Concept Architecture
Concept
Theoretically, Latin Hypercube Sampling is a stratified sampling technique designed to improve the efficiency of Monte Carlo simulation by ensuring that the full range of each uncertain input parameter is systematically represented. It reduces sampling variability by dividing each input distribution into equally probable intervals and selecting one sample from each interval. In health economics, Latin Hypercube Sampling is widely used in probabilistic sensitivity analysis to achieve more precise estimates with fewer simulation iterations than simple random sampling.
Mathematically, Latin Hypercube Sampling partitions the cumulative distribution function of each input parameter into n equiprobable strata. One value is randomly selected from each stratum, and the sampled values are randomly combined across parameters to form simulation inputs. This sampling design provides more uniform coverage of the multidimensional parameter space while preserving the marginal distributions of individual parameters.
In practice, Latin Hypercube Sampling is implemented by specifying probability distributions for uncertain model parameters, dividing each distribution into equal probability intervals and generating stratified random samples. The method is routinely applied in decision trees, Markov models, microsimulation and probabilistic sensitivity analysis to improve computational efficiency and reduce Monte Carlo error.
Purpose
Used to improve the efficiency and precision of probabilistic sensitivity analysis by providing more uniform sampling of uncertain model parameters and reducing Monte Carlo error.
Mathematical Formulae
Primary Formula
Stratum probability:
P? = 1 / n
Sampling interval:
(i ? 1) / n � F(x?) < i / n
where:
F(x) = cumulative distribution function
i = 1, 2, ?, n
Supporting Formulae
Sample quantile:
x? = F??(u?)
where:
(i ? 1) / n � u? < i / n
Related Mathematical Methods
- Monte Carlo Simulation
- Probabilistic Sensitivity Analysis
- Stratified Sampling
- Importance Sampling
- Quasi-Monte Carlo Simulation
- Variance Reduction Techniques
Example
A probabilistic sensitivity analysis requires 1,000 simulations of treatment costs and utility values. Rather than selecting all parameter values through simple random sampling, each probability distribution is divided into 1,000 equally probable intervals. One observation is drawn from each interval and randomly paired across parameters, producing more representative coverage of the uncertainty space and reducing simulation error.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| RAND | =RAND() | Generate random values within each probability stratum. |
| PERCENTILE.INC | =PERCENTILE.INC(DataRange,Probability) | Calculate quantiles defining Latin Hypercube strata. |
| SORTBY | =SORTBY(A2:A1001,RANDARRAY(1000)) | Randomly permute sampled values before combining parameters. |
| RANK.EQ | =RANK.EQ(A2,A$2:A$1001) | Assign observations to sampling strata. |
VBA (Optional)
VBA can automate Latin Hypercube Sampling by generating stratified parameter samples and constructing multidimensional simulation input matrices.
Sources
- McKay MD, Beckman RJ, Conover WJ. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics. 1979;21(2):239?245.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
- Saltelli A, Chan K, Scott EM. Sensitivity Analysis. John Wiley & Sons.
- NICE. Health Technology Evaluation Manual.
- ISPOR-SMDM Modeling Good Research Practices Task Force Reports.
Related Concepts (5)
Library
Tools & Resources
1
SAVI — Sheffield Accelerated Value of Information — Mark Strong, Jeremy Oakley & Penny Breeze (University of Sheffield), Web application ed., 2024 (University of Sheffield)
A free, open-access web calculator that computes value-of-information measures (EVPI, partial EVPI/EVPPI and EVSI) directly from a model’s probabilistic sensitivity analysis output — no need to re-run the model. Also reports payer strategy-specific and uncertainty burden.
Web Tool (R Shiny)View source →
Frequently Asked Questions (6)
What is Latin hypercube sampling?
A sampling technique dividing each input's range into equally probable intervals and sampling each exactly once, giving more even coverage than simple random sampling.
Source: McKay, Beckman & Conover 1979
Why can simple random sampling leave gaps that Latin hypercube sampling avoids?
Simple random sampling can by chance cluster its draws and leave parts of an input's range unsampled, especially when the number of draws is limited, so some plausible values are missed. Latin hypercube sampling avoids this by dividing each input's range into equally likely intervals and ensuring exactly one draw falls in each, giving even coverage across the whole range. This more uniform spread yields a more stable estimate from fewer runs. It removes the clumping that plain random sampling can suffer. Briggs and colleagues (2006) describe it.
Source: Briggs et al. 2006
How does Latin hypercube sampling work?
Latin hypercube sampling works by dividing each input's distribution into a chosen number of equally probable intervals and drawing one value from each interval, then randomly pairing the values across inputs so that every interval of every input appears exactly once in the sample. This ensures each input is sampled evenly across its full range, avoiding the clustering and gaps that can occur with simple random sampling. The result is a set of input combinations that covers the space more uniformly for the same number of samples.
Source: McKay, Beckman & Conover 1979
Why is Latin hypercube sampling used?
Latin hypercube sampling is used because its even coverage of each input's range lets the output distribution and its summaries be estimated with fewer samples than simple random sampling, improving efficiency, which matters when each model run is costly. By avoiding the clustering and gaps of purely random draws, it reduces the sampling variability of estimates for a given number of runs. This makes Latin hypercube sampling attractive for probabilistic analysis of models where reducing the number of runs while retaining precision is valuable.
Source: Saltelli et al. 2008
How does Latin hypercube sampling differ from simple random sampling?
Latin hypercube sampling stratifies each input's range into equally probable intervals and samples each once, guaranteeing even coverage of every input, whereas simple random sampling draws independently, which can leave some regions clustered and others empty by chance. Consequently, Latin hypercube sampling gives more uniform coverage and lower sampling variability for the same number of samples. Simple random sampling is easier and its samples are fully independent, but for efficient coverage of the input space Latin hypercube sampling generally performs better.
Source: McKay, Beckman & Conover 1979
What are the limitations of Latin hypercube sampling?
Latin hypercube sampling ensures even coverage of each input individually but does not by itself control the joint coverage of interactions among many inputs, and imposing a desired correlation structure requires additional steps. Its samples are not fully independent, which can complicate some error calculations. The efficiency gain over simple random sampling varies with the model. These limitations mean Latin hypercube sampling is used where even marginal coverage aids efficiency, with care taken over correlations and over analyses that assume independent samples.
Source: McKay, Beckman & Conover 1979
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Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 28 Oct 2025
Content version: 1.0.0
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