Moore, Yorio, Haas, Bell and Greenawald (2020) showed that, at the level of US mines, counts of lower-severity incidents in one year — including near misses — statistically predict the probability of a fatal event in the next year, reviving the predictive premise of Heinrich's safety pyramid while explicitly disclaiming causal interpretation. The open questions posed in that paper define the problem: no one knows how underreporting of lower-severity events distorts the estimated odds ratios and the triangular severity gradient; whether the association reflects common causes across severity levels, mediation by safety climate and culture, or reporting behavior; what proportion of decline in high-severity events (if any) reductions in lower-severity incidents can be expected to cause; and whether the relationship generalizes beyond US mining. The problem is open.

Background

The safety pyramid (or accident triangle) is the best-known statistical image in occupational safety. Formulated by the American insurance engineer H. W. Heinrich in his 1931 book Industrial Accident Prevention, it asserts that in an industrial population roughly 300 no-injury incidents accompany every 29 minor injuries and one major injury. The figure carries two distinct claims: a relatively stable ratio between event counts at different severity levels, and an implied shared causal basis — so that acting on the numerous low-severity events should also prevent the rare high-severity ones. Both claims legitimize widespread practice: near-miss reporting systems (a near miss is an unplanned event that could plausibly have caused injury but did not), recordable-injury-rate targets, and the reading of minor-injury trends as a proxy for fatal risk.

Modern empirical tests of these two tenets disagree. Heinrich's original database was never published, and subsequent analyses span the spectrum. Marshall, Hirmas and Singer (2018) fitted a Bayesian two-part model (accident counts modeled with a Poisson–gamma distribution and the severity mix with a multinomial–Dirichlet distribution — standard Bayesian count and categorical models) to more than 50,000 Chilean companies and found that the severity mix does change statistically as accident rates fall — the pyramid is "statistically invalid" — but by margins small enough that minor-accident rates remain useful for forecasting overall safety performance. Cooper (2019) showed that in the United Kingdom serious injuries and fatalities barely declined over three decades while minor injuries fell by about two thirds — the divergence at the heart of what practitioners call serious-injury-and-fatality (SIF) prevention. Bellamy (2015), analyzing roughly 23,000 serious reportable incidents, concluded that low-severity events can inform the causes of high-severity events only within the same hazard category (for example falls or machinery), not across categories — a partial reading of the common cause hypothesis, the proposition that events of different severity share the same underlying causes. Conversely, Zhou, Liu and Wang (2025) report power-law size–frequency distributions of Chinese workplace-accident fatalities with industry-dependent exponents, offered as a theoretical basis for Heinrich's law, and Yorio and Moore (2018) found the triangular form — lower-severity incident counts predicting establishment-level fatality probability — in a dataset of more than 25,000 US mining establishments, dependent on how severity is delineated.

The immediate source of the present problem is Moore, Yorio, Haas, Bell and Greenawald (2020), a team from the US National Institute for Occupational Safety and Health (NIOSH, the US occupational-safety research agency) analyzing the Mine Safety and Health Administration's (MSHA, the US mine-safety regulator) mandatory reporting databases, which cover essentially all US mining establishments. They fitted longitudinal logistic regressions by generalized estimating equations (GEE — a regression method for repeated observations of the same unit over time that accounts for within-unit correlation), predicting whether a mine experiences a fatal event in a given year from the previous year's counts of incidents at graded severity levels (permanently disabling injuries, days-lost injuries, reportable injuries, and near misses; alternatively, total or average lost/restricted workdays), controlling for employee hours worked. Across roughly 27,000 mines observed 2000–2012, prior-year lower-severity incidents — including near misses — significantly predicted subsequent fatality risk: for example, hours-adjusted odds ratios (the multiplicative change in the odds of an outcome per unit increase in a predictor) of about 1.37 per prior-year permanently disabling injury, 1.02 per prior-year near miss, and about 2.7 for mines with more than 100 total lost/restricted days in the prior year relative to zero-day mines. The triangular gradient — larger effects for more severe categories — appeared most clearly when severity was measured by total lost/restricted days. A companion paper by the same group (Yorio et al. 2020), on a 2006–2017 panel of 24,910 mining establishments, confirmed the association and additionally found a cyclic relationship in which a fatal event increases subsequent near-miss reporting.

The authors frame all of this as prediction, not causation, and the paper's discussion states the open caveats. First, lower-severity events are underreported in surveillance data — organizational research shows weaker safety climates, that is, weaker shared worker perceptions of the priority given to safety, predict greater underreporting — and no one knows how this distortion affects the estimated odds ratios or the shape of the triangle. Second, the results cannot establish a fixed quantitative decline in high-severity events from reductions in lower-severity incidents; at most an unknown proportion of decline could be expected. Third, the study cannot determine whether a common cause underlies all severity levels or whether cultural factors mediate the predictive relationship. Fourth, generalizability to other industries, and the mechanisms (for example safety-culture change) through which reducing lower-severity incidents might reduce fatality risk, remain untested. These caveats are the problem stated below.

Problem Statement

Moore et al. (2020) established a statistical association between prior-year lower-severity incident counts and subsequent-year fatality probability at the level of US mines, but could not say how much of that association is real, why it exists, or where else it holds. The open problem, as posed by the paper's discussion, is to convert this predictive relationship into a bias-qualified, causally grounded one. Its discussion poses four open questions: (1) quantify the impact of underreporting of lower-severity events on the estimated odds ratios and on the apparent triangular (severity-graded) shape; (2) identify the causal structure that produces the association — whether severity levels share common causes (overall, or only within hazard categories), whether the association is mediated by safety climate and culture change or by managerial corrective action, or whether it is partly an artifact of reporting behavior; (3) determine whether reductions in lower-severity incidents themselves cause reductions in high-severity events, and if so what proportion of decline can be expected, given that the pyramid by itself licenses no fixed ratio and the source's results cannot establish one; and (4) establish whether the mine-level predictive relationship generalizes to other industries and reporting regimes, at least one of them beyond US mining. Together these questions serve one objective: a causal, reporting-bias-qualified validation of the safety pyramid's predictive premise. The sub-questions are independent rather than mutually blocking.

References

  1. Moore SM, Yorio PL, Haas EJ, Bell JL, Greenawald LA (2020). Heinrich Revisited: a New Data-Driven Examination of the Safety Pyramid. Mining, Metallurgy & Exploration 37(6):1857–1863. doi:10.1007/s42461-020-00263-0. https://doi.org/10.1007/s42461-020-00263-0
  2. Yorio PL, Moore SM (2018). Examining Factors that Influence the Existence of Heinrich's Safety Triangle Using Site-Specific H&S Data from More than 25,000 Establishments. Risk Analysis 38(4):839–852. doi:10.1111/risa.12869. https://doi.org/10.1111/risa.12869
  3. Yorio PL, Haas EJ, Bell JL, Moore SM, Greenawald LA (2020). Lagging or leading? Exploring the temporal relationship among lagging indicators in mining establishments 2006–2017. Journal of Safety Research 74:179–185. doi:10.1016/j.jsr.2020.06.018. https://doi.org/10.1016/j.jsr.2020.06.018
  4. Marshall P, Hirmas A, Singer M (2018). Heinrich's pyramid and occupational safety: A statistical validation methodology. Safety Science 101:180–189. doi:10.1016/j.ssci.2017.09.005. https://doi.org/10.1016/j.ssci.2017.09.005
  5. Bellamy LJ (2015). Exploring the relationship between major hazard, fatal and non-fatal accidents through outcomes and causes. Safety Science 71:93–103. doi:10.1016/j.ssci.2014.02.009. https://doi.org/10.1016/j.ssci.2014.02.009
  6. Thoroman B, Salmon P, Goode N (2020). Applying AcciMap to test the common cause hypothesis using aviation near misses. Applied Ergonomics 87:103110. doi:10.1016/j.apergo.2020.103110. https://doi.org/10.1016/j.apergo.2020.103110
  7. Cooper MD (2019). The efficacy of industrial safety science constructs for addressing serious injuries & fatalities (SIFs). Safety Science 120:164–178. doi:10.1016/j.ssci.2019.06.038. https://doi.org/10.1016/j.ssci.2019.06.038
  8. Bayona A, Hallowell MR, Bhandari S (2024). The Things That Hurt People Are Not the Same as the Things That Kill People: Key Differences in the Proximal Causes of Low- and High-Severity Construction Injuries. Journal of Construction Engineering and Management 150(8):04024089. doi:10.1061/jcemd4.coeng-14545. https://doi.org/10.1061/jcemd4.coeng-14545
  9. Rocha R, Diniz EPHY, Parreiras M, Almeida I (2025). The illusion of safety indicators in the mining industry. International Journal of Occupational Safety and Ergonomics (advance online publication):1–13. doi:10.1080/10803548.2025.2580782. https://doi.org/10.1080/10803548.2025.2580782
  10. Zhou F, Liu X, Wang F (2025). Size–Frequency Distribution Characteristic of Fatalities Due to Workplace Accidents and Industry Dependency. Mathematics 13(12):2021. doi:10.3390/math13122021. https://doi.org/10.3390/math13122021
  11. Inagaki M, Nagata T, Odagami K, Adi NP, Mori K (2024). Relationship between a company's adequate response to near-misses and occupational accidents: a 1-year prospective cohort study. Journal of Occupational Health 66(1):uiae053. doi:10.1093/joccuh/uiae053. https://doi.org/10.1093/joccuh/uiae053
  12. Probst TM, Brubaker TL, Barsotti A (2008). Organizational injury rate underreporting: The moderating effect of organizational safety climate. Journal of Applied Psychology 93(5):1147–1154. doi:10.1037/0021-9010.93.5.1147. https://doi.org/10.1037/0021-9010.93.5.1147
  13. Onwuka C (2020). A Quantitative Test of the Predictive Validity of Heinrich's Accident Pyramid. African Journal of Health, Safety and Environment 1(1):01–10. doi:10.52417/ajhse.v1i1.18. https://doi.org/10.52417/AJHSE.V1I1.18
  14. Li Z, Yao M, Luo Z, Wang X, Liu T, Huang Q, Su C (2024). A chemical accident cause text mining method based on improved accident triangle. BMC Public Health 24(1):39. doi:10.1186/s12889-023-17510-w. https://doi.org/10.1186/s12889-023-17510-w
  15. Šimić Z, Peinador Veira M, Banov R (2022). Correlation between events with different safety significance in nuclear power plants. Nuclear Engineering and Technology 54(7):2510–2518. doi:10.1016/j.net.2022.01.034. https://doi.org/10.1016/j.net.2022.01.034
  16. Heinrich HW (1931). Industrial Accident Prevention: A Scientific Approach. McGraw-Hill, New York. (Pre-ISBN monograph; first-edition catalog record OpenLibrary OL6754051M, https://openlibrary.org/books/OL6754051M.)