I am currently working on a longitudinal analysis (with only 2 time measurements, T1 and T2). In this non-randomized data, I have 2 time measurements of fasting glucose as my outcome, i.e. Y1 and Y2 and a biomarker measured in T1 (X) as the exposure (a continuous variable).
I am interested in examining whether the biomarker of interest predicts the change of fasting glucose (Y2-Y1 or vice versa). Based on the literature review, the biomarker of interest is inversely associated with fasting glucose. Therefore I assumed that the higher the biomarker levels (X), the lower the change of fasting glucose (Y2-Y1).
I'm currently doing linear regression analyses with different outcomes and yielded discrepant results:
1) Dependent variable (DV): fasting glucose measured in T2 (Y2)
Independent variable (IV): biomarker of interest (X) and adjusted for age, sex, bmi - without adjusting for fasting glucose measured in T1 (Y1).
Results: as expected there is significant inverse association between X and Y2
2) DV: Y2-Y1
IV: X and adjusted for age, sex, bmi - without adjusting for fasting glucose measured in T1 (Y1). Results: there is significant positive association between X and (Y2-Y1)
3) DV: Y2
IV: X and adjusted for age, sex, bmi - plus adjusted for fasting glucose measured in T1 (Y1). Results: no significant (but positive) association between X and Y2 adjusted for Y1.
I cannot explain the discrepancy and I do not know which method I should use. Any pointers about which method I should use are appreciated. Thank you!