Descriptive statistics were calculated for each variable of interest (Stata 9.2; Stata Software Corp., College Station, TX). The χ2 test or the Fisher exact test was used to compare patient characteristics that were categorical. The Wilcoxon two-sample rank sum test and paired t-test were used to compare patient characteristics that were continuous. Both the Wilcoxon matched-pairs signed rank sum test and the sign test of matched pairs were used to compare estimated functional vision measures between DR cases and controls. Because of multiple independent statistical comparisons, Bonferroni adjusted P < 0.008 was considered statistically significant (α < 0.05).
Each of the study subjects responded to selected subsets of the 509 items of the AI. All the data that were collected as part of this study were merged into a single database keyed to the subject, and Rasch analysis was performed on the combined data. Separate Rasch analyses were also performed on the responses to each of the subsets of Tasks that made up the four functional domains (reading, mobility, visual motor, and visual information processing) and of the Goal-level items. We included 228 study subjects (case and controls) and 1635 nonstudy subjects in each of these Rasch analyses. Bivariate regressions were performed on each domain item measures estimated from each domain analysis versus corresponding item measures from the merged data analysis and on AI item measures estimated from difficulty ratings of Goals versus the corresponding item measures from the merged data analysis. These regressions were then used to equate person measure estimates from each domain to person measure estimates from AI Goal and Task difficulty ratings. All the Rasch analyses were performed with commercial software (Winsteps, ver. 3.16; Winsteps, Chicago, IL). In each of these Rasch analyses, some of the cases or controls were not measured because of missed responses or extreme values. Hence, all unmeasured subjects and their matched counterparts were excluded from six comparisons. This protocol created a different number of matched pairs in six statistical comparisons related to all Goal-level items and each functional domain
(Fig. 1) . Rasch measurement theory is built on the premise that the latent variable—in this case, functional vision—is unidimensional and that the person’s vision-related ability is independent of the visual ability necessary to satisfy the item content. Furthermore, Rasch measurement theory assumes that the observed variable—in this case, the subjects’ ratings for each item—will order the subjects in the same way for each item and order the items in the same way for each person. This pattern of ordering is called a Guttman scale.
18 19 However, because it is probabilistic, Rasch measurement theory assumes that the required ordering will be disrupted by random errors in the observed variable. This random disordering of the observed responses produces a probabilistic Guttman scale.
18 19 Therefore, if visual ability is not strictly unidimensional, or if other variables contribute to the pattern of the subjects’ responses, then the pattern of observed responses will differ significantly from the expected responses. The degree of departure of observed responses from expected responses is captured in a χ
2-like statistic called the infit mean square.