How to examine effect of time over four time points across two experimental conditions?

Question

My experiment entails comparing a mock-infected group with a virus-infected group across 4 different time points (3,5,8,10 weeks) looking at the proportion of immune cells.

I have already compared the mock and virus infected groups at each time point by using an unpaired t-test.

How can I compare the mock values over time to see if there are significant differences with cell proportions and whether the virus infected groups follow similar kinetics?

Answer 1

You could do the following:

• Linear and quadratic contrasts of the effect of time
  • This would look at the overall effect of time
• Group by linear time and group by quadratic time interaction effects
  • This would look at whether the effect of time is similar across groups; of course, the null hypothesis is that the linear and quadratic effects are the same.

You could also consider a more sophisticated non-linear model of time, but I imagine you would want more time points if you were trying to get a precise characterisation of the effect of time. You could also incorporate higher order polynomial effects (e.g., cubic effects), but with only four time points, even looking at quadratic effects seems to me to be pushing the upper limit of reasonable complexity.

Answer 2

I think you can model the virus v. mock as a dummy variable, i.e. virus=1 for the virus group, virus=0 for the mock group. Then time as an explanatory variable. Here is the model for R (propCell is the proportion of immune cell):

propCell~time*virus

Of course, you would also need to check for linearity of the time variable and then modify the interaction as required, etc; basically all the usual steps you would take for regression models anyway. The interaction term should be what you are interested in.