Threshold Effects of Rehabilitation Intensity on Functional Recovery After Ischaemic Stroke: A Panel Threshold Regression Analysis of Australian Hospital Data

BackgroundOptimal rehabilitation dosing after ischaemic stroke remains contested. Linear assumptions underlying conventional regression models may mask clinically important threshold effects, whereby functional gains accelerate or plateau beyond specific intensity thresholds. This study applied panel threshold regression to Australian hospital administrative data to identify endogenous breakpoints in the dose-response relationship between rehabilitation intensity and functional recovery. MethodsWe used a retrospective longitudinal cohort derived from the Australian Stroke Clinical Registry (AuSCR) and the National Hospital Cost Data Collection (NHCDC) for fiscal years 2018-2019 to 2022-2023. The analytical sample comprised 18,742 hospitalised ischaemic stroke patients across 48 public hospitals in five Australian states. The primary exposure was daily rehabilitation intensity (minutes of physiotherapy, occupational therapy, and speech pathology per inpatient day). The primary outcome was change in the modified Rankin Scale (mRS) score from admission to discharge. We employed Hansens (1999) panel threshold regression framework to test for single, double, and triple threshold effects, using bootstrap p-values (n=500) to establish statistical significance. Fixed-effects estimation controlled for unobserved hospital heterogeneity. Secondary outcomes included acute length of stay and discharge destination. Cost-related parameters were benchmarked against published Australian cost-effectiveness data. ResultsThe panel threshold model identified two statistically significant breakpoints in the intensity-recovery relationship (p<0.001 for both). Below the first threshold (27.4 minutes/day; 95% CI: 24.8-29.6), each additional minute of daily rehabilitation was associated with a 0.008-point reduction in mRS score (beta = -0.008, 95% CI: -0.011 to -0.005, p<0.001). Between the two thresholds (27.4 to 54.7 minutes/day; 95% CI: 51.2-58.9), the marginal benefit approximately doubled (beta = -0.018, 95% CI: -0.022 to -0.013, p<0.001). Above the upper threshold (>54.7 minutes/day), the marginal effect diminished substantially (beta = -0.004, 95% CI: -0.009 to 0.002, p=0.186), suggesting a ceiling effect. These dose-response patterns were consistent across age subgroups, stroke severity strata, and hospital volume tertiles. ConclusionsRehabilitation intensity thresholds exist in stroke inpatient recovery and are non-linear. Patients receiving between 27 and 55 minutes of daily multidisciplinary therapy derive disproportionate functional benefit per unit of resource investment. Scheduling rehabilitation below the lower threshold represents a clinically and economically suboptimal allocation of inpatient resources. These findings have direct implications for workforce planning, clinical pathway design, and value-based commissioning in Australian public hospitals.