Survey-weighted and small-area estimation
Household survey data are analysed with their sampling design, and small-area models borrow strength across districts to estimate subnational coverage, with credible intervals mapped beside the estimates.
GCRI · Health Nexus
Statistics for health evidence
Probability and statistics turn incomplete, delayed and biased health data into estimates with stated uncertainty. In this field they handle survey sampling, small numbers, under-reporting and shifting baselines, so that every indicator carries a range and the assumptions behind it rather than a single, overconfident number.
01Contents
Statistics for health evidence in five parts.
02Application
What probability and statistics does here.
Probability and statistics provide the mathematical framework for describing uncertainty and learning from data. They underpin estimation, testing and prediction in every risk discipline. In health and biosecurity, statistical methods quantify the likelihood and uncertainty of losses across interconnected systems. They make the evidence behind risk decisions explicit and reproducible. The canonical description is on the STEM Commons.
Expected baselines for excess mortality
Models fitted to past mortality with trend and seasonality give the expected count against which observed deaths are compared, and the baseline’s uncertainty is carried into the excess.
Correcting for under-ascertainment
Capture-recapture, serosurveys and multiplier methods estimate how many infections surveillance misses, so case counts are read against what they are likely to represent.
03Monitor
Tail fit.
The screen a team would use to follow this method: its measures, states and decisions. Names are examples and values are illustrative.
Tail fit
Health · Statistics for health evidence · Run R-6555
Shape parameter uncertainGCRI · Health Nexus
Return level curve
Method card
- Method
- Probability and statistics
- Approach
- peaks over threshold
- Threshold
- 97th percentile
- Label
- MODELLED
Parameters
generalised Pareto fit
| Shape ξ | 0.28 | −0.04 | 0.48 | heavy tail if above zero |
| Scale σ | 2.3 | 1.0 | 7.5 | units of the variable |
| Exceedances | 136 | declustered |
04Data
What the method consumes.
Datasets and records used by probability and statistics on this platform, with the role each plays and the label its values carry. Sources are listed in the source register.
| Data | Role | Label |
|---|---|---|
| DHS and MICS microdata | Design-based and model-based estimation | ESTIMATED |
| Vital registration series | Baseline modelling | Published statistics |
| Serosurveys | Calibration of ascertainment | OBSERVED |
| Routine reporting with completeness metadata | Adjustment for missing reports | REPORTED |
05Sector signature
The sector signature of statistics for health evidence.
The sectors statistics for health evidence touches and how strongly they depend on each other: what a study has to observe and model together.
Select corners · hover lines6 / 15 relations
Signature
Health and its partners
Health gives workforce for operations to infrastructure (0.3), farm labour to food (0.3) and utility workforce to water (0.2).
W · E · I · F · H · B
- Sectors
- 4 of 6
- Relations
- 6 of 15
- Coupling
- 0.42 share of total
Strongest relations in play
- Water → Food · irrigation0.8
- Food → Health · nutrition0.7
- Infrastructure → Water · pipes, dams and treatment works0.6
- Water → Health · drinking water and sanitation0.7
06Validation
How results are checked.
Results are checked through diagnostics, cross-validation and sensitivity to assumptions. Independent replication confirms findings.
| Check | How it is done |
|---|---|
| Design-based variance | Standard errors account for clustering, stratification and survey weights |
| Posterior predictive checks | Models must reproduce the observed data before they are used to estimate or predict |
| Sensitivity to priors and baselines | Results are recomputed under alternative assumptions and the spread is reported |
Inference depends on assumptions about independence, distribution and sampling that may not hold. Small or biased samples limit reliability.
07Methods and evidence
How statistics for health evidence is modelled, measured and tested.
The model, its assumptions, its data and its uncertainty, in the form a scientist or engineer would check. Structures follow published methods. The values drawn are illustrative, not findings.
Model, equations and assumptions
The model structure used for statistics for health evidence, the assumptions it makes and how each is tested.
Risk of element i
Ri = f(Hi, Ei, Vi, Ci)hazard, exposure, vulnerability and coping capacityExpected annual loss
EAL = ∑k pk · Lkover events k with annual probability pkCoupled systems
xt+1 = A xt + B ut + εtA carries the couplings, u the shock, ε the error| Assumption | Why it is made | How it is tested |
|---|---|---|
| Hazard and exposure are independent within an event | Keeps the loss integral tractable | Compare with a copula fit on joint records |
| Couplings are linear near the operating point | Lets shocks propagate through A | Perturb beyond the linear range and compare |
| Vulnerability curves transfer between places | Local curves are rarely available | Validate against observed losses where they exist |
- Inputs
- versioned datasets with provenance
- Outputs
- distributions, never single numbers
- Code
- released with the model card and tests
- Reproduction
- same data, code, environment and seed
FAIR guiding principles · GO FAIR and FORCE11W3C PROV · World Wide Web ConsortiumGuidance on consistent treatment of uncertainties · IPCCCEOS Analysis Ready Data · Committee on Earth Observation Satellites
08Connections
Topics that rely on this method.
09Process
How the process runs.
Process
Statistics for health evidence: Catastrophe model pipeline
Catastrophe models usually have hazard, vulnerability, exposure and financial modules, and produce loss tables, average annual loss, exceedance curves, PML and TVaR.
01 Hazard
- 01Event catalogueDataset · Model developerThe hazard module holds a large catalogue of simulated events that represents a wide range of plausible scenarios.
- 03Hazard moduleModel · Model developerFor each event the hazard module gives the local hazard intensity that the vulnerability module reads.
02 Exposure and damage
- 02ExposureDataset · Referral hospitalThe exposure module houses the portfolio data, such as location-specific information.
- 04Vulnerability moduleModel · Model developerThe vulnerability module quantifies the expected damage to the exposures from an event.
03 Financial
- 05Financial moduleModel · Referral hospitalThe financial module calculates losses from all event scenarios. Ground-up, gross and net losses differ as shown below.
- 06Event loss tableDataset · Referral hospitalAn event loss table lists each event with its annual occurrence probability and its loss for the portfolio.
- 07Year loss tableDataset · Referral hospitalSome models also sample simulated years from event losses. This outline does not describe their format.
04 Metrics
- 08Exceedance probability curvesModel · Referral hospitalThe occurrence curve gives the chance that the largest loss in a year exceeds an amount. The aggregate curve does so for the sum of losses.
- 09AAL, PML and TVaRModel · Referral hospitalAverage annual loss sums event probability times loss. PML is one point on the occurrence curve.
05 Use of results
- 10Use of resultsDecision · Referral hospitalThe tail metrics are used when considering a portfolio’s exposure and the level of catastrophe reinsurance an insurer requires.
Outline of an external standard or method, from its public sources. It describes what the framework says, not a record of any run. It does not show that Nexus or any partner performs, certifies or approves a step. A gate is a step of the method, never a Nexus approval.
10Stewardship
Who maintains the method.
Systems Science and Modelling stewards probability and statistics for the Consortium and reviews how it is applied across platforms.
11Connected
Where this page leads across the Consortium.
12Questions
Questions and answers.
What are the limits of probability and statistics in this field?
Inference depends on assumptions about independence, distribution and sampling that may not hold. Small or biased samples limit reliability.
How are results checked?
Results are checked through diagnostics, cross-validation and sensitivity to assumptions. Independent replication confirms findings.
Are the values on this page real?
The data names, roles and checks are real descriptions of practice. The canvas shows a design of the method’s use, not a run; no result is reported here.
Where else is this method applied?
The canonical method page lists every platform that applies it.
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