2.3. Quantification of Multisensory Integration Using the Race Model Inequality

When two sources of sensory information are presented concurrently, they offer synergistic information that give rise to faster responses [25]. Race models, commonly implemented to examine multisensory effects, are robust probability (P) models that compare the cumulative distribution function (CDF) of combined unisensory visual (V) and unisensory somatosensory (S) reaction times with an upper limit of one (min (P(RT_V ≤ t) + P(RT_S ≤ t), 1) to the CDF of multisensory visual-somatosensory (VS) reaction times (P(RTVS ≤ t)) [26,27,28]). For any latency t, the race model inequality (RMI) holds when the CDF of the actual multisensory condition (P(RT_VS ≤ t)) is less than or equal to the predicted CDF (min (P(RT_V ≤ t) + P(RT_S ≤ t), 1)). Note that CDFs take all RTs into account. Acceptance of the above RMI suggests that unisensory signals are processed in parallel, such that the fastest unisensory signal produces the actual response (i.e., the “winner” of the race). However, when the actual CDF is greater than the predicted CDF, the RMI is rejected and the RT facilitation is the result of multisensory interactions that allow signals from redundant information to integrate or combine non-linearly.

Methods to calculate the race model violation have been previously described [14]. Figure 2a depicts the group-averaged difference between actual and predicted CDFs (dashed trace) for the entire cohort, where positive values (gray shaded area between 0 and 10th percentile) are indicative of VS integration (i.e., violation of the race model). The RMI was tested using Gondan’s permutation test over the fastest 10% of responses and robust violation was observed (tmax = 14.40, tcrit = 2.08, p < 0.001) [29,30]. As in our most recent work [7,16,17], the area-under-the-curve (AUC) during the group averaged violated percentile bins (0–10th) served as the independent measure of magnitude of VS integration. Note, the higher the magnitude, the better (i.e., more efficient) the VS integration ability.

Test of the race model. (a) The CDF difference waves over the trajectory of averaged responses for the overall cohort. The grey box highlights the group averaged violated percentile bins (0–10th). (b) The CDF difference waves over the trajectory of averaged responses for individuals without diabetes (black trace), individuals with diabetes (white trace), and individuals with diabetes on insulin therapy (dashed trace).