Hi,

I tried going through the available materials online for this issue, but I did not manage to find many great resources. I would greatly appreciate any guidance or advice you could provide.

I have mice tumor growth volumes across time for 4 different treatment arms. I want to compare the tumor growth trajectories and show that there is a statistically significant difference between the growth curves. I believe the most appropriate way to do this is by linear mixed-effects modelling, but I’m not sure about the appropriate way to perform and interpret the results using the lme4 and lmerTest libraries in R. Take note that I have missing data for some of the samples in varying days, but I think the mixed-effects modelling should handle this.

This is how I’m doing it right now with a dataframe containing four columns (volume, day, arm, and mouse):

```
library(lme4)
library(lmerTest)
df$volume <- log(df$volume) # Converting the volumes in mm cubed to their logs
df$arm <- factor(df$arm, levels = c("A", "B", "C ", "D")) #Converting the arms to factors, with the control arm set to the first level
mod <- lmer(volume ~ day * arm + (1+ day|mouse), data = df) # Performing the modelling
summary(mod) # Printing the results
```

My questions:

- Is this the appropriate way to perform this analysis?
- I am unsure as to how to interpret the results. Am I correct to assume that, for example, if I want to see whether tumor growth in arm B is significantly different compared to arm A, I have to look at the day:armB estimate and p-values? And that a positive estimate indicates that the increase in tumor sizes is higher in arm B and a negative estimate means the increase in tumor size is lower in arm B?
- What is the appropriate way to also check whether there is a significant difference between arms C and D? Should I simply relevel the arm factor so that either C or D is the baseline and then look at the estimate/p-value for the other arm?
- Finally, there seems to be a shift in tumor behaviors between arm C and arm D at the final 20% of the days in the study, where the tumors in arm C appear to became resistant to the treatment while the tumors in arm D appear to still respond. However, the differences between the two arms are not significant based on this analysis, but I believe this is due to the fact that the two arms show a completely similar trajectory in the primary part of the study (80% of days). How should I accommodate this change in behavior of tumors and appropriately compare these two arms?

Any and all help with this is really appreciated.