For a manuscript intended for submission to a medical (or psychological) journal, I have cognitive data from 16 patients and 32 age- and gender-matched healthy controls at four time points (pre-treatment T0, and three post-treatment time points T1, T2, and T3 in patients; in controls at the same intervals), i.e., I have two healthy controls matched with each patient. The cognitive measure, though technically discrete, can for most purposes be thought of as normally distributed.
Example of what the data looks like:
subject gender age T0 T1 T2 T3 p1 male 12 30 39 44 45 p2 female 15 37 38 40 36 ... ... ... ... ... ... ... ca1 male 12 38 41 52 48 ca2 female 15 43 42 40 41 ... ... ... ... ... ... ... cb1 male 12 29 39 49 61 cb2 female 15 49 52 53 59 ... ... ... ... ... ... ...
I want to know: 1. Do patients differ from controls before treatment (T0)? 2a. Do patients differ from controls after treatment? 2b. Do pre-existing differences as in 1, if any, change?
However, I know that the cognitive measure is (normally, i.e., in healthy controls) significantly predicted by
a. age, gender, and their interaction
b. repeated measurement
I would therefore like to retain the matching in the analysis. However, I am not sure how to achieve this. Would it be feasible to perform a repeated measures analysis of variance with two "within-subject" factors (time: T0,T1,T2,T3, and subject type: patient, controla, controlb) and then use contrasts to achieve the desired grouping? If so, how do I set this up properly in R?
Another option I came up with is to calculate a set of 32 difference scores for each assessment (p1T0-ca1T0,...,p16T0-ca16T0,p1T0-cb1T0,...,p16T0-cb16T0) and then use one-sample t-tests to test for the significance of the average difference (although that may require explicit correction for multiple comparisons). However, I am not certain that is statistically valid (at least in terms of the degrees of freedom applied, normally 32-1 = 31).
Is the anova technique feasible and proper? Should I go with the simple t-test method, and in that case, would it be correct to use 31 degrees of freedom? Or do I need another class of methods entirely?