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arxiv: 2605.23456 · v1 · pith:UFDTFYNVnew · submitted 2026-05-22 · ⚛️ physics.med-ph

RadMaps: A Geospatial Framework for Simultaneously Modelling Capacity and Geographic Constraints on Radiotherapy Access

Laurence Wroe , Archie Brown , Sophia Martin , Alika Ho , Steinar Stapnes This is my paper

Pith reviewed 2026-05-25 02:33 UTC · model grok-4.3

classification ⚛️ physics.med-ph
keywords radiotherapy accessgeospatial frameworkcapacity constraintsgeographic constraintsH3 gridcancer incidenceaccess modeling
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The pith

RadMaps reveals that capacity and geographic constraints together limit global radiotherapy access to 60%.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Radiotherapy access is limited by both the number of treatment machines and how far patients live from facilities. Prior analyses examined these limits separately. RadMaps models them simultaneously on a global hexagonal grid by allocating demand greedily to the nearest facility within capacity and distance limits. Globally, with a 200 km threshold, capacity alone allows 70% access, geography alone 91%, but both together only 60%. This demonstrates that the barriers reinforce each other to create larger gaps than either would suggest.

Core claim

The RadMaps framework, when applied globally with a 200 km step-function access threshold, computes a capacity-only access of 70%, a geography-only access of 91%, and a combined RT access of 60%, showing the compounding effect of the two constraints.

What carries the argument

A greedy nearest-first allocation algorithm that assigns demand to facilities subject to both capacity and geographic constraints, producing a localised access metric for every H3 hexagon.

If this is right

  • The tool can localise access deficits at sub-national scale in individual countries.
  • It identifies distinct access profiles including capacity-limited, geographically-limited, and doubly-constrained regions.
  • The modular framework supports infrastructure planning and policy prioritisation at regional to global scales.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The allocation method could be tested against real-world patient flow data to validate its accuracy.
  • Extending the model to include public transport times might change access estimates in urban versus rural areas.
  • Similar simultaneous constraint modeling could be applied to other healthcare services like chemotherapy or surgery.

Load-bearing premise

The greedy nearest-first allocation algorithm accurately assigns demand to facilities under simultaneous capacity and geographic constraints.

What would settle it

Direct measurement of actual radiotherapy utilization rates in a country compared against the model's predicted access percentages for its regions.

Figures

Figures reproduced from arXiv: 2605.23456 by Alika Ho, Archie Brown, Laurence Wroe, Sophia Martin, Steinar Stapnes.

Figure 1
Figure 1. Figure 1: Modelling pipeline used by RadMaps to calculate radiotherapy access maps and [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Global distribution of population density and radiotherapy demand at H3 [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Global distribution of radiotherapy deficit and access ratio at H3 Resolution-3. [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The capacity-only (AC), geography-only (AG), and RadMaps (ARM) radiother￾apy access metrics as a percentage of demand for the six analysed countries. drive of a radiotherapy centre. Furthermore, the significant drop in the com￾bined RadMaps metric to 35 % suggests a maldistribution of this capacity. Facilities are particularly lacking in the high-density Uttar Pradesh and Bihar regions in the northeast. Ni… view at source ↗
read the original abstract

Background: Access to radiotherapy (RT) is constrained by two compounding factors: insufficient machine capacity to meet patient demand and geographic distance from treatment facilities. Existing analyses address these factors separately, constraining the insights available to planners and policymakers. This paper presents RadMaps, an open-source geospatial framework that simultaneously models capacity and geographic constraints on RT access at any spatial scale. Methods: RadMaps operates on Uber's H3 hexagonal grid and integrates population density data with national cancer incidence estimates and RT facility inventories. RT demand is estimated using cancer-site-specific RT utilisation rates, and geographic access is modelled via configurable decay functions using either distance, driving time, or public transport time. A greedy nearest-first allocation algorithm assigns demand to facilities subject to both capacity and geographic constraints, producing a localised access metric for every H3 hexagon. Results: Applied globally with a 200 km step-function access threshold, RadMaps computes a capacity-only access of 70 %, a geography-only access of 91 %, and a combined RT access of 60 %, illustrating the compounding effect of capacity and geographic constraints to significantly reduce effective access. High-resolution analyses of six countries demonstrate the tool's ability to localise access deficits at sub-national scale and reveal distinct access profiles: capacity-limited, geographically-limited, and doubly-constrained. Conclusions: RadMaps provides a flexible, open-access framework for visualising and identifying RT access gaps at regional to global scales, with applications in infrastructure planning and policy prioritisation. RadMaps' modular framework is also readily extensible to other spatial access modelling applications.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper presents RadMaps, an open-source geospatial framework operating on Uber's H3 hexagonal grid that integrates population density, cancer incidence estimates, and RT facility inventories to simultaneously model capacity and geographic constraints on radiotherapy access. Demand is estimated via site-specific utilisation rates and assigned via a greedy nearest-first algorithm subject to configurable decay functions (distance or time); global application with a 200 km step-function threshold yields capacity-only access of 70%, geography-only access of 91%, and combined access of 60%, with sub-national profiles shown for six countries.

Significance. If externally validated, the framework's modular, open-source design would be a useful contribution for visualising and prioritising RT access gaps at multiple scales. The explicit separation of capacity-only, geography-only, and joint metrics, together with the provision of reproducible code, strengthens the potential utility for infrastructure planning.

major comments (2)
  1. [Results] Results section: the central global figures (70 % capacity-only, 91 % geography-only, 60 % combined) are presented as direct evidence of compounding constraints without reported sensitivity analyses on the 200 km threshold, utilisation rates, or decay functions, and without comparison to independent national RT utilisation or travel-distance statistics; this absence is load-bearing for the claim that the model illustrates a significant reduction in effective access.
  2. [Methods] Methods section: the greedy nearest-first allocation algorithm is invoked to generate the localised access metric for every H3 hexagon under simultaneous constraints, yet no robustness checks against alternative assignment rules (e.g., capacity-proportional or optimisation-based) are provided, leaving the quantitative outputs dependent on an untested modeling choice.
minor comments (1)
  1. [Abstract] Abstract: the description of 'configurable decay functions' does not indicate which function (step-function at 200 km) was used for the global results, reducing clarity for readers.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and constructive feedback. We agree that additional robustness checks will strengthen the manuscript and address concerns about the sensitivity of the reported global access estimates. Below we respond point-by-point to the major comments.

read point-by-point responses

  1. Referee: [Results] Results section: the central global figures (70 % capacity-only, 91 % geography-only, 60 % combined) are presented as direct evidence of compounding constraints without reported sensitivity analyses on the 200 km threshold, utilisation rates, or decay functions, and without comparison to independent national RT utilisation or travel-distance statistics; this absence is load-bearing for the claim that the model illustrates a significant reduction in effective access.

    Authors: We agree that the absence of sensitivity analyses and external comparisons limits the strength of the claim regarding compounding constraints. In the revised manuscript we will add a dedicated sensitivity analysis subsection in Results, testing the 200 km threshold at 100 km, 150 km and 250 km, varying utilisation rates within published ranges for each cancer site, and comparing step-function versus linear and exponential decay. Where independent national RT utilisation or travel-time statistics exist in the literature, we will add direct comparisons and report agreement or discrepancies. These additions will be presented alongside the original global figures. revision: yes

  2. Referee: [Methods] Methods section: the greedy nearest-first allocation algorithm is invoked to generate the localised access metric for every H3 hexagon under simultaneous constraints, yet no robustness checks against alternative assignment rules (e.g., capacity-proportional or optimisation-based) are provided, leaving the quantitative outputs dependent on an untested modeling choice.

    Authors: The greedy nearest-first rule was chosen for computational tractability at global scale and because it approximates observed patient behaviour of selecting the closest facility with available capacity. We acknowledge that alternative rules could affect quantitative outputs. In the revision we will add a supplementary analysis applying a capacity-proportional allocation rule to the six profiled countries and report the resulting changes in combined access percentages. This will allow readers to assess the sensitivity of the headline metrics to the allocation choice and will be discussed in the Methods and Results sections. revision: yes

Circularity Check

0 steps flagged

No circularity; model outputs computed from external inputs via explicit algorithm

full rationale

The paper presents RadMaps as a geospatial simulation that ingests external population, incidence, and facility inventories, applies configurable decay functions and a greedy nearest-first allocation procedure, and emits access percentages as direct model outputs. No equations, fitted parameters, or self-citations are shown that would make the reported 70/91/60 % figures equivalent to the inputs by construction. The derivation chain is self-contained against the stated data sources and algorithmic choices; the central claims are simulation results rather than tautological reductions.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The framework depends on external geospatial data and standard allocation logic rather than new physical postulates.

free parameters (2)
  • access threshold = 200 km
    200 km step-function chosen for the global analysis
  • decay functions
    Configurable functions for distance or travel time; parameters not specified
axioms (2)
  • domain assumption National cancer incidence estimates and site-specific RT utilisation rates accurately reflect local demand
    Used to estimate demand in each hexagon
  • domain assumption Greedy nearest-first allocation produces a realistic assignment of patients to facilities
    Invoked to generate the localised access metric

pith-pipeline@v0.9.0 · 5824 in / 1366 out tokens · 36637 ms · 2026-05-25T02:33:04.031640+00:00 · methodology

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