Multivariate severity assessment and humane endpoint prediction for laboratory animal studies using the RELSA (RELative Severity Assessment) score and ARIMA-based foRcast forecasting. Use when combining welfare readouts — body weight or weight loss, body temperature, clinical or nesting scores, biomarkers, activity, heart rate, burrowing, wheel running — into one severity score per animal per day, when asking which animals are at risk of reaching a humane endpoint or when one will be reached, when defining attention/danger zones or thresholds on a severity scale by kernel density estimation, or when reporting severity for a 3Rs, refinement, animal-welfare, or EU Directive 2010/63/EU severity-assessment context. Covers directionality ("turned" variables), baseline normalization, reference sets, RELSA weights, ARIMA prediction intervals, and RMSE/PICP/MPIW evaluation.
Multivariate severity assessment and humane endpoint prediction for laboratory animal studies using the RELSA (RELative Severity Assessment) score and ARIMA-based foRcast forecasting. Use when combining welfare readouts — body weight or weight loss, body temperature, clinical or nesting scores, biomarkers, activity, heart rate, burrowing, wheel running — into one severity score per animal per day, when asking which animals are at risk of reaching a humane endpoint or when one will be reached, when defining attention/danger zones or thresholds on a severity scale by kernel density estimation, or when reporting severity for a 3Rs, refinement, animal-welfare, or EU Directive 2010/63/EU severity-assessment context. Covers directionality ("turned" variables), baseline normalization, reference sets, RELSA weights, ARIMA prediction intervals, and RMSE/PICP/MPIW evaluation.
license
MIT
allowed-tools
Read Write Edit Bash
compatibility
Requires Python >=3.10 with numpy, pandas, and scipy; statsmodels >=0.14 for forecasting and matplotlib for figures. Tested with numpy 2.5, pandas 3.0, scipy 1.18, statsmodels 0.14.6. No network access needed.
metadata
{"version":"1.0","skill-author":"K-Dense Inc."}
RELSA severity assessment and humane endpoint forecasting
Overview
Severity assessment in animal research is legally mandatory and scientifically load-bearing:
it drives humane endpoint decisions, and poor welfare monitoring degrades reproducibility.
The usual practice evaluates each readout in isolation — weight loss here, a clinical score
there — which makes it hard to say how badly an individual animal is actually doing.
This skill implements two published procedures that address that:
RELSA (Talbot et al., 2022) combines several outcome measures into one score per animal
per time point, expressed relative to a reference set of known burden. RELSA = 0 is
baseline; RELSA = 1 means the animal has reached the reference set's maximum deviation.
foRcast (Lutscher et al., 2026) fits an ARIMA model to an individual animal's RELSA
trajectory and forecasts the next score with a 95% prediction interval, so animals heading
for a humane endpoint can be identified before they get there. Kernel density estimation on
the RELSA scale supplies candidate attention and danger zones for interpretation.
The point is refinement: give at-risk animals attention earlier, and avoid euthanising
animals that would have recovered. Both procedures are aids to severity assessment, not
decision rules — see Boundaries.
When to use this skill
Combining weight loss, temperature, clinical scoring, biomarkers, or telemetry into a single
per-animal severity score
Asking which animals in a cohort are at risk of reaching a humane endpoint, or predicting
the severity score at a coming time point
Comparing severity between treatment groups, interventions, or animal models on a common
relative scale
Defining thresholds or zones on a severity scale from the data
Writing the severity-assessment section of an animal welfare report, a 3Rs/refinement
analysis, or an application under EU Directive 2010/63/EU
For general forecasting of a time series that is not a severity score, use
timesfm-forecasting or statsmodels. For study design and sample size, use
experimental-design and statistical-power.
relsa_score.py and kde_thresholds.py need only numpy/pandas/scipy; statsmodels is required
for forecasting and matplotlib only for figures.
Data format
One row per animal per time point, in a CSV:
id
treatment
condition
day
temp
weight
score
il6
M01
treated
endpoint
-1
37.15
25.17
0
35.1
M01
treated
endpoint
0
37.26
25.25
0
39.5
M01
treated
endpoint
1
35.83
23.12
4
162.0
id and a time column (day, time, hour, …) are required; treatment and condition
are optional labels used for grouping and for selecting the reference set.
Time may be days, hours, or minutes — just keep it monotonic per animal. The RELSA
convention codes the baseline time point as -1.
One row per animal per time point. Average hourly telemetry to one value per interval
first (the published models average heart rate, HRV, and temperature, and sum activity).
Leave missing measurements empty. They are dropped from the score, never imputed — a
missing value treated as "no deviation" biases severity downward.
assets/example_cohort.csv is a small synthetic cohort (6 mice, 9 days, temperature, body
weight, an 0–8 clinical score, and an IL-6-like biomarker) used by every command below, so
each one is runnable as written.
The four decisions that determine the result
Make these explicitly and write them into the methods. Nothing else about the procedure
matters as much.
1. Directionality — which variables rise under worsening? Falling is the default (body
weight, activity, food intake, burrowing, wheel running). Variables that rise must be
declared as --turned: clinical scores, inflammatory biomarkers, fever, tachycardia. Get
this wrong and the variable contributes nothing at all, silently, because deviations in the
"wrong" direction are floored at zero. Body temperature is model-dependent — it falls in
sepsis and endotoxaemia, rises in fever models. Nothing in the data can settle this for you:
in the published sepsis model activity legitimately swings further above baseline than below,
so only a variable that never once moves the declared way is detectable, and
build_reference() warns about exactly that case.
2. The reference set — relative to what? RELSA scores mean nothing without it. Use the
group assumed to carry the greatest burden in your model (the published studies use the
highest-dose or endpoint-reaching treatment group). Too mild a reference pushes every score
above 1; too severe compresses everything toward 0. Save it with --save-reference and reuse
it with --load-reference so later cohorts stay on the same scale.
3. Scores with a zero baseline. A clinical score of 0 in a healthy animal cannot be
ratio-normalized — 0/0 is undefined. Use --score-scale score=8 to map the score's scale
instead (healthy → 100%, worst possible → 200%), which also marks it as turned. This mapping
is a modelling choice about how much one score point is worth relative to one percent of body
weight; state it. The alternative is to keep the score out of RELSA and use it as an
independent endpoint criterion.
4. Which variables are measured throughout. Because the score averages over whichever
variables are available, a variable that appears or disappears mid-trajectory moves the score
by itself. In the published sepsis data, adding body weight — recorded only on the day of
euthanasia — drops that animal's endpoint score from 0.93 to 0.83 for no biological reason.
relsa_scores() warns when composition changes; score the variables present throughout.
The reference model is echoed so the scale is auditable:
reference model: assets/example_cohort.csv [condition=endpoint]
animals=2 rows=18 baseline_time=-1.0
variable turned max reached max delta
weight no 82.40 17.60
temp no 92.79 7.21
score yes 187.50 87.50
il6 yes 797.72 697.72
relsa_scores.csv holds each variable's weight alongside the score, which is what makes a
score explainable — here M01 deteriorating to its endpoint, M03 peaking on day 3 and
recovering:
id time predicted lower upper model actual
M01 5.0 0.932585 0.670443 1.194728 ARIMA(1,1,0) 1.00
M02 6.0 0.955696 0.748309 1.163084 ARIMA(1,1,0) 0.94
group id model n rmse picp mpiw
endpoint M01 ARIMA(1,1,0) 1 0.0674 100.0 0.524
endpoint M02 ARIMA(1,1,0) 1 0.0157 100.0 0.415
endpoint -- endpoint -- 2 0.0489 100.0 0.470
OVERALL 2 0.0489 100.0 0.470
Report all three metrics together. RMSE is point accuracy, PICP the percentage of
actual values inside the interval, and MPIW the mean interval width in RELSA units — a
model can reach PICP = 100% by making the interval so wide it says nothing, which is exactly
what the paper's pancreatic cancer row (PICP 100%, MPIW 7.35, i.e. 735% of the RELSA range)
shows.
For live monitoring, forecast one step ahead at every time point instead:
python scripts/forecast_relsa.py relsa_scores.csv --mode rolling --animals M03
Two things to know before trusting a forecast:
Interpolation is on by default (--interpolate-step 0.1), because one measurement per
day is far too sparse for ARIMA. It buys usable model selection and narrower intervals at
the cost of honest uncertainty. Set --interpolate-step 0 when measurement frequency
allows.
ARIMA cannot predict a cliff. It assumes stationarity and linearity, so an abrupt
collapse in the last hours before an endpoint will not be forecast from a smooth prior
trajectory — the paper's own failure case. Act on the upper bound of the interval, and
never let a low forecast override an animal that looks unwell.
Step 3 — put the score in context with severity zones
KDE on 33 RELSA scores (bandwidth = 0.1502)
candidate thresholds (density minima): 0.703
density modes: 0.264, 0.866
normal [0.000, 0.703) n=25 (75.8%)
danger >= 0.703 n=8 (24.2%)
Thresholds are the minima of the score density — the sparse valleys between clusters of
scores. Include endpoint animals, survivors, and shams: the zones are meant to separate
those states, so all of them must be represented.
Check the bandwidth before believing a threshold. On the published sepsis data this
implementation finds minima at 0.355 and 0.655 (published: 0.337 and 0.643) — but a 10%
larger bandwidth removes both minima entirely. Run the sweep in
references/thresholds-and-zones.md and report the sweep, not a bare pair of numbers. An
empty threshold list is a legitimate answer: the scores form one cluster and there is no
data-driven place to cut.
Boundaries: state these when you report
RELSA is an aid to severity assessment, not a decisive parameter. An animal with a low
RELSA score that shows other signs of distress must still be handled accordingly. Neither
procedure is a validated predictor of death.
KDE zones are not regulatory severity gradings. EU Directive 2010/63/EU's categories
(non-recovery, mild, moderate, severe) are assigned prospectively by a different process.
The paper is explicit that its thresholds "should not be confused with regulatory severity
gradings" and are not directly translatable to them.
Scores are not comparable across reference sets or models. RELSA is relative by
construction, and clinical scoring is not harmonized between laboratories. Always report
the reference set with the score.
The published evidence is a proof of concept: 13 animals across seven models, five of
those rows resting on one or two animals. The overall RMSE of 0.069 and PICP of 96% come
from 13 endpoint predictions.
An underestimated score is the dangerous error, because it discourages attention and can
delay a euthanasia decision, whereas an overestimate merely prompts extra care.
Reporting checklist
A severity analysis is reproducible only if all of this is stated:
Outcome measures, their units, and their directionality (which were turned, and why).
The baseline time point or window, and which variables were normalized.
Any score mapping applied to ordinal variables, with its scale.
The reference set: which animals, which group, how many, and why they are assumed to
carry the greatest burden.
Humane endpoint criteria actually applied in the study, separately from the RELSA score.
For forecasts: interpolation step, the selected ARIMA order per animal, and RMSE, PICP,
and MPIW.
For thresholds: the bandwidth, the number of scores, and a bandwidth sensitivity sweep.
Software versions, and the statement that thresholds are model-specific and not regulatory
gradings.
Common pitfalls
Wrong directionality — a rising variable not listed in --turned contributes exactly
zero, silently, and no warning is possible unless it never once falls. Check the reference
model table yourself: max reached should be below 100 for a falling variable and above 100
for a turned one, and max delta should be a plausible size for that measure.
Normalizing a percentage twice — bwc [%] and mapped scores are already on the percent
scale; passing them to --normalize flattens them.
A zero baseline — a clinical score of 0 makes the ratio undefined; the variable becomes
all-NaN with a warning. Use --score-scale.
A reference set that does not express the burden — a variable that never deviates in it
raises an error rather than dividing by zero, and one that barely deviates inflates every
score.
Changing variable composition along a trajectory — see decision 4 above.
Reading MPIW as a good thing — a wide interval raises PICP while destroying the
forecast's usefulness.
Reporting a KDE threshold without its bandwidth — thresholds can vanish under a 10%
bandwidth change.
Treating the forecast as permission to wait — the model cannot see abrupt
deterioration, and the humane endpoint criteria of the protocol always take precedence.
Comparing RELSA scores between models — only valid within one reference frame.
Resources
Scripts
scripts/relsa_score.py — the RELSA procedure: prepare(), build_reference(),
relsa_scores(), relsa_weights(), and a ReferenceModel that serialises to JSON.
Reproduces the R package's published worked example to two decimals.
scripts/forecast_relsa.py — the foRcast tool: auto_arima() (Hyndman–Khandakar stepwise
AICc selection), forecast_animal(), predict_endpoint(), rolling_forecast(),
forecast_indirect(), summarize(), and Figure-1-style plots.
scripts/kde_thresholds.py — severity zones: bw_nrd0() (R's bandwidth), density_curve(),
find_thresholds(), zone assignment, and Figure-3-style density plots.
scripts/_common.py — RELSA-format I/O, validation, score_to_percent(),
percent_of_baseline(), and forecast_metrics() (RMSE/PICP/MPIW).
References
references/relsa-method.md — the four steps in full, the score/zero-baseline problem, the
variable-composition trap, parity notes against the R package, and the outcome measures and
endpoint criteria of all seven published models.
references/forecasting.md — ARIMA selection, why interpolation is a distortion, direct vs
indirect prediction, the metrics, the published Table 1, and what this port reproduces.
references/thresholds-and-zones.md — KDE method, published thresholds, the bandwidth
sensitivity sweep, the regulatory boundary, and alternatives when KDE gives nothing.
Assets
assets/example_cohort.csv — synthetic 6-mouse cohort with temperature, body weight, a
clinical score, and a biomarker; illustrative only, not real data.
Related skills
experimental-design, statistical-power — designing the study and sizing the groups.
statsmodels, timesfm-forecasting — general time-series modelling.
statistical-analysis, scientific-visualization — group comparisons and figures.
Key references
Talbot, S. R. et al. (2022). RELSA — a multidimensional procedure for the comparative
assessment of well-being and the quantitative determination of severity in experimental
procedures. Front. Vet. Sci. 9:937711. R package: https://github.com/mytalbot/RELSA
Lutscher, S. et al. (2026). Refining humane endpoint detection by time-series forecasting
and threshold definition using a multivariate severity score. Front. Physiol. 17:1869563.
Hyndman, R. J. & Khandakar, Y. (2008). Automatic time series forecasting: the forecast
package for R. J. Stat. Softw. 27, 1–22.
EU Commission (2010). Directive 2010/63/EU on the protection of animals used for scientific
purposes.
