Logistic regression or two sample t-test on clinical data

Question

I have a database with healthy subjects and people with memory losses. For both groups, I have obtained from a MRI scan the volume of lesions they have on the brain. So I have one categorical variable indicating the group and a continuous variable indicating volume of lesions.

I would like to test if theres a relation between the volume of lesions and the memory losses. Firstly I considered making a two-sample t-test to see if the mean of the lesion volume differed between both groups. Now I have received a suggestion about making logistic regression, using the group as an independent variable.

After reading the following post: Logistic regression or T test?, it is not clear to me which test is more suitable for my data.

Does each test confirm different hypothesis? Do you have any suggestion of what should I have into account to choose a test?

Answer 1

Since a nonparametric test is available - the Wilcoxon test - a better question might be how to choose between the Wilcoxon test and logistic regression. You can use either one for this problem. The logistic model approach generalizes to a multivariate comparison, e.g., is there an association between any of 5 brain measures and memory loss. This idea was developed by Peter O'Brien: http://www.citeulike.org/user/harrelfe/article/13264639

Think of linear logistic regression as competing with a t-test that assumes equal variance in the two groups. Think of quadratic logistic regression as competing with a two-sample t-test with unequal variances. A cubic logistic model would allow skewness to differ.