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arxiv: 2405.10742 · v2 · submitted 2024-05-17 · 📊 stat.ME · stat.AP

Efficient Sampling in Disease Surveillance through Subpopulations: Sampling Canaries in the Coal Mine

Ivo V. Stoepker This is my paper

Pith reviewed 2026-05-24 01:10 UTC · model grok-4.3

classification 📊 stat.ME stat.AP
keywords disease surveillancesubpopulation samplingsampling efficiencyoutbreak detectionbaseline disease riskexact binomial testsstratified sampling
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The pith

Sampling subpopulations with higher baseline disease risk increases detection efficiency.

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

The paper examines how to choose which subpopulation to sample from for better outbreak detection in endemic diseases. It establishes that, under certain assumptions, the relative efficiency of sampling one subpopulation versus another is the inverse of their baseline disease risk ratio. This means targeting groups with higher natural disease rates can lead to better use of sampling resources. The findings account for the discrete nature of exact binomial tests, which can make power curves non-monotonic with sample size. A case study with COVID-19 data from the Netherlands supports the approach.

Core claim

The relative sampling efficiency between two subpopulations is inversely proportional to the ratio of their respective baseline disease risks. This implies one can increase sampling efficiency by sampling from the subpopulation with higher baseline disease risk. The results require careful treatment of the power curves of exact binomial tests as a function of their sample size, which are non-monotonic due to the underlying discreteness.

What carries the argument

The inverse proportionality between relative sampling efficiency and the ratio of baseline disease risks.

If this is right

  • Choosing the subpopulation with higher baseline risk improves sampling efficiency for outbreak detection.
  • The efficiency relationship holds after accounting for non-monotonic power curves in exact binomial tests.
  • Stratified sampling can be optimized by focusing on groups like age cohorts or travelers with elevated risks.
  • The approach is illustrated in a case study of COVID-19 cases in the Netherlands.

Where Pith is reading between the lines

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

  • Similar logic might apply to other surveillance tasks where detection power depends on baseline rates.
  • Resource allocation in public health could prioritize high-risk groups for routine testing to maximize early warning.
  • Extensions could explore how this interacts with varying subpopulation sizes or costs of sampling.

Load-bearing premise

The assumptions under which the relative sampling efficiency is inversely proportional to the baseline disease risk ratio, including the specific treatment of non-monotonic power curves of exact binomial tests.

What would settle it

A simulation or empirical study showing that the relative efficiency does not follow the inverse ratio when sampling from higher versus lower risk subpopulations under the model's conditions.

Figures

Figures reproduced from arXiv: 2405.10742 by Ivo V. Stoepker.

Figure 1
Figure 1. Figure 1: Power at 5% significance of the binomial test (3) as a function of the sample size n under the alternative as in (1) where qj = 1.5pj for j = 1, 2. Two curves are depicted corresponding to the null p1 = 0.015 and p2 = 0.01 respectively. The curves are only defined for integer n, but depicted as smooth lines for legibility. The results in [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Graphical results discussed in Section 4 [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Histograms of the time until detection when a negative binomial GLR control chart is used on independent samples from (20) for ν = 1.5. Vertical lines indicate the observed average time until detection. The GLR statistic is computed through the surveillance package (Salmon et al., 2016). Results presented use a window-limited GLR control chart with a width of 20 datapoints, and set up to detect increases i… view at source ↗
read the original abstract

We consider outbreak detection settings of endemic diseases where the population under study consists of various subpopulations available for stratified surveillance. These subpopulations can for example be based on age cohorts, but may also correspond to other subgroups of the population under study such as international travellers. Rather than sampling uniformly across the population, one may elevate the effectiveness of the detection methodology by optimally choosing a sampling subpopulation. We show (under some assumptions) the relative sampling efficiency between two subpopulations is inversely proportional to the ratio of their respective baseline disease risks. This implies one can increase sampling efficiency by sampling from the subpopulation with higher baseline disease risk. Our results require careful treatment of the power curves of exact binomial tests as a function of their sample size, which are non-monotonic due to the underlying discreteness. A case study of COVID-19 cases in the Netherlands illustrates our theoretical findings.

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

1 major / 1 minor

Summary. The manuscript considers stratified sampling for outbreak detection in endemic diseases, where subpopulations (e.g., age cohorts or travelers) have different baseline risks. It claims that, under some assumptions, the relative sampling efficiency between two subpopulations is inversely proportional to the ratio of their baseline disease risks. This is said to imply that sampling from the higher-risk subpopulation increases efficiency. The work emphasizes the need to handle non-monotonic power curves of exact binomial tests arising from discreteness and includes a COVID-19 case study in the Netherlands.

Significance. If the stated relationship holds after correction of the apparent inconsistency, the result would supply a simple rule for choosing subpopulations in surveillance, potentially improving detection power for a given sample size. The explicit treatment of non-monotonic exact-test power curves is a technical strength that distinguishes the work from standard large-sample approximations.

major comments (1)
  1. [Abstract] Abstract: the sentence 'the relative sampling efficiency between two subpopulations is inversely proportional to the ratio of their respective baseline disease risks' implies that if risk_A > risk_B then efficiency_A < efficiency_B (under any standard definition of relative efficiency as a ratio). The immediately following sentence asserts the opposite practical implication. This contradiction is load-bearing because the entire recommendation for subpopulation selection rests on the direction of the claimed relationship.
minor comments (1)
  1. The assumptions required for the proportionality result are described only as 'some assumptions' in the abstract; a clear statement of these assumptions (including how non-monotonicity is handled) should appear in the main text, preferably with a derivation or theorem statement.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and for identifying the inconsistency in the abstract. We agree that the current wording creates a contradiction between the stated mathematical relationship and the practical implication, and we will revise the abstract to resolve this.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the sentence 'the relative sampling efficiency between two subpopulations is inversely proportional to the ratio of their respective baseline disease risks' implies that if risk_A > risk_B then efficiency_A < efficiency_B (under any standard definition of relative efficiency as a ratio). The immediately following sentence asserts the opposite practical implication. This contradiction is load-bearing because the entire recommendation for subpopulation selection rests on the direction of the claimed relationship.

    Authors: We acknowledge the referee's observation. The abstract's use of 'inversely proportional to the ratio of their respective baseline disease risks' does produce the logical implication described (eff_A < eff_B when risk_A > risk_B), which conflicts with the following sentence recommending sampling from the higher-risk subpopulation. This appears to be an imprecise phrasing in the abstract alone. The manuscript body derives the efficiency relationship under the stated assumptions and uses the 'canaries in the coal mine' framing to indicate that higher baseline risk improves detection efficiency. We will revise the abstract to eliminate the contradiction, for instance by rephrasing the proportionality statement and explicitly defining the ratio so that the mathematical claim aligns with the practical recommendation. This change will appear in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation presented as independent mathematical result under assumptions

full rationale

The paper derives the claimed proportionality from assumptions on the non-monotonic power curves of exact binomial tests as a function of sample size. No self-definitional reductions, fitted inputs renamed as predictions, or load-bearing self-citations are present in the provided text. The central claim is positioned as following from those assumptions rather than reducing to them by construction, and the derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on unspecified assumptions about baseline disease risks being estimable and on the statistical properties of exact binomial tests; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption Power curves of exact binomial tests are non-monotonic due to the underlying discreteness
    Explicitly stated in the abstract as requiring careful treatment for the efficiency result to hold

pith-pipeline@v0.9.0 · 5670 in / 1268 out tokens · 29639 ms · 2026-05-24T01:10:56.284698+00:00 · methodology

discussion (0)

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Reference graph

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