Concept Architecture
Concept
Theoretically, Stratified Sampling is a probability sampling technique in which a population is divided into mutually exclusive and collectively exhaustive subgroups, known as strata, before sampling is performed independently within each stratum. It is designed to improve sampling efficiency and estimation precision by ensuring that important population subgroups are adequately represented. In health economics, stratified sampling is used in survey design, clinical studies, simulation methods and probabilistic sensitivity analysis to reduce sampling variability.
Mathematically, stratified sampling estimates population characteristics by combining weighted estimates from individual strata. Sampling may be proportional to stratum size or based on alternative allocation strategies such as optimal allocation. The overall estimator incorporates contributions from all strata, while the variance of the estimator depends on the within-stratum variances and sampling fractions.
In practice, stratified sampling is implemented by defining relevant strata, such as age groups, disease severity or treatment categories, and drawing independent samples from each subgroup. The method is routinely applied in health surveys, economic evaluations, epidemiological studies and simulation methods, including Latin Hypercube Sampling, where probability distributions are divided into equal-probability strata to improve computational efficiency.
Purpose
Used to improve sampling efficiency and estimation precision by ensuring appropriate representation of predefined population subgroups or probability strata in health economic analyses.
Mathematical Formulae
Primary Formula
Population mean:
x??? = ?W?x??
where:
W? = N? / N
N? = size of stratum h
N = total population size
x?? = sample mean within stratum h
Supporting Formulae
Population variance:
Var(x???) = ?W?� ? ((1 ? f?)S?� / n?)
where:
f? = n? / N?
S?� = variance within stratum h
n? = sample size in stratum h
Related Mathematical Methods
- Simple Random Sampling
- Latin Hypercube Sampling
- Monte Carlo Simulation
- Probability Sampling
- Survey Sampling
- Variance Reduction Techniques
Example
A national health utility survey divides patients into four age groups before sampling. Separate random samples are drawn from each stratum in proportion to the number of patients in each age group. The weighted estimates from the four strata are combined to estimate the overall population mean utility, ensuring that all age groups are appropriately represented.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| SUMPRODUCT | =SUMPRODUCT(WeightRange,MeanRange) | Calculate weighted estimates across strata. |
| COUNTIFS | =COUNTIFS(StratumRange,A2) | Determine the number of observations within each stratum. |
| AVERAGEIFS | =AVERAGEIFS(ValueRange,StratumRange,A2) | Calculate stratum-specific means. |
| VAR.S | =VAR.S(StratumValues) | Estimate within-stratum variance. |
VBA (Optional)
VBA can automate stratified sampling, generate proportional or optimal samples within each stratum and calculate weighted population estimates for health economic analyses.
Sources
- Cochran WG. Sampling Techniques. John Wiley & Sons.
- Lohr SL. Sampling: Design and Analysis. Chapman & Hall/CRC.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
- NICE. NICE Health Technology Evaluations: The Manual.
Related Concepts (4)
Library
Publications
1
Statistical Analysis of Cost-Effectiveness Data — Willan & Briggs, 1st Edition ed., 2006 (John Wiley & Sons)
A synthesis of statistical methods for analysing cost-effectiveness data, including net-benefit regression, confidence intervals for the ICER, cost-effectiveness acceptability curves, and covariate adjustment. Part of the Wiley Statistics in Practice series.
BookView source →
Frequently Asked Questions (6)
What is stratified sampling?
A sampling technique dividing a population into distinct subgroups, called strata, and drawing a separate sample from each to ensure adequate representation.
Source: Neyman 1934
Why divide a population into strata before sampling?
Sampling a whole population at random can, by chance, over-represent some subgroups and miss others, especially small but important ones. Stratified sampling divides the population into strata and draws from each separately, guaranteeing that every subgroup is represented in proportion to a chosen scheme rather than left to chance. This ensures adequate coverage of each stratum and, because it removes the between-stratum variation from the sampling error, yields a more precise overall estimate. It controls what random sampling leaves to luck. Law (2015) describes this technique.
Source: Law 2015
How does stratified sampling work?
Stratified sampling works by partitioning the population into strata defined by a characteristic, then drawing a sample from each stratum, often independently, and combining the results with appropriate weights reflecting each stratum's size. The allocation of the sample across strata can be proportional to their sizes or, for greater efficiency, chosen to give more samples to more variable strata, as in Neyman allocation. Sampling within each stratum ensures all subgroups are represented, and combining the stratum estimates gives an overall estimate that accounts for the strata.
Source: Neyman 1934
Why is stratified sampling used?
Stratified sampling is used to ensure that all subgroups of a population are adequately represented and to improve the precision of estimates when the subgroups differ from one another. By sampling within each stratum, it avoids the risk that random sampling might under-represent small but important subgroups, and by removing between-stratum variation from the sampling error, it can give more precise overall estimates than simple random sampling for the same sample size. So it is chosen where subgroup representation or improved precision from stratification is valuable.
Source: Law & Kelton 2000
How does stratified sampling improve precision?
Stratified sampling improves precision by ensuring each stratum is sampled, so the overall estimate's error depends on the variability within strata rather than the larger variability across the whole population, removing the between-stratum differences from the sampling error. When strata are internally more homogeneous than the population as a whole, this reduces the variance of the estimate for a given sample size. Allocating more of the sample to more variable strata, as in Neyman allocation, further improves precision, making stratified sampling more efficient than simple random sampling in such cases.
Source: Neyman 1934
What are the limitations of stratified sampling?
Stratified sampling requires that the strata can be defined and that each unit's stratum is known before sampling, which needs suitable information about the population, and it is more complex to design and analyse than simple random sampling, with the weighting and allocation to arrange. Its precision gains depend on the strata being meaningfully different; poorly chosen strata add complexity for little benefit. These limitations mean stratified sampling is used where the population has identifiable, relevant subgroups and the information to define them is available.
Source: Neyman 1934
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 29 Oct 2025
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