I am seeking your feedback on a series of preclinical experiments.
Setting: We are conducting a three-arm therapy trial in a disease murine model. Some measurements will be taken from live subjects, while others will require the mice to be ethically euthanized.
In this experiment, measurements will be taken from randomly selected mice in each treatment group at three different time points, without performing autopsies. I am considering using an ANOVA with a fixed effect factor for the treatment group, a random effect factor for the time-point of measurement, and possibly an interaction term to provide a single coefficient for comparing treatments at each time point. Is there something to take into account with an interaction between a fixed and a random factor ?
This one is more complex. We have a repeated measure design, where each mouse is measured multiple times. However, they will be randomly euthanized at three different time points to also allow for autopsy measurements (for another experiment). Therefore, I am considering a linear mixed model, but with a random effect factor to account for the random euthanasia. This creates missing values, which I believe can be handled under the assumption of Missing Completely at Random (MCAR).
Thanks for your advice.
For the first model, it is questionable whether random effects will fit a correlation pattern which is probably a serial correlation structure such as AR(1). You can use a purely AR(1) model with generalized least squares or add an AR(1) structure to a mixed effects model. But with only 3 time points you might as well just used an unstructured covariance matrix. Time itself is always a fixed effects. If there are random effects in the model it is the animals who represent these effects, not time. Interactions with time as as easy to interpret as interacting age and sex.
For the second experiment, you have missing data completely at random. Using any full-likelihood model such as GLS or mixed effects models or their Bayesian counterparts will handle the complete data appropriately with no need for imputation.
Thank you for your kind reply.
Regarding the first model: I’m not sure if I explained it correctly initially, but this is not a repeated measures experiment. At each time point, mice from each group are randomized to be measured. I am not measuring the same units serially. That’s the reason I excluded a mixed model and why I am considering time as a random effect: the time of measurement is randomized.
Then you improperly called this a repeated measurement design. This kind of pre-planned animal sacrifice time model just involves a univariate response and it easy to analyze as no correlation structure is involved. You can still plot response as a function time (sacrifice) time.
I thought I had mentioned it only for the second experiment, but I realize now that I wasn’t clear after all. I understand there’s no correlation between measurements, but shouldn’t I take into account the time at which each mouse is randomized for measurement in the way I proposed ?
Take time into account just as you would weight at baseline. But there is one difference: if the response that is measured at the time of sacrifice has different tendencies depending on animal age, you might need a sacrifice time by response value interaction in the model.