We introduce Robust Bayesian Sequential Borrowing (RBSB), a framework for extrapolating evidence across adjacent subgroups in multi-population clinical programmes where studies are conducted in sequence and populations are ordered by clinical proximity. Conventional approaches weight all historical sources uniformly or exclude distant populations entirely, failing to reflect the natural gradient of similarity in such programmes. RBSB encodes the programme order through path-dependent borrowing via robust mixture priors that combine an informative component with a unit-information component to guard against prior-data conflict. Posterior weights, derived in closed form from marginal likelihood ratios, provide transparent dynamic attenuation when heterogeneity arises between sequential populations. The framework supports prospective evaluation of Bayesian Type I error, power, and extends naturally to assurance at both the study and programme level. Simulation studies demonstrate superior false-positive control relative to full pooling, while preserving substantial efficiency gains over standalone analyses. A case study of the START trial illustrates the approach across adult, adolescent, and paediatric populations. RBSB offers a practical, regulator-aligned method for disciplined evidence borrowing that exploits temporal and biological proximity while preventing implausible extrapolation across distant populations.

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