Concept Architecture
Concept
Theoretically, Morris Method is a screening method for global sensitivity analysis that identifies influential input parameters in complex mathematical models using elementary effects. It provides a computationally efficient approach for distinguishing parameters with negligible, linear or non-linear influences on model outputs before more computationally intensive variance-based methods are applied. In health economics, the Morris method is used to screen uncertain model parameters in decision analytic models, microsimulation and probabilistic sensitivity analysis.
Mathematically, the Morris method perturbs one input parameter at a time across multiple randomly selected points in the parameter space and calculates an elementary effect for each perturbation. Summary statistics of these elementary effects, particularly the mean absolute elementary effect and its standard deviation, quantify the overall importance of each parameter and the extent of non-linearity or interaction with other parameters.
In practice, the Morris method is implemented by specifying plausible ranges for uncertain model inputs, generating a series of trajectories through the parameter space and calculating elementary effects for each parameter. Parameters identified as influential are subsequently investigated using more detailed global sensitivity analyses, while non-influential parameters may be fixed at baseline values to reduce computational burden.
Purpose
Used to screen model input parameters, identify influential sources of uncertainty and prioritise parameters for detailed global sensitivity analysis in health economic models.
Mathematical Formulae
Primary Formula
Elementary effect:
EE? = (Y(X?, ?, X? + ?, ?, X?) ? Y(X)) / ?
where:
EE? = elementary effect of parameter i
Y = model output
? = input perturbation
Supporting Formulae
Mean absolute elementary effect:
?* = (1/r) ? ?|EE?|
Standard deviation of elementary effects:
� = �((1/(r ? 1)) ? ?(EE? ? EE?)�)
where:
r = number of trajectories
Related Mathematical Methods
- Global Sensitivity Analysis
- Elementary Effect
- Variance-Based Sensitivity Analysis
- Sobol Sensitivity Analysis
- Monte Carlo Simulation
- Parameter Screening
Example
A Markov model contains 40 uncertain input parameters. Applying the Morris method identifies treatment efficacy and disease progression probabilities as having the largest mean absolute elementary effects and high standard deviations, indicating both strong influence and important interaction effects. These parameters are subsequently examined using Sobol global sensitivity analysis, while less influential parameters remain fixed.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| ABS | =ABS(B2) | Calculate the absolute elementary effect for each parameter perturbation. |
| AVERAGE | =AVERAGE(C2:C51) | Estimate the mean elementary effect across simulation trajectories. |
| STDEV.S | =STDEV.S(C2:C51) | Quantify variability in elementary effects, indicating interaction or non-linearity. |
| RANK.EQ | =RANK.EQ(D2,D$2:D$41,0) | Rank parameters according to their importance for model screening. |
VBA (Optional)
VBA can automate Morris sampling trajectories, calculate elementary effects and rank model parameters according to their influence on health economic outcomes.
Sources
- Morris MD. Factorial sampling plans for preliminary computational experiments. Technometrics. 1991;33(2):161?174.
- Saltelli A, Ratto M, Andres T, et al. Global Sensitivity Analysis: The Primer. John Wiley & Sons.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
- NICE. Health Technology Evaluation Manual.
Related Concepts (3)
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 the Morris method?
A global sensitivity analysis technique efficiently screening many input parameters for negligible, linear, or interactive effects, using relatively few model runs.
Source: Morris 1991
Why is the Morris method economical compared with other global methods?
Fuller variance-based sensitivity methods can need very many model runs, which is costly when a model is slow. The Morris method screens efficiently by computing a set of elementary effects, each from a small change in one input, using far fewer runs, and classifies inputs as negligible, roughly linear, or involved in interactions. This lets a modeller quickly discard unimportant inputs and focus a more expensive analysis on the rest. It trades some detail for speed. Saltelli and colleagues (2008) describe it.
Source: Saltelli et al. 2008
How does the Morris method work?
The Morris method works by computing elementary effects for each input, each being the change in output from a small discrete step in that input, at several points sampled across the input space along efficient trajectories. For each input, the mean of the absolute elementary effects measures overall influence, and their standard deviation indicates non-linearity or interaction. Plotting these two summaries classifies inputs as negligible, having roughly linear effects, or having non-linear or interactive effects, providing an efficient screening of many parameters with modest computation.
Source: Morris 1991
Why is the Morris method used?
The Morris method is used to screen many input parameters efficiently, identifying which are negligible and which are influential, at far lower computational cost than variance-based methods, so it suits models with numerous inputs or expensive runs. It captures effects across the whole input range, unlike local one-way analysis, and distinguishes linear from non-linear or interactive effects. This makes it valuable as a first step, focusing subsequent, more detailed analysis on the parameters that matter and allowing negligible ones to be set aside.
Source: Saltelli et al. 2008
What do the results of the Morris method indicate?
The results of the Morris method indicate, for each input, its overall influence and the nature of its effect: a small mean of absolute elementary effects marks a negligible input; a large mean with a small standard deviation marks an influential input with a roughly linear, additive effect; and a large standard deviation marks an input with non-linear effects or interactions with others. This classification helps decide which inputs can be fixed and which warrant closer, quantitative analysis of their contribution to output uncertainty.
Source: Morris 1991
What are the limitations of the Morris method?
The Morris method provides a qualitative screening rather than a precise quantitative decomposition of output variance, so it ranks and classifies inputs but does not give exact contributions as variance-based indices do, and its standard-deviation measure signals interaction or non-linearity together without separating them. Results depend on the chosen step sizes and sampling. It is best as a preliminary screen. These limitations mean the Morris method is used to identify influential inputs efficiently, with variance-based methods applied afterwards where precise attribution is needed.
Source: Saltelli et al. 2008
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 28 Oct 2025
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