Universal Suffering Units (USU): A Calibrated Additive Unit of Experienced Suffering

Denis Mikhaylov

doi:10.20944/preprints202511.1315.v2

Submitted:

21 June 2026

Posted:

23 June 2026

You are already at the latest version

Abstract

Background: Policy and humanitarian decisions often require comparing heterogeneous harms (e.g., infectious disease, injury, disasters, displacement) that are reported in non-commensurate units. Time-based summary measures such as disability-adjusted life years (DALYs) and quality-adjusted life years (QALYs) quantify health loss, but are not designed to provide an explicitly calibrated, experience-based unit that can be applied transparently across health and selected non-health harms. Methods: We define Universal Suffering Units (USU) as an additive aggregate of intensity-over-time profiles on a bounded 0–10 ladder, with optional convexity via an exponent p and an explicit overlap rule for co-occurring harms. The unit is calibrated so that a reference renal-colic trajectory equals 1.0 USU. We propagate parametric uncertainty via Monte Carlo simulation (N = 20,000; fixed seed) and provide fully reproducible worked examples using public data. Results: In two worked examples (dengue illness episodes and flood-related internal displacement), USU combines affected population, modeled intensity, and duration on a common scale and yields medians, uncertainty intervals, and sensitivity analyses. A limited convergence check shows that the dengue results are broadly consistent in rank with a disability-weight framework. Conclusions: USU provides a calibrated unit for aggregating experienced suffering while keeping state mappings, overlap treatment, and uncertainty assumptions explicit. It is intended to complement DALYs/QALYs and operational indicators, not replace them.

Keywords:

Universal Suffering Units (USU)

;

population health

;

health metrics

;

burden of disease

;

disability-adjusted life years (DALYs)

;

quality-adjusted life years (QALYs)

;

suffering measurement

;

pain measurement

;

disability weights

;

Monte Carlo simulation

Subject:

Public Health and Healthcare - Public, Environmental and Occupational Health

Background

Policy and humanitarian decisions routinely require comparisons across heterogeneous harms, including infectious disease, injury, disasters, displacement, violence exposure, and psychological distress. These harms are usually monitored with different indicators. Decision-makers therefore rely on parallel counts (cases, deaths, people displaced, affected households) and sector-specific severity frameworks, while cross-sector comparison remains difficult because there is no agreed method for translating multisector burdens into a common scale of lived experience. Humanitarian basic-needs guidance notes both the need for joint assessment across sectors and the limitations of existing approaches to integrated prioritization [1].

Time-based health metrics have made major advances in comparability within health. Disability-adjusted life years (DALYs) and related burden-of-disease frameworks summarize health loss over time using disability weights, enabling cross-condition comparisons in population health and priority setting [2,3,4,5,6]. Quality-adjusted life years (QALYs) and cost-utility analysis similarly provide a dominant framework for evaluating health interventions by combining survival and health-related quality of life [7,8,9]. These approaches are indispensable for many applications, but they are health-state constructs: they are not designed to represent many non-health harms (e.g., displacement-related disruption, fear, grief) as experienced states on a common, anchored experiential scale, nor to provide an explicit calibration to familiar sensations that can be interpreted in psychologically grounded units.

At the individual level, clinical science often measures symptom severity using self-report intensity scales, especially in pain research, supported by long-standing work on visual analogue and numeric rating methods [10,11,12,13]. Research on experienced utility and memory of aversive episodes separately motivates representing unpleasant experience as an intensity-over-time profile rather than relying only on event counts or retrospective summaries [14,15]. Together, these literatures suggest a tractable time-profiled representation while underscoring the need to state the calibration and aggregation choices.

We therefore propose Universal Suffering Units (USU), a calibrated additive unit for aggregating intensity over time across people on a bounded ladder. The method records the assumptions used for state definitions, intensity, duration, overlap, and totals rather than asserting a single true mapping, so alternative choices can be evaluated and substituted.

Related Work and Positioning

USU is designed to complement, not replace, established time-based measures. DALYs and QALYs remain the appropriate primary instruments for many health-economic and burden-of-disease questions [2,3,4,5,6,7,8]. USU instead targets the experienced burden of events and states, including harms that are difficult to represent as health-state utilities or disability weights. Work in palliative care and global health has also advanced the measurement of serious health-related suffering and its population burden [16,17]. USU adds a calibration anchor and a general additive unit that can be applied, with stated state definitions, across aversive experiences.

A related line of work frames pain as a time series and quantifies burden as “time in pain,” providing a practical structure for recording intensity trajectories and uncertainty in time-profile parameters [18]. USU shares this intensity-over-time perspective but has a different aim: it defines a calibrated unit for aggregation across individuals and heterogeneous states, including selected non-pain harms, and reports sensitivity to curvature and mapping choices.

USU anchors its scale to an interpretable benchmark on a 0–10 intensity ladder. The ladder is conceptually aligned with established pain-intensity measurement traditions (visual analogue and numeric rating scales), which treat self-reported ratings as informative while acknowledging context dependence and measurement limitations [10,11,12,13]. USU also differs from composite national indices: each modeled state has a stated definition, intensity, duration, overlap treatment, and uncertainty range.

Terminology

We use “suffering” rather than “pain” because the target is overall negative experience, including physical pain as well as dyspnoea, nausea, panic, grief, and other aversive affective states. Contemporary pain definitions include sensory and emotional components, but suffering is not reducible to nociception [13,19]. The calibration anchor is pain-based because pain scales are widely used and renal colic provides a concrete, clinically documented trajectory; the target construct nevertheless extends beyond pain. The intensity-over-time framing is also consistent with work on real-time and retrospective evaluation of aversive episodes and duration neglect [14,15,20,21].

Methods

Study Design and Setting

This study develops and demonstrates Universal Suffering Units (USU), specifies calibration to a renal-colic reference trajectory, and describes uncertainty and sensitivity reporting. Worked examples use publicly available aggregate data and the accompanying calculation files; no primary data collection or human-participant recruitment was conducted.

Core Definition and Notation

In this paper, experienced suffering means the momentary intensity of negative subjective experience: how bad it feels to be in a given state at a given time. It includes physical pain, other aversive somatic sensations (e.g., dyspnoea, nausea, fatigue), and affective states (e.g., fear, panic, grief) insofar as they contribute to the experience of the moment. We represent this construct as a scalar intensity Iᵢ(t) for individual i at time t, constrained to 0 ≤ Iᵢ(t) ≤ 10, where 0 indicates no suffering and 10 an extreme, overwhelming experience. This is a deliberate simplification, not a claim that suffering is intrinsically one-dimensional.

USU does not measure moral worth, social value, rights violations, or net welfare. Intensity inputs may come from standardized 0–10 ratings, structured elicitation against anchors, or mappings from validated symptom instruments, provided the mapping is documented. Ratings and access to analgesia can vary across people and settings, so applications should examine alternative anchors or mappings where appropriate.

Let Iᵢ(t) denote suffering intensity for person i at time t, with 0 ≤ Iᵢ(t) ≤ 10, and let p ≥ 1 control curvature. Over a reporting window from t₀ to t₁, total USU is defined as:

{U S U}_{t o t a l} = k \sum_{i} \int_{t_{0}}^{t_{1}} {[I_{i} (t)]}^{p} d t

The sum runs over individuals, time is expressed in days in the worked examples, and k is the calibration constant chosen so that the specified renal-colic reference trajectory equals 1.0 USU.

The 0–10 ladder follows widely used clinical numeric rating scales for pain and distress [10,11,12,13]. Treating it as cardinal is a modeling assumption: the ladder remains subjective and context-dependent, and alternative mappings should be examined in sensitivity analyses. In applications, Iᵢ(t) is constructed from event- or condition-specific states with stated assumptions and uncertainty ranges.

The exponent p controls curvature, allowing greater weight to higher intensities; sensitivity is reported across plausible values.

USU is defined only over experienced time. It assigns no USU after death; mortality is reported separately, for example as deaths and/or years of life lost, rather than embedded in the experienced-suffering integral.

Default exponent p. We use p = 1.25 (modest convexity) in the worked examples. This convention reflects the possibility that higher intensities receive disproportionate weight in evaluations of aversive episodes [14,15,20,21]. Because p is not empirically identified here, we report sensitivity that includes p = 1.

Anchoring and Calibration (Renal Colic = 1.0 USU)

USU is anchored by choosing k so that the reference trajectory for acute renal colic (“kidney-stone pain”) equals 1.0 USU. At the default p = 1.25, the specified curve integrates to 3.304016 intensity-days, giving k = 0.302662 (see Supplementary Files S1 and S3).

We use acute renal colic (ureteral stone pain) as the calibration benchmark for pragmatic reasons: it is intense, time-bounded, routinely measured, supported by published pain scores and analgesic-response curves [22,23], and familiar to many clinicians. It is a calibration convention, not an assumption of universal comparability. Perceived intensity may vary by age, culture, treatment access, and context. The reference can therefore be replaced or recalibrated; an alternative curve rescales results by a constant while preserving the framework’s structure and within-analysis comparisons.

We represent renal colic as a piecewise intensity-over-time curve on the 0–10 scale, informed by clinical descriptions of ureteral colic and visual analogue scale reporting in emergency care [22,23].

USU aggregates the cumulative burden of aversive experience (the area under an intensity-over-time curve, optionally convexified by p). This is analogous to common acute pain trial endpoints such as summed pain intensity difference (SPID) and total pain relief (TOTPAR) that summarize pain trajectories over time via area-under-curve methods [23]. Therefore, multi-day moderate states can exceed 1.0 USU even if their peak intensity is far below the renal-colic benchmark.

Reference Trajectory

The renal-colic benchmark is a stylized piecewise-constant profile representing an acute episode with an early severe phase and subsequent partial relief. The supplementary files specify a 6-hour profile on the 0–10 ladder: 7.5 for 1.0 h, 8.5 for 1.5 h, 9.0 for 1.0 h, 8.0 for 1.0 h, 7.0 for 0.5 h, and 6.5 for 1.0 h (Supplementary File S1: anchors_renal_colic_segments_v1.3.xlsx). This profile represents sustained high-intensity colicky pain followed by partial relief after treatment [22,23]. The segment values are modeling assumptions that can be inspected, adjusted, or replaced.

Cordell et al. report mean baseline renal-colic pain intensities of approximately 73–80 mm on a 100-mm visual analogue scale at emergency-department presentation (about 7–8/10), partial relief during the first 15–30 minutes after intravenous analgesia, and 6-hour summary endpoints (SPID and TOTPAR) that capture persistent burden and recurrent analgesic need [23]. Teichman describes severe wave-like pain with recurrent exacerbations, consistent with an early high-intensity phase [22]. These patterns motivate an auditable reference profile; they do not establish a universal clinical time course.

Anchoring fixes the unit; it is not an ethical claim. Because k is stated, alternative anchors can be substituted and results rescaled.

For intuition, we provide an informal ladder for smaller quantities: a blood-draw needle prick ≈ 0.001 USU, a paper cut or stubbed toe ≈ 0.01, and a painful fingertip burn ≈ 0.1. These anchors support elicitation and communication but do not alter the formal definition.

Data Sources and Processing

Key inputs, including intensity, duration, and in some modules severity mix, are uncertain. We represent them as distributions and propagate parametric uncertainty by Monte Carlo simulation [24].

We used N = 20,000 pseudo-random draws in Python 3.11.2 with NumPy 1.24.0 (np.random.default_rng(42), PCG64). The fixed seed (42), together with the specified NumPy version, PCG64 generator, inputs, and sampling sequence, permits exact reproduction of the supplied draws. For each draw, we sampled uncertain intensity and duration parameters from the Inputs sheet, calculated each module’s contribution, and summed modules over the reporting window. We report the median and the 5th and 95th percentiles as a 90% uncertainty interval.

We report sensitivity to p and propagate uncertainty in intensity and duration through the specified triangular distributions.

For each module and draw, USU equals the affected count multiplied by the calibrated intensity-time integral for the state template, with the renal-colic calibration applied consistently. Module definitions and assumptions are recorded in a versioned input table (USU Catalogue); Supplementary File S2 contains the excerpt used here.

Parameter values and ranges are listed in the Inputs tabs of Supplementary Files S3 and S4 and in Supplementary File S2. Supplementary File S5 contains the Python script used to recompute the Monte Carlo draws and summary statistics.

Triangular distributions are used because these examples specify a minimum, mode, and maximum but lack empirical variance estimates. Applications with richer data should replace them with empirically fitted distributions, such as beta or log-normal distributions where appropriate.

Aggregation and Comorbidity

When multiple harms co-occur in the same person-time, summing their separate intensities can double-count experienced burden. We therefore use a bounded overlap rule on the common 0–10 ladder.

Suppose m states occur at the same time, with intensities I₁,…,Iₘ ∈ [0,10]. Let I₍₁₎ be the largest value and I₍₂₎,…,I₍ₘ₎ the remaining values in descending order. The combined intensity is:

I_{c o m b i n e d} = m i n (10, I_{(1)} + λ \sum_{j = 2}^{m} I_{(j)})

where λ is constrained to 0 ≤ λ ≤ 1; the default is λ = 0.3 when overlap is modeled.

This rule is a modeling convention. The combined intensity is entered into the USU integral, and applications with co-occurring states should report sensitivity to λ and, where evidence supports it, alternative interaction models.

Statistical Analysis

The worked examples use public surveillance and humanitarian datasets, including PAHO dengue reports and IDMC displacement summaries, together with stated assumptions [25,26]. Each module cites its primary sources, and assumption provenance is documented in Supplementary Files S1 and S2; access dates are reported in the reference list where applicable.

To keep early applications tractable and auditable, we include only components with (i) a clear state definition, (ii) defensible intensity and duration assumptions, and (iii) a quantitative population measure (cases, people displaced, etc.).

Proxy Use and Scope Statements

If a parameter is missing for the target year, we either (a) leave the component unfilled, or (b) use a post-year proxy explicitly labeled as such, with a rationale and a sensitivity flag.

Because early applications may omit relevant components, reported USU totals are partial estimates rather than complete accounts of total suffering. Each aggregate should state the included components and time windows; cross-country rankings are discouraged unless coverage is comparable.

The Results section applies this procedure to public-data worked examples with input tables and citations that permit independent recomputation.

The worked examples are implemented in spreadsheets that separate inputs, catalogue assumptions, and outputs; calculations are formula-based and contain no macros.

The templates and worked spreadsheets are provided as supplementary materials.

Use of AI-Assisted Tools

Large language models (ChatGPT versions 5.1 Pro, 5.2 Pro, and 5.5 Pro, and Gemini Pro; accessed September 2025–June 2026) assisted with drafting, editing, consistency checks, and supporting documentation. The author reviewed and fact-checked all outputs and accepts full responsibility for the manuscript’s originality, accuracy, and integrity.

Results

Worked Example 1: Dengue Outbreak (Brazil, 2024; Epidemiological Weeks 1–23)

Data. We used 7,866,769 dengue cases reported for Brazil during epidemiological weeks 1–23 of 2024 in a PAHO/WHO epidemiological update [25]. Under-ascertainment is not modeled in this illustration.

State mapping. We model non-severe and severe dengue. The PAHO/WHO report lists 5,210 severe cases, giving a severe-case proportion of 5,210/7,866,769 = 0.00066228 (0.06623%) [25]. Daily intensity is triangular: non-severe (4, 5, 6) and severe (7, 8, 9). These bands are author assumptions informed by typical symptom descriptions and used to demonstrate anchored scaling [27,28]. Duration is triangular: non-severe (2, 4, 7) days and severe (4, 7, 14) days, informed by clinical course descriptions and recovery windows [27,28]. Supplementary File S3 provides the calculation walkthrough.

Computation. For each Monte Carlo draw, we sample the severe-case count, intensities, and durations; calculate per-case USU; and sum across cases. We report the median and 90% uncertainty interval and examine sensitivity to p.

Results. For p = 1.25, median dengue USU for epidemiological weeks 1–23 is 75.9 million (90% uncertainty interval 46.9–112.9 million). Approximately 99% of total USU arises from non-severe cases because they dominate incidence.

Sensitivity to curvature (p). Holding other assumptions fixed, median dengue USU is 85.2 million at p = 1, 75.9 million at p = 1.25, and 67.5 million at p = 1.5. These p values are illustrative rather than empirically identified.

Per-episode values represent cumulative burden relative to a short high-intensity benchmark; they do not imply that an episode has the same peak experience as multiple benchmark events.

Worked Example 2: Flood-Related Internal Displacement (Rio Grande do Sul, Brazil, 2024; End-June Snapshot)

Data. We use IDMC’s end-June 2024 estimate of approximately 389,000 people still living in internal displacement in Rio Grande do Sul as a result of the floods [26]. This stock estimate is the affected count for the snapshot example.

State mapping. We model a “flood-related internal displacement” state. Daily intensity is triangular (5, 6, 7) on the 0–10 ladder, and duration is triangular (7, 20, 45) days. These are author-defined scenario inputs intended to represent heterogeneous disruption during displacement, including possible loss of shelter, services, safety, and routine. The IDMC count establishes the number living in displacement but does not show that all 389,000 people were in emergency shelters; the template is therefore a scenario proxy, not a directly observed shelter condition [26,29].

Results. For p = 1.25, median flood-related displacement USU is 25.6 million (90% uncertainty interval 13.0–42.8 million). Median sensitivity values decrease from 27.5 million at p = 1 to 25.6 million at p = 1.25 and 23.9 million at p = 1.5.

Limitations. This illustration combines an end-June stock with modeled duration and intensity ranges. It is an order-of-magnitude scenario, not a comprehensive estimate of disaster burden.

Convergence Check Against a YLD Framework (Dengue Example)

As a limited convergent-validity check, we examine whether the dengue USU totals and a standard disability-weight construction rank the same Monte Carlo draws similarly when durations are matched.

For each Monte Carlo draw, we calculate implied years lived with disability (YLD) using the GBD 2013 disability weights for moderate and severe acute infectious disease (0.051 and 0.133, respectively) [3]. Using the same sampled durations as in the USU draws:

{Y L D}_{d r a w} = (N_{t o t a l} - N_{s e v, d r a w}) {D W}_{m o d} \frac{d_{n o n s e v, d r a w}}{365} + N_{s e v, d r a w} {D W}_{s e v} \frac{d_{s e v, d r a w}}{365}

where the terms denote total cases, the draw-specific severe-case count, and the draw-specific non-severe and severe durations in days. For Brazil during epidemiological weeks 1–23, implied YLD has a median of 4,704 years (90% uncertainty interval 2,989–6,769).

Across 20,000 draws, total USU and total YLD show a strong rank association (Spearman ρ = 0.92 at p = 1.25). Recalibrating the renal-colic reference at each p gives ρ = 0.94 at p = 1.0, 0.89 at p = 1.5, and 0.82 at p = 2.0.

This comparison does not show that USU reproduces DALYs: the two calculations share population and duration inputs. It only tests whether they rank the same simulated draws similarly in a health example. Full calculations are provided in the YLD_Convergence tab of Supplementary File S3.

Discussion

The worked examples demonstrate the USU framework rather than estimate comprehensive burden. They nevertheless illustrate several properties that matter for interpretation and use.

Comparability Across Harm Types and the Incidence-Duration Trade-Off

USU places acute illness and displacement on one additive scale by representing both as intensity-over-time profiles anchored to the same reference. In the dengue example, a large number of moderate, days-long episodes drives the total [25,27,28]. In the displacement example, a smaller population accumulates substantial USU because the modeled state lasts for weeks [26,29]. The incidence-duration trade-off is therefore visible in a way that case counts or displaced-person counts alone do not capture. Module-level decompositions and per-case values should be reported alongside totals.

Interpreting Magnitudes Across Very Different Experiences

A longer episode of moderate suffering can exceed a shorter episode of extreme suffering because USU integrates intensity over time, paralleling severity × duration accounting in other time-based measures. An unintuitive comparison should prompt reassessment of the intensity mapping, duration range, and p; it should not be read as literal experiential equivalence. Uncertainty and sensitivity results should therefore accompany point estimates.

How the Same Events Would Be Summarized Using DALYs/QALYs Versus USU

A DALY-based summary would represent dengue through disability weights multiplied by duration, plus years of life lost when deaths are included, within a health-state valuation framework [2,3,4,5]. USU instead uses an anchored intensity-over-time profile. QALY-based summaries likewise combine time with health-utility decrements and are designed primarily for health-economic evaluation; applying them to non-health harms such as displacement requires additional mappings [7,8,9]. USU is complementary: it offers an anchored experience-based unit for selected health and non-health states.

Severity Distributions and Concentration of Burden

Because USU is additive and can apply convexity through p, rare severe cases contribute much more per case, while high-incidence moderate states may still dominate totals. Reporting the severity distribution is therefore important for interpretation [3].

Uncertainty Propagation and Sensitivity Reporting

Input ranges can be propagated to totals: Monte Carlo simulation yields medians and uncertainty intervals, and sensitivity analyses show how results depend on choices such as p [24]. This follows standard simulation practice and can be paired with structured elicitation when inputs depend on expert judgment [24,30].

Scope and Completeness

USU totals depend on the modules and time windows included. Partial-window examples are therefore partial accounts, not guaranteed lower bounds, because both omissions and modeling assumptions affect the result. Each estimate should include a scope statement. For broader compilations, a qualitative coverage tier may help communicate completeness; cross-setting comparisons require comparable coverage.

Relation to Other Suffering Constructs

Palliative-care research has developed methods for measuring serious health-related suffering to estimate unmet need [17]. USU shares the motivation to make suffering measurable but is structured as a calibrated additive unit for cross-domain aggregation rather than a service-need metric. The animal-welfare literature has likewise proposed cumulative pain as intensity-by-time exposure across individuals [31]. USU is distinguished here by its human clinical reference trajectory, routine uncertainty and sensitivity reporting, and a stated rule for overlapping harms.

Implications for Applications

USU is most directly useful for event-level comparisons and intervention evaluation when affected population, duration, and an intensity profile can be characterized. For a person or cohort, it reduces to a calibrated integral over time. This focus is consistent with evidence that real-time and retrospective evaluations of aversive episodes can diverge [14,15,20,21]. Broader aggregation is possible when coverage is sufficient and overlap is handled. Because each anchor, mapping, and overlap rule is recorded, alternatives can be substituted. The main uncertainties in the examples are intensity, duration, and scope.

Future Work

Several extensions would strengthen USU. Standardized elicitation protocols are needed to map diverse experiences onto the 0–10 ladder with documented reliability and context sensitivity; structured expert judgment offers one starting point [30]. Candidate methods include calibration questions, mappings from patient-reported outcome measures, and repeated within-person sampling for longer states. Future work should also test whether the renal-colic and secondary anchors are stable across populations or require context-specific calibration. Open software and reporting standards should make uncertainty intervals and sensitivity analyses routine. Stated-preference methods, time-trade-off tasks, or discrete-choice experiments could help estimate p for specific populations. Finally, a versioned public catalogue of modeled states would support reuse while keeping the definition of USU separate from application-specific assumptions.

Limitations

USU does not remove subjectivity. Mapping a state to the 0–10 ladder requires judgment, and the framework treats that ladder as an approximate interval scale for integration. Ranges, uncertainty propagation, and sensitivity to alternative transformations reduce but do not eliminate this limitation [30].

Calibration also depends on the reference episode. Renal colic is clinically familiar and routinely measured, but it is a physical-pain anchor and may not transfer uniformly across populations or forms of suffering. Recall effects and context can further shift intensity reports; applications should test alternative anchors or recalibrate when warranted [13,14,15].

Public data may omit cases or use heterogeneous definitions, biasing affected counts [25,26]. The overlap rule is simplified, and richer interaction models may be needed where comorbidity is important. Finally, the examples cover selected events and partial windows; they are methodological demonstrations, not national burden accounts.

Conclusions

We introduced Universal Suffering Units (USU), a calibrated additive unit for experienced suffering over time anchored to a renal-colic reference. The framework separates calibration, state mapping, overlap, and uncertainty so that alternative assumptions can be evaluated. Two public-data examples demonstrate feasibility and identify sensitivity to intensity, duration, and curvature. USU is intended to complement, not replace, DALYs/QALYs and operational indicators [2,3,4,5,6,7].

List of Abbreviations

DALY Disability-adjusted life year; DW Disability weight; GBD Global Burden of Disease; IDMC Internal Displacement Monitoring Centre; PAHO Pan American Health Organization; QALY Quality-adjusted life year; SPID Summed pain intensity difference; TOTPAR Total pain relief; USU Universal Suffering Unit; WHO World Health Organization; WSI World Suffering Index; YLD Years lived with disability.

Supplementary Materials

The following supporting information can be downloaded at the website of this paper posted on Preprints.org. The following supporting information is submitted with this preprint: Supplementary File S1 (S1_File.zip). Supplementary package containing the renal-colic reference segments, calibration documentation, a minimal input template, worked-example input/output spreadsheets, assumption provenance, and exponent-sensitivity outputs. Supplementary File S2 (S2_File.xlsx). Minimal USU catalogue of states and default parameter bands used by the worked examples. Supplementary File S3 (S3_File.xlsx). Brazil dengue 2024 calculation walkthrough, including step-by-step calculations, Monte Carlo uncertainty propagation (seed 42), and the YLD_Convergence outputs used in the dengue convergence check. Supplementary File S4 (S4_File.xlsx). Rio Grande do Sul floods 2024 internal-displacement calculation walkthrough with step-by-step calculations and Monte Carlo uncertainty propagation (seed 42). Supplementary File S5 (S5_File.py). Python script used to recompute the Monte Carlo draws and summary statistics for the dengue and flood-displacement worked examples (seed 42; NumPy PCG64).

Ethics statement

Not applicable. This methodological study used only aggregated, publicly available secondary data and involved no interaction with participants or access to identifiable information; institutional ethics review was therefore not required.

Informed consent statement

Not applicable.

Data availability statement

All numerical inputs and derived results reported in the worked examples are included in this preprint and Supplementary Files S1–S5. These materials include machine-readable spreadsheets and the Python script used to recompute the Monte Carlo draws and summary statistics with fixed seed 42; see the README tabs in Supplementary Files S3 and S4.

Author Contributions

DM is the sole author. He conceived the study, conducted the analyses, and wrote the manuscript.

Funding

The author received no specific funding for this work.

Acknowledgments

DM acknowledges a paid independent methodological review focused on methods and reproducibility; the reviewer requested anonymity.

Conflicts of interest

DM is the founder of the World Suffering Index (WSI) project, which is in early stages of development and is designed to apply USU in country-level reporting. DM declares no financial competing interests (no patents, products in development, or marketed products associated with this work).

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