME=="t2"]<-Y[GROUP=="Verum" & TIME=="t2"] + 0.3  > Y[GROUP=="Verum" & TIME=="t3"]<-Y[GROUP=="Verum" & TIME=="t3"] + 0.9  > Y[GROUP=="Verum" & TIME=="t4"]<-Y[GROUP=="Verum" & TIME=="t4"] + 0.9  > DF<-data.frame(Y, ID, GROUP, TIME) >  > I have heard of different ways to analyse the data > 1) Comparing the endpoint t4 between the groups (t-test), ignoring baseline Don't even consider this > 2) Comparing the difference t4 minus t0 between the two groups (t-test) This is not optimal > 3) Comparing the endpoint t4 with t0 as a covariate between the groups (ANOVA - how can this model be calculated in R?) Using t0 as a covariate is the way to go.  A question is whether to just  use t4.  Generally this is not optimum. > 4) Taking a summary score (im not sure but this may be a suggestion of Altman) istead of t4 > 5) ANOVA (repeated measurements) times t0 to t5, group placebo/verum), subject as random factor - interested in interaction times*groups (How to do this in R?) > 6) as 5) but times t1 to t5, ignoring baseline (How to do this in R?) > 7) as 6) but additional covariate baseline t0 (How to do this in R?) >  > What will be best? - (Advantages / disadvantages?) > How to analyse these models in R with nested and random effects and possible covariate(ID, group - at least I think so) and random parameter ID)? Or is there a more simple possibility? It's not obvious that random effects are needed if you take the  correlation into account in a good way.  Generalized least squares using  for example an AR1 correlation structure (and there are many others) is  something I often prefer.  A detailed case study with R code (similar to  your situation) is in http://biostat.mc.vanderbilt.edu/FrankHarrellGLS .    This includes details about why t0 is best to consider as a covariate.    One reason is that the t0 effect may not be linear. If you want to focus on t4 it is easy to specify a contrast (after  fitting is completed) that tests t4.  If time is continuous this  contrast would involve predicted values at the 4th time, otherwise  testing single parameters. Frank Harrell >  > Perhaps somebody can recommend a book or weblink where these different strategies of analysing are discussed - preferable with examples with raw data which I can recalculate. And if there is the R syntax includede - this would be best! >  > Any help will be appreciate! >  > Thanks! > Karl --  Frank E Harrell Jr   Professor and Chair           School of Medicine                       Department of Biostatistics   Vanderbilt University ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.