Pooling Different Crossover Data within A Study

Question

I am trying to analyze a double-blind study that has 3 separate crossovers:

1. Dose X mg
2. Dose Y mg
3. Dose Z mg

In each cohort, subjects are randomized to either 'Treatment-Placebo' or 'Placebo-Treatment'.

Example dummy data:

Subject   Sequence   Period    Treatment   Endpoint    Baseline
001       Trt-Pbc    1         Xmg         12.1        10.0
001       Trt-Pbc    2         Placebo     14.1        11.2
002       Trt-Pbc    1         Ymg         9.8         8.8
002       Trt-Pbc    2         Placebo     11.7        9.9
003       Pbc-Trt    1         Placebo     17.2        11.1
003       Pbc-Trt    2         Zmg         14.3        11.9   
(Baseline is period-specific)

The crossovers are distinct within the study - by which I mean that the subjects enrolled to a cohort do not participate in another cohort (subjects participate in only ONE cohort).

My intention is to analyze these cohorts separately by running a mixed-model to see if there is a treatment effect of each dose versus placebo.

I have been asked if it is possible to 'pool' these data to analyze. My first reaction is that this will not make sense. What question would this even address - 'Any Dose' versus 'Placebo'?

Can this be done? If so, how?

Answer 1

Welcome to the site, Chris. You could set up this model in a couple of different ways. I would recommend you get all conditions in the same model as was suggested by the question you were asked. First, I am going to assume that you have coded Treatment as a factor variable with Placebo==0, Xmg==1, and Ymg==2. Likewise, I am assuming that Sequence is a factor variable with Trt-Pbc==0 and Pbc=Trt==1. Here's one model you could run:

m1 <- lmer(Endpoint ~ Sequence + Treatment + Sequence:Treatment + Baseline + (1|Subject), data=df)

This model estimates separate "main effects" for Sequence and Treatment and then their interaction (Sequence:Treatment). With two variables that are interacting, their "main effects" represent the effect of that variable at the 0 value of the other variable. So for Sequence, it is telling you about the Endpoint difference in the two conditions when Treatment==0, i.e., for the Placebo condition.

Keeping in mind that your goal is to "to see if there is a treatment effect of each dose versus placebo," you will be particularly interested in the "main effect" of Treatment, where you get estimates of the effect of different dosages vs. Placebo when Sequence==0, i.e., Trt-Pbc==0.

Then the interaction will give you the dosage effect for the second condition (Sequence==1 or Pbc-Trt==1). You can use post-estimation tests to compare the various permutations of interest. For example whether the Yg vs. placebo effect is the same or different across cohorts. Package options for doing such tests in R include lsmeans, emmeans, or multcomp. The ggeffects and effects packages are also great for graphing your results.