The distribution of most variables did not meet the criteria for normal distribution and were therefore normalized by conversion to natural log (ln) values. Using the converted data in simple regression (univariate) analyses, we observed that the natural log of VIP-positive fiber density on blood vessels tended to decline as a function of the natural log of age, but the correlation was not significant (
P = 0.0785;
Fig. 3 ). Similarly, only a modest age-related decline in the natural log of vessel diameter as a function of the natural log of age was observed, and this correlation too was not significant (
P = 0.7324;
Fig. 4 ). However, multiple regression (multivariate) analyses revealed that the relationship of age with both VIP-positive fiber density and vessel diameter was markedly confounded by both variables related to the tissue specimens: time elapsed between death and fixation of the tissue, and time spent by the tissue in fixative. Once these variables were controlled for, inclusive also of gender and experimenter (see the Methods section), the fully adjusted multivariate models revealed a strong correlation of the natural log of age with both the log of blood vessel VIP-positive fiber abundance (F = 5.99,
P = 0.0003, adjusted
R 2 = 0.51) and the natural log of choroidal vessel diameter (F = 9.35,
P < 0.0001, adjusted
R 2 = 0.63). By the multivariate analysis, ln VIP staining was estimated to decline with the natural log of age more strongly than did ln vessel diameter. Specifically, the slope (β) estimate for ln VIP staining was −0.45 ± 0.17 (SE;
P = 0.017), whereas that for ln-vessel diameter was −0.19 ± 0.06, SE;
P = 0.005). After adjustment for the same variables (gender, death-to-fixation time, time in fixative, and the experimental variables), multiple regression analysis showed that the natural log of VIP-positive fiber density correlated positively with choroidal vessel diameter (F = 5.40,
P = 0.0006, and adjusted
R 2 = 0.48 for the fully adjusted multivariate model). The slope for this relationship was estimated at 0.99 ± 0.47 (SE;
P = 0.044). With few exceptions, the predicted values generated by the fully adjusted model corresponded fairly well to the observed values.