Severity Modelling

Why severity is a separate modelling target from collision frequency, and what the literature says about each

Why collision severity is a separate modelling target from frequency, what the literature says about each, and what post-event variables must be excluded from Open Road Risk Stage 2.

Open Road Risk’s Stage 2 outcome is the count of injury collisions per link-year, regardless of severity. All police-reported injury crashes — slight, serious, and fatal — are pooled into a single integer count and modelled against an exposure offset. This is a pragmatic choice at national scale with sparse data, but it comes with a known limitation: the mechanisms that cause a collision to be fatal or serious are not the same as those that cause a collision to occur in the first place, and conflating the two can misidentify which roads are highest-priority for intervention.

This page documents what the reviewed literature says about severity as a distinct modelling target, where the boundaries between frequency and severity lie, and what the leakage implications are for the current pipeline.

STATS19 underreporting and its effect on the Stage 2 outcome

Open Road Risk’s Stage 2 outcome pools all police-reported injury collisions — slight, serious, and fatal — into a single count. Savolainen et al. (2011) review meta-analyses of crash underreporting rates and document a systematic pattern: reporting rates are strongly outcome-dependent. Elvik and Myssen (1999) find underreporting rates of approximately 30% for serious injuries, 75% for slight injuries, and 90% for very slight injuries. Fatal crashes are nearly 100% reported; property-damage-only crashes are excluded from STATS19 by design.

The consequence for Open Road Risk is that the Stage 2 outcome underweights slight-injury crashes relative to their true frequency, particularly on lower-traffic links where police response and reporting practices may differ from high-traffic corridors. Links with predominantly slight-injury crashes will have their collision count systematically underestimated relative to their true risk. This is not a modelling choice that can be corrected without independent data on reporting rates; it should be documented as a known limitation of the outcome variable.

Note

The underreporting rates above (Elvik & Myssen 1999) are from a European meta-analysis; UK-specific STATS19 reporting rates may differ and have evolved over time as insurance reporting requirements have changed. Verify against current DfT or TRL underreporting studies before using these figures in formal documentation.

DfT’s 2024 reported-road-casualties annual report provides current UK context for this limitation. It states that non-fatal casualties, especially slight injuries, are substantially under-reported to police, and that adjusted serious/slight injury figures are needed because some police forces changed injury-severity reporting systems from 2016 onwards. Open Road Risk’s Stage 2 outcome uses police-reported injury collisions, so it inherits these reporting limitations even though it does not currently model severity separately.

Savolainen et al. (2011) also confirm that joint frequency-severity models are feasible using the non-crash-specific data that Open Road Risk already has. Their footnote 1 states explicitly that joint models “can only use non-crash-specific data (roadway geometry, traffic volumes, etc.)” — which is exactly the feature set in Stage 2. If a severity dimension is ever added, the existing features are compatible with a joint approach without requiring per-crash data.

Frequency and severity are different estimands

The distinction runs through every paper in this section. A crash-frequency model asks: given this road’s features and traffic exposure, how many injury collisions per year are expected? A severity model asks: given that a collision has occurred, how serious is it likely to be?

Quddus, Wang and Ison (2010) make this explicit. Their paper estimates an ordered response model for M25 crash injury severity (slight / serious / fatal), using individual STATS19 crash records matched to 15-minute UKHA traffic data. They are explicit that their model “makes no attempt to estimate the actual probability of a specific accident occurring” — it conditions on a crash having happened and then models the severity outcome. The exposure variable (traffic flow) enters as a predictor of conditional severity, not as a rate denominator.

This has a concrete consequence for feature interpretation. In the Quddus et al. model, higher traffic flow is associated with less severe outcomes (more crashes, but lower mean severity per crash) — the opposite direction from what a frequency model would suggest. If these two effects were conflated in a single model, the sign and magnitude of the flow coefficient would be uninterpretable.

Michalaki et al. (2015) model motorway severity (hard shoulder vs. main carriageway, 2005–2011) and arrive at the same conclusion structurally. Their model uses post-crash STATS19 variables — contributory factors, number of vehicles, single-vehicle flag — as severity predictors. These are valid in a conditional severity model. They would constitute post-event data leakage in a collision frequency or risk ranking model.

Ma et al. (2019) distinguish the two estimands explicitly in their conclusions: “Fatality rates represent the rates of fatal accidents over all accidents, while accident rates mean the proportion of accidents over traffic volume. These are two different problems.”

Warning

Leakage boundary. The following STATS19 variables are valid for explanatory severity analysis (conditional on a crash), but must not enter Open Road Risk Stage 2 as predictors, because they are observed only after the crash occurs:

Number of vehicles involved
Number of casualties
Single-vehicle crash flag
Contributory factor codes (police officer’s opinion of cause)
Crash type / manoeuvre codes
Road surface condition at crash time
Lighting condition at crash time (observed at crash, not from infrastructure data)
Pedestrian / motorcycle involvement flag (at crash level)

These variables describe the accident. They cannot be known before the accident. Using them in a frequency or risk-ranking model creates a model that appears strong in-sample but has no prospective predictive validity.

DfT’s CF/RSF transition guidance strengthens the same boundary from a data-provenance perspective. Contributory factors and road safety factors are officer-recorded judgements assigned after a collision; they are not pre-collision road attributes. The 2024 transition from contributory factors to road safety factors also creates a structural break, with directly recorded RSFs not comparable to CF-converted records for trend analysis. If Open Road Risk ever uses these fields, they should remain diagnostic context only, not Stage 2 predictors.

What the literature says about severity mechanisms

Traffic flow and severity

Quddus et al. (2010) find that higher traffic flow on the M25 is associated with lower conditional crash severity across all model specifications (PC-GOLOGIT, HCM, GOLOGIT). The marginal effect of log traffic flow reduces serious injury probability by 0.034 and fatal probability by 0.006 per unit, while increasing slight injury probability by 0.040. The mechanism is plausible: high-flow conditions impose lower free-flow speeds through congestion, reducing crash energy.

The congestion index (total delay) was statistically insignificant for severity across all model specifications and both congestion measures tested. The paper concludes there is no evidence that M25 congestion affects crash severity in this dataset. This null result is specific to the M25 motorway, and should not be generalised to all road types — but it does caution against prioritising congestion as a Stage 2 feature on the basis of motorway evidence alone.

Michalaki et al. (2015) find that non-peak (quiet) traffic hours are associated with higher severity on motorways. The mechanism is the same as Quddus et al. in reverse: free-flow conditions in quiet periods allow higher impact speeds, increasing injury severity per collision. This finding also validates the relevance of Stage 1b WebTRIS time profiles as a severity-context feature — not as a frequency predictor, but as evidence that the peak/off-peak fraction of traffic matters for the severity composition of collisions.

HGV involvement and severity

Michalaki et al. (2015) find that HGV involvement strongly increases crash severity on motorways, with a coefficient of 0.336 for main carriageway and 0.757 for hard shoulder crashes. The hard shoulder result is notably larger — a collision involving an HGV on the hard shoulder has a fatal probability approximately 7.3 percentage points higher than without HGV involvement. HGV proportion from AADF is already a candidate Stage 2 feature in Open Road Risk; this paper provides direct severity evidence supporting its inclusion, while noting that HGV proportion on a link (derivable from AADF) is not the same as HGV involvement in a specific crash (a post-event STATS19 variable).

Ma et al. (2019) find motorcycle and pedestrian involvement are the second and third strongest conditional fatality predictors in their Los Angeles dataset. Fatality rates are approximately 3.5× higher for motorcycle-involved crashes and 7× higher for pedestrian-involved crashes relative to baseline. These are again crash-level variables and cannot be used in a prospective frequency model, but they support the rationale for separate vulnerable-road-user analysis.

Hard shoulder vs. main carriageway

Michalaki et al. (2015) provide a concrete example of how severity structure differs within a single road class. Hard shoulder crashes represent approximately 1.6% of M25 injury collisions but have a fatal share of 8.4% compared to 1.8% on the main carriageway — roughly five times higher. The factors driving this difference include HGV involvement, driver fatigue, and absence of daylight, all of which are more prevalent on the hard shoulder.

For Open Road Risk, this reinforces the general principle that facility type matters for severity composition. A link-year model pooling all motorway crashes will systematically underestimate severity on links with high hard-shoulder crash exposure.

Casualties per collision

National Highways (2022) separates collision-rate comparison from casualty-rate comparison. For casualties per collision, the proposed approach avoids assuming a simple Poisson or negative binomial distribution because standard parametric count distributions fitted poorly in their development work. This is relevant if Open Road Risk ever moves from collision frequency to casualty-weighted outcomes: casualty severity should be treated as an additional outcome layer or diagnostic, not folded into the current frequency target by assuming a standard count distribution at link-year scale.

Lighting

Ma et al. (2019) find lighting condition is a top-8 fatality predictor in their XGBoost classifier. Crashes in dark conditions without functioning street lights have fatality rates approximately 3× those of daytime crashes. OSM lighting data is already a candidate feature in Open Road Risk with noted sparse coverage; this finding supports prioritising its inclusion where coverage allows, while treating it as a road-environment descriptor rather than a crash-time observation.

When severity levels should be modelled jointly

Boulieri et al. (2016) fit a Bayesian multivariate model to ward-level England STATS19 data (2005–2013), modelling slight and severe/fatal crash counts jointly under a correlated MCAR prior structure. They find:

The multivariate model (MBYM) has a DIC approximately 135,000 units lower than independent univariate models — a very large improvement — driven by the spatial cross-severity correlation (ρ_total ≈ 0.74).
Approximately 60–65% of spatial variability in crash rates is spatially structured rather than unstructured heterogeneity, even after controlling for traffic-volume exposure.
Bayesian spatial smoothing substantially reorders hotspot rankings for high-severity (rare) outcomes — 0.26% of top-100 areas shifted by more than 15 rank positions — but has little effect on the more common slight injury rankings.
Severe and slight crashes follow different temporal trends: near-linear decline for slight injuries, but a flatter trend for severe/fatal after 2010.

The practical implication for Open Road Risk is not to replicate the full MBYM at 2.17M links — the paper’s OpenBUGS models ran for 20–27 hours at 7,932 wards, and MCMC at link scale is computationally infeasible. The implication is that severity levels are correlated but distinct, and that hotspot rankings based on rare (KSI) counts alone are substantially changed by smoothing. A crude KSI rate ranking will be particularly unstable and should not be used without some form of shrinkage or smoothing. The EB shrinkage diagnostic variant already in Open Road Risk addresses this problem for total collisions; extending it to the KSI sub-band is a logical next step.

Gilardi et al. (2022) reach a compatible finding on OS road segments in Leeds: the spatial correlation between severe and slight crash random effects is ρ_φ ≈ 0.83–0.90 and ρ_θ ≈ 0.40, suggesting that the spatial patterns of the two severity levels are strongly co-located but not identical. Their multivariate model substantially improves estimation of severe crash rates (balanced accuracy 0.675 for severe vs. 0.631 without cross-severity correlation) by borrowing strength from the more common slight crash pattern.

Both papers support the same directional conclusion: modelling slight and severe/KSI separately without accounting for their correlation loses information, and small-count severity bands (KSI, fatal) need either multi-level borrowing of strength or EB shrinkage to produce stable rankings.

Note

Gao et al. (2024) use a severity-weighted composite response variable y = Σ(collision_count × severity_weight) with weights 1/2/3 for minor/serious/fatal. This approach conflates frequency and severity into a single score. It is documented here as a design choice to avoid: the composite score cannot separate exposure-driven collision frequency from severity-driven injury burden, and the numeric weights (1/2/3) are arbitrary rather than estimated. Open Road Risk’s current approach — modelling total injury frequency, with severity as a future separate layer — is more principled than this composite.

Ordered response models for severity

When a severity model is eventually added to Open Road Risk, the ordered structure of the outcome (slight < serious < fatal) is a methodological constraint on model choice.

Both Quddus et al. (2010) and Michalaki et al. (2015) use ordered logit as the starting point and then find that the proportional-odds assumption is violated — different variables have different effects at different severity thresholds. Both papers use partially constrained generalized ordered logit (PC-GOLOGIT), which relaxes the proportional-odds constraint for the variables that violate it while retaining it for the rest.

The practical lesson: do not default to simple ordered logit without testing the Brant test for proportional odds. If violated, PC-GOLOGIT is the appropriate response. Quddus et al. also find that random effects at the intersection/group level were not significant in this motorway case study (ICC too low to justify multilevel structure) — spatial clustering of severity, at least at county level, is weak once motorway-type is controlled.

Post-event variables: a catalogue for Open Road Risk

The table below compiles the post-event variables that appear across these papers. All are valid in conditional severity models; none should enter Stage 2 as production features.

Variable	Paper	Role in severity model	Leakage risk for Stage 2
Contributory factor codes	Michalaki 2015; Quddus 2010	Strong severity predictors; police judgement on cause	High — recorded post-crash; subjective
Single-vehicle crash flag	Quddus 2010; Ma 2019	Positive fatality predictor	High — post-event by definition
Number of vehicles / parties	Quddus 2010; Ma 2019	Associated with severity	High — crash property
Number of casualties	Quddus 2010	Heteroskedasticity source	High — outcome-adjacent
Road surface condition at crash	Quddus 2010; Michalaki 2015	Wet surface → lower severity (speed effect)	High — observed at crash time
Lighting condition at crash time	Quddus 2010; Michalaki 2015; Ma 2019	Darkness → higher severity	Medium — can be partially pre-event (OSM infrastructure lighting) or post-event (crash-time condition)
Crash type / manoeuvre	Ma 2019	Rear-end vs. angle vs. head-on patterns	High — describes crash geometry
Pedestrian / motorcycle involvement	Ma 2019; Michalaki 2015	Strong fatality predictors	High — crash property
ETOH / alcohol flag	Ma 2019	Strongest fatality predictor in LA dataset	High — STATS19 police assessment at crash

Note on lighting: OSM lit=yes/no is a road-infrastructure attribute that is known before any crash and is not post-event. STATS19 lighting condition at crash time (Light Conditions field) is an observation at the crash moment and is post-event. These are different variables and should not be conflated.

KSI vs slight: different predictor sets

Wang, Quddus and Ison (2011; LIT-059) fit separate Bayesian Poisson models for KSI (fatal + serious combined) and slight injury crash counts on 70 M25 motorway segments. Their results show that the number of lanes is significant for slight injury crashes but not for KSI, while gradient is consistently significant for both. This provides direct empirical evidence that KSI and slight injury crashes have different predictor structures — fitting a single combined model conflates these into one coefficient set that may misrepresent both. For Open Road Risk, this supports the case for separate KSI and slight models as a diagnostic step, while noting that KSI counts at link-year level will be very sparse and require EB shrinkage or Bayesian smoothing before the rankings are reliable.

Note

For a consolidated view of how the findings on this page map to the current pipeline state, open gaps, and recommended diagnostic actions, see the Literature–Pipeline Alignment page.

References

ID	Citation
LIT-005	Boulieri, A., Liverani, S., de Hoogh, K. & Blangiardo, M. (2016). A space-time multivariate Bayesian model to analyse road traffic accidents by severity. Journal of the Royal Statistical Society Series A, 179(2), 535–553.
LIT-034	Gao, X. et al. (2024). Uncertainty-aware probabilistic graph neural networks for road-level traffic crash prediction. arXiv:2309.05072v4.
LIT-012/013/014	Gilardi, A., Mateu, J., Borgoni, R. & Lovelace, R. (2022). Multivariate hierarchical analysis of car crashes data considering a spatial network lattice. JRSS-A, 185(3), 1150–1177. DOI: 10.1111/rssa.12823
LIT-020	Ma, J. et al. (2019). Analyzing the leading causes of traffic fatalities using XGBoost and grid-based analysis. IEEE Access, 7, 148057–148071. DOI: 10.1109/ACCESS.2019.2946401
LIT-022/023	Michalaki, P., Quddus, M.A., Pitfield, D. & Huetson, A. (2015). Exploring the factors affecting motorway accident severity in England using the generalised ordered logistic regression model. Journal of Safety Research, 55, 89–96. DOI: 10.1016/j.jsr.2015.09.004
LIT-027/039	Quddus, M.A., Wang, C. & Ison, S.G. (2010). Road traffic congestion and crash severity: an econometric analysis using ordered response models. Journal of Transportation Engineering, 136(5), 424–435. DOI: 10.1061/(ASCE)TE.1943-5436.0000044
LIT-058	Department for Transport (2025). Reported Road Casualties Great Britain, Annual Report: 2024. Accredited Official Statistics.
LIT-057	Department for Transport (2025). Guide to road safety and contributory factors for reported road casualties Great Britain.
LIT-055	National Highways (2022). Statistical methods for comparing road traffic collision and casualty rates: proposed approach. National Highways PR81/22.
LIT-053	Savolainen, P.T., Mannering, F.L., Lord, D. & Quddus, M.A. (2011). The statistical analysis of highway crash-injury severities: a review and assessment of methodological alternatives. Accident Analysis and Prevention, 43(5), 1666–1676. DOI: 10.1016/j.aap.2011.03.025
LIT-059	Wang, C., Quddus, M.A. & Ison, S.G. (2011). Predicting accident frequency at their severity levels and its application in site ranking using a two-stage mixed multivariate model. Accident Analysis and Prevention, 43(6), 1979–1990. DOI: 10.1016/j.aap.2011.05.016