Robust Timing for Medical Screening

In many real-world screening environments, the hard part is to assess how quickly risk rises. Protocols calibrated to one “typical” intensity can therefore be precise yet unreliable. Indeed, if the true environment is slower or faster, the same timing rule may test too early (wasting resources and yielding uninformative results) or too late (missing opportunities to intervene). Prof. Weber studies an implementable policy built around two decision thresholds on a clinician’s current belief about disease risk. Below a lower threshold, the best action is to wait. In an intermediate region, testing becomes worthwhile because the result is likely to change the decision. Above an upper threshold, treatment is justified even without further testing. Crucially, the rule allows retesting after negative results, capturing the common “window period” logic where early tests may be negative simply because it is too soon for a clear signal.

The paper [1] evaluates any candidate policy by comparing its realized value with the value of the best policy one could have chosen if the true speed had been known in advance. This ratio-based benchmark provides a scale-free guarantee: it measures how close a fixed ex-ante rule comes to the ex-post best outcome under realized conditions. A relatively robust rule is then chosen to maximize its worst-case relative performance across the entire uncertainty range.

Instead of assuming a fully specified stochastic model of prevalence, the paper keeps the underlying drift deterministic but allows its speed to be uncertain within a plausible range. This focuses attention on a key source of misspecification in practice: cohort conditions differ, environments change, and estimated intensities drift over time. The question becomes: how sensitive is an “optimal” timing rule to getting the speed wrong?

A central technical contribution is a fast evaluator for the expected long-run value of a two-threshold rule. That makes it practical to compute good thresholds by straightforward search, and to show how the recommended rule shifts when test costs, test accuracy, treatment benefits, or the uncertainty range change—features that are often hidden in more opaque models.

The numerical example is motivated by screening close contacts after a known tuberculosis exposure. In this setting, immunologic conversion can be delayed, so timing and retesting decisions play out over weeks to years. At the same time, effective intensity can vary across outbreaks and settings, making speed uncertainty clinically consequential. The robust rule is shown to perform close to the ex-post best policy across the full range of plausible speeds, while remaining simple enough to interpret operationally.

This research builds on earlier work at the Chair of Operations, Economics and Strategy (OES) on relatively robust decision-making, which focuses on ensuring reliable performance under incomplete information [2–8]. It also extends earlier OES contributions on dynamic information acquisition in product markets, optimal control, and medical applications [9–12].

Abstract: Medical tests are investments in information whose value depends on the prior probability of disease, on how that belief evolves over time, and on actions taken after evidence is observed. Deterministic prevalence dynamics are tractable, but policies calibrated under a single intensity can be unreliable when epidemiological speeds are misspecified. We model belief as evolving deterministically under an autonomous differential equation whose drift is scaled by an unknown multiplicative speed factor. The decision maker may wait, test at a cost, and treat (or not treat) after outcomes, with retesting possible after negative results. For stationary policies defined by two belief thresholds, we obtain a closed-form expression for the expected discounted value, yielding a fast evaluator for computing optimal thresholds. Relative robustness is measured by a performance ratio that compares the value of a candidate threshold pair with the ex-post optimal value under the realized speed factor; relatively robust thresholds maximize the worst-case ratio over an ambiguity interval. We provide a grid-search procedure and a numerical illustration motivated by post-exposure tuberculosis infection screening, where timing decisions unfold over weeks to years and intensity ambiguity is clinically consequential.

References

[1] Weber, T.A. (2026) “Relatively Robust Timing of Medical Tests under Ambiguous Prevalence Dynamics,” International Research Conference on Smart Computing and Systems Engineering (SCSE), IEEE, pp. 1—10.
[DOI: https://doi.org/10.1109/SCSE70081.2026.11499885]

[2] Weber, T.A. (2026) “Relatively Robust Multicriteria Decisions,” Management Science, Vol. 72, No. 4, pp. 3175—3203.
[DOI: https://doi.org/10.1287/mnsc.2025.00510]*

[3] Weber, T.A. (2025) “A Measure of Decision-Based Payoff Uncertainty,” International Conference on Problems of Cybernetics and Informatics (PCI), IEEE, pp. 1—5.
[DOI: https://doi.org/10.1109/PCI66488.2025.11219738]

[4] Weber, T.A. (2025) “Relatively Robust Economic Order Quantity with Optimal Laplacian Confidence Intervals,” International Research Conference on Smart Computing and Systems Engineering (SCSE), IEEE, pp. 1—6.
[DOI: https://doi.org/10.1109/SCSE65633.2025.11030973]

[5] Weber, T.A. (2025) “Monopoly Pricing with Unknown Demand,” Scandinavian Journal of Economics, Vol. 127, No. 1, pp. 235–285.
[DOI: https://doi.org/10.1111/sjoe.12564]*

[6] Weber, T.A. (2024) “Optimal Depth of Discharge for Electric Batteries with Robust Capacity-Shrinkage Estimator,” International Conference on Smart Grid and Renewable Energy (SGRE), Doha, Qatar, pp. 1–5.
[DOI: https://doi.org/10.1109/SGRE59715.2024.10428801]

[7] Weber, T.A. (2023) “Relatively Robust Decisions,” Theory and Decision, Vol. 94, No. 1, pp. 35–62.
[DOI: https://doi.org/10.1007/s11238-022-09866-z]*

[8] Han, J. and Weber, T.A. (2023) “Price Discrimination with Robust Beliefs,” European Journal of Operational Research, Vol. 306, No. 2, pp. 795–809.
[DOI: https://doi.org/10.1016/j.ejor.2022.08.022]*

[9] Weber, T.A. (2019) “Dynamic Learning in Markets: Pricing, Advertising, and Information Acquisition,” Hawaii International Conference on System Sciences(HICSS), pp. 6628—6637.
[DOI: https://doi.org/10.24251/HICSS.2019.794]

[10] Cipriano, L.E. and Weber, T.A. (2018) “Population-Level Intervention and Information Collection in Dynamic Healthcare Policy,” Health Care Management Science, Vol. 21, No. 4, pp. 604—631.
[DOI: https://doi.org/10.1007/s10729-017-9415-5]*

[11] Cipriano, L.E., Goldhaber-Fiebert, J.D., Liu, S., and Weber, T.A. (2018) “Optimal Information Collection Policies in a Markov Decision Process Framework,” Medical Decision Making, Vol. 38, No. 7, pp. 797—809.
[DOI: https://doi.org/10.1177/0272989X18793401]*

[12] Weber, T.A. and Nguyen, V.A. (2018) “A Linear-Quadratic Gaussian Approach to Dynamic Information Acquisition,” European Journal of Operational Research, Vol. 270, No. 1, pp. 260—281.
[DOI: https://doi.org/10.1016/j.ejor.2018.03.003]*

(*Open Access)