I have a question regarding adjusting vs matching when the confounding status is largely different between groups. For instance, men are more prone to have Parkinson's disease and vascular diseases; whereas, females are more susceptible to Alzheimer's disease and MS.
Say that one wishes to assess the vascular risk to Parkinson and dementia. In this case, age and sex are known to be strong confounders to both the risk and the outcome. Should adjusting the confounder in the regression more reliable or matching?
I am asking because I got very different results in a very well sampled population-based cohort. On one hand, the vascular risk was highly associated with the outcomes (OR=14.4 [5.92,35.2]) but it was completely gone after I matched the two groups (disease vs disease-free)(OR=1.29 [0.92,1.82]). The results were pretty robust in the matching groups (I've tried to match with different ratios and different methods several times).
I personally think that with a great difference in age and sex distribution, regression adjustment may not be able to account for confounding fully. Therefore, the results from matching are more reliable. One evidence to it is that after matching, the PD only contributes to a 0.1 increment on the score of vascular risk. Therefore, it is unlikely that the association was real.