# Is this a repeated measures ANOVA problem?

Here is the problem I have (the figure below tries to depict the problem):

1. There are two groups of patients - the BURN_GRP and the TVC_GRP, and all the patients are different (i.e. no patients in the BURN_GRP appear in the TVC_GRP and vice versa).
2. The number of patients in each group is different, 125 vs. 219 (but I can randomly discard patients from the TVC_GRP in order to have the same number of patients in each group).
3. Each patient has four measures of their SA_VAL taken over time (6 hours apart).
4. I would like to test the hypothesis that the average SA_VAL of the patients in the BURN_GRP is statistically significantly different than the average SA_VAL of the patients in the TVC_GRP.

If there were no repeated measures I would perform a standard (non-paired) t-test. However, now that there are four (non-independent) measures for each patient I am unsure about how to proceed. I think it might be a repeated measure ANOVA. Is it? If so, how would I go about modeling it in R?

There are two solutions here:

1.) If systematic differences between the four time-points are not expected or not of interest (simple replications): Just calculate the average SA_VAL for each subject and compare the resulting MEAN_SA_VALs between both groups using an unpaired t.test or wilcox.test (aka Mann-Whitney U). If you suspect/observe that variances differ between groups , use the var.equal = FALSE option of t.test. Simple as that.

2.) If there is the possibility that SA_VALs can change systematically over the course of the four measurements then you should definitely use a model that takes a potential main effects with time and more importantly interaction effects between time and group into account. This is a little complicated because R's aov function usually used for repeated-measures ANOVA is designed for balanced designs. But you should not discard data, since this only means a loss of valuable information and statistical power.

What you can do is to create a mixed model with functions lme (nlme package), or lmer (lme4 package) and then run an ANOVA. The model should look like this:

model1 <- lmer(SA_VAL ~ time+group+time:group+(1+time|subject),data=df)
anova(model1)


If the effects of time on SA_VAL are linear in both groups, you may use time as a continuous regressor (0,6,12,18). If you expect other effects of time, define time as a factor (factor(time)).

Bonus: The mixed model will even be able to handle subjects with missing data-points (missing at random). Malus: Working with mixed models can become quite involved, so you may require some reading. Btw: here you can find a lme/lmer example that matches your design very closely.

• If there are systematic differences between the four time points, then what hypothesis is being tested? – derNincompoop Dec 22 '16 at 2:35