Addendum to a Critical Note: On Possible Sampling Bias and Inverted Propensity Score Matching in Kim et al. Study (Biomark Res, 13:114, 2025)

Addendum to a Critical Note: On Possible Sampling Bias and Inverted Propensity Score Matching in Kim et al. Study (Biomark Res, 13:114, 2025) Marco Roccetti Department of Computer Science and Engineering, University of Bologna, 40126, Italy; [email protected] Abstract This addendum proposes a plausible explanation for the epidemiological paradox identified in our previous short note regarding the Kim HJ et al. cohort study on cancer incidence postCOVID-19 vaccination in South Korea. Specifically, it hypothesizes that the 1:4 propensity score matching (PSM) employed may have been inverted in direction, i.e., controls were matched based on vaccinated individuals rather than vice versa. Considering the cohort's composition, where vaccinated individuals outnumber unvaccinated by approximately fourfold, such inversion would undermine the representativeness of the control group and bias the estimated incidence rates. This sampling bias hypothesis could explain the apparent contradictions in crude cancer incidence rates reported and warrants further investigation. Keywords: Propensity Score Matching, Inversion or Misapplication of the 1:4 Matching, Crude Incidence Rate, Epidemiological Paradox, COVID-19 Vaccination, Cancer Incidence Introduction In the original study by Kim HJ et al. [1], a large cohort of 8,407,849 South Korean individuals was reduced via 1:4 propensity score matching (PSM) to 2,975,035 individuals (595,007 unvaccinated and 2,380,028 vaccinated). The matched cohort was then used to compare cancer incidence between COVID-19 vaccinated and unvaccinated groups. Our prior critical short note [2] highlighted a paradox: despite the study reporting a higher crude cancer incidence rate (CR) in vaccinated individuals (42.63 per 10,000) than unvaccinated (33.43 per 10,000), the overall cohort’s CR (40.78 per 10,000) was markedly lower than South Korea’s official national average CR (~52.46 per 10,000). This discrepancy suggested a representativeness problem. Sampling Bias Hypothesis: Direction of PSM Matching Propensity score matching aims to reduce confounding by matching treated individuals with comparable untreated controls. In vaccine effectiveness or adverse effect studies, the natural and appropriate approach is to match each COVID-19 vaccinated individual (treated) with one or more unvaccinated individuals (controls). This ensures that the control group is constructed relative to the treated group. However, given the cohort sizes reported, vaccinated individuals (2,380,028) outnumber unvaccinated (595,007) by a ratio close to four. A 1:4 PSM would typically imply matching each unvaccinated individual to four vaccinated controls, yet the reported data show the opposite: 595,007 unvaccinated and 2,380,028 vaccinated. This suggests that the matching may have been performed “in reverse” i.e., the control group (unvaccinated) was constructed by matching vaccinated individuals rather than the other way around. Such inversion would produce a matched cohort not representative of the true underlying population structure. Implications The situation has far-reaching implications: 1. Underrepresentation of Unvaccinated Population: If controls (unvaccinated) are chosen based on vaccinated individuals, the smaller unvaccinated pool is overextended, potentially selecting unrepresentative samples. 2. Bias in Cancer Incidence Estimates: The skewed matching direction could lead to artificially reduced crude incidence rates overall, explaining the paradoxical discrepancy with national averages. 3. Confounding Effects: The inversion could obscure confounders and distort hazard ratios or risk estimates derived from the cohort. Conclusion This addendum posits that the key paradox noted in [2] may be explained by the directionality of the propensity score matching procedure. Confirming this hypothesis requires access to the underlying dataset and detailed methodology, currently unavailable. We reiterate the call for public access to the Korean National Health Insurance database used by Kim et al. [1], to enable independent validation and clarify these methodological issues. Funding: This research received no external funding Data Availability Statement: The data presented here is either included directly or was extracted from the referenced documents. All calculations are easily reproducible based on the definitions provided Ethics approval and consent to participate: This study uses publicly available, aggregated data that contains no private information. Therefore, ethical approval is not required Consent for publication: Not applicable. Conflicts of Interest: The author declares no competing interests. References 1. Kim HJ, Kim M-H, Choi MG, Chun EM. 1-year risks of cancers associated with COVID-19 vaccination: a large population-based cohort study in South Korea. Biomark Res. 2025;13:114. https://doi.org/10.1186/s40364-025-00831-w 2. Roccetti M. A Critical Note on Contradictions in South Korean Cancer Incidence Rates: The Paradoxical Disconnect of Crude Rates Derived from the Kim HJ et al. Cohort (Biomark Res, 13:114, 2025) Revealing Concurrent Increases in the COVID19 Vaccinated and Overall Decrease (short version). Researchgate Preprint October 2025. https://doi.org/10.13140/RG.2.2.17016.10244