Concept Architecture
Concept
Theoretically, Standardised Mortality Ratio Application is the application of the Standardised Mortality Ratio (SMR) to adjust mortality estimates by comparing observed deaths within a study population with the number of deaths expected on the basis of age-, sex- or population-specific mortality rates from a reference population. The approach exists to quantify relative mortality and to calibrate survival estimates when direct mortality observations are incomplete or when extrapolating long-term survival. In health economics, SMRs are frequently applied to estimate excess mortality associated with disease or to adjust general population life tables within decision models.
Mathematically, SMR application involves calculating the ratio of observed to expected deaths and applying this ratio to baseline mortality hazards derived from a reference population. An SMR greater than one indicates excess mortality relative to the general population, whereas an SMR below one indicates lower mortality. The adjusted mortality hazard can subsequently be incorporated into survival models and state-transition models.
In practice, SMRs are estimated from registry data, observational studies or clinical trial follow-up and are commonly used in health technology assessment to extrapolate long-term survival beyond observed data. Health economic models frequently combine national life tables with disease-specific SMRs to estimate mortality among patients after treatment or disease remission.
Purpose
Used to adjust population mortality rates for disease-specific excess mortality, enabling long-term survival estimation and mortality extrapolation in health economic models and health technology assessments.
Mathematical Formulae
Primary Formula
SMR = O / E
where:
- O = observed deaths
- E = expected deaths
Supporting Formulae
Expected deaths:
E = ?(PY? ? m?)
where:
- PY? = person-years within stratum i
- m? = reference mortality rate for stratum i
Adjusted mortality hazard:
h?(t) = SMR ? h?(t)
where:
- h?(t) = general population mortality hazard
Related Mathematical Methods
- Standardised Mortality Ratio
- Indirect Standardisation
- Life Table Analysis
- Relative Survival Analysis
- Survival Extrapolation
- Excess Mortality Modelling
Example
A health economic model evaluates long-term survival following treatment for chronic heart failure.
Observed deaths during follow-up:
O = 45
Expected deaths based on national life tables:
E = 30
Standardised Mortality Ratio:
SMR = 45 � 30 = 1.50
If the annual general population mortality hazard at a given age is 0.040, the adjusted hazard incorporated into the model is:
h?(t) = 1.50 ? 0.040 = 0.060
This represents a 50% higher mortality risk than that of the age- and sex-matched general population.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| SUMPRODUCT | =SUMPRODUCT(PersonYears,MortalityRates) | Calculate expected deaths from life tables |
| SUM | =SUM(ObservedDeaths) | Calculate total observed deaths |
| IFERROR | =IFERROR(B2/C2,"") | Calculate the Standardised Mortality Ratio |
| INDEX | =INDEX(LifeTable,MATCH(Age,Ages,0)) | Retrieve age-specific mortality rates |
| XLOOKUP | =XLOOKUP(Age,AgeRange,MortalityRate) | Apply reference mortality rates for survival modelling |
VBA (Optional)
A VBA procedure can automatically merge life-table mortality rates with patient cohorts, calculate Standardised Mortality Ratios and generate adjusted mortality hazards for health economic models.
Sources
- Dickman PW, Adami HO. Interpreting Trends in Cancer Patient Survival.
- Pohar Perme M, Stare J, Est�ve J. On Estimation in Relative Survival. Biometrics. 2012.
- NICE. Health Technology Evaluation Manual.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
- ISPOR-SMDM Modeling Good Research Practices Task Force Reports.
Related Concepts (2)
Library
Publications
1
NICE DSU Technical Support Document 21: Flexible methods for survival analysis — Rutherford, Lambert, Sweeting, Pennington, Crowther, Abrams & Latimer, TSD 21 ed., 2020 (NICE Decision Support Unit (University of Sheffield))
Guidance extending standard survival analysis to flexible parametric methods — spline-based models, fractional polynomials, mixture and cure models, and relative-survival approaches — for capturing complex hazard functions in economic evaluation.
Frequently Asked Questions (6)
How is the standardised mortality ratio applied in a model?
The use of a standardised mortality ratio to adjust survival estimates for background mortality within a health economic model.
Source: Ederer, Axtell & Cutler 1961
Why might a patient group's background mortality exceed the general population's?
Patients with a chronic condition often face a higher risk of death from other causes than the general population, because of shared risk factors, comorbidity, or the frailty that accompanies illness. A standardised mortality ratio captures this by expressing their all-cause mortality as a multiple of the rate expected in the general population. Applying that multiple to population life tables within a model raises the background mortality to a level appropriate for the patients, rather than assuming they die of other causes at the general rate. It corrects an otherwise optimistic background. Latimer (2013) describes applying an SMR to background mortality.
Source: Latimer 2013
What is a standardised mortality ratio?
A standardised mortality ratio is the ratio of the number of deaths observed in a population to the number expected if that population experienced the general population's age- and sex-specific mortality rates. An SMR above one indicates higher mortality than the general population, and below one lower mortality. It summarises the relative mortality of a group in a single figure, adjusting for its age and sex structure through the expected deaths, and it is used to quantify excess or reduced mortality relative to a standard.
Source: Chiang 1984
Why apply a standardised mortality ratio in modelling?
An SMR is applied in modelling to represent the mortality of a patient population whose death rates differ from the general population's, when direct mortality data are limited but an SMR is available. Multiplying general population rates by the SMR gives the population's mortality, capturing its elevated or reduced risk while retaining the age pattern of the life tables. This provides a convenient way to incorporate a group's relative mortality into a model using established background rates scaled by the ratio.
Source: Ederer, Axtell & Cutler 1961
How does the standardised mortality ratio adjust background mortality?
The standardised mortality ratio adjusts background mortality by scaling the general population's age- and sex-specific rates by the ratio, so that a population with an SMR of, say, two faces twice the general mortality at each age. This preserves the shape of age-related mortality while raising or lowering its level to match the population's observed relative mortality. Applying the SMR thus produces mortality rates for the modelled population that reflect both the general age pattern and the group's excess or reduced risk.
Source: Ederer, Axtell & Cutler 1961
What are the limitations of applying a standardised mortality ratio?
Applying an SMR assumes that the population's mortality is a constant multiple of the general population's across ages, which may not hold if the relative risk varies with age, and it depends on the SMR being accurate and applicable to the modelled population. Using a single SMR can oversimplify a complex mortality pattern. The approach also inherits the general population rates' assumptions. These limitations mean the SMR's suitability and constancy across ages are considered, and its influence on results may be examined.
Source: Chiang 1984
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 23 Oct 2025
Content version: 1.0.0
Canonical Identity
- Term code
- HE-EM-SM-081
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