Concept Architecture
Concept
Theoretically, Correlation is a statistical measure that quantifies the strength and direction of association between two random variables. It provides a measure of linear dependence without implying causation and forms a fundamental component of multivariate statistical analysis. In health economics, correlation is used to characterise relationships among model parameters, clinical outcomes, costs, utilities and epidemiological variables, particularly where parameter dependence must be preserved in probabilistic analyses.
Mathematically, correlation is represented by a standardised covariance that ranges from ?1 to +1. A value of +1 indicates perfect positive linear association, ?1 indicates perfect negative linear association, and 0 indicates no linear association. Correlation coefficients are dimensionless, allowing relationships between variables measured on different scales to be compared directly.
In practice, correlation is estimated from observed data using correlation coefficients such as Pearson's product-moment correlation coefficient or Spearman's rank correlation coefficient, depending on the nature of the data. Estimated correlations are incorporated into variance-covariance matrices, multivariate probability distributions and probabilistic sensitivity analyses to ensure that dependent model parameters are simulated appropriately.
Purpose
Used to quantify the strength and direction of association between variables, preserve parameter dependence in probabilistic sensitivity analysis and support multivariate statistical modelling in health economics.
Mathematical Formulae
Primary Formula
Pearson correlation coefficient:
? = Cov(X, Y) / (�?�?)
Sample correlation coefficient:
r = ?((x? ? x?)(y? ? ?)) � �(?(x? ? x?)� ? ?(y? ? ?)�)
Supporting Formulae
Covariance:
Cov(X, Y) = E[(X ? ??)(Y ? ??)]
Relationship with covariance:
Cov(X, Y) = ?�?�?
Range:
?1 � ? � 1
Related Mathematical Methods
- Covariance Analysis
- Variance-Covariance Matrix
- Pearson Correlation
- Spearman Rank Correlation
- Cholesky Decomposition
- Multivariate Normal Distribution
- Probabilistic Sensitivity Analysis
Example
A health economist evaluates the relationship between treatment costs and quality-adjusted life-years (QALYs) across 500 simulated patients. The estimated Pearson correlation coefficient is 0.68, indicating a moderately strong positive association. This correlation is incorporated into the variance-covariance matrix before conducting probabilistic sensitivity analysis to preserve the observed dependence between costs and health outcomes.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| CORREL | =CORREL(A2:A501,B2:B501) | Calculate the Pearson correlation coefficient between two health economic variables. |
| COVARIANCE.S | =COVARIANCE.S(A2:A501,B2:B501) | Estimate covariance prior to constructing a variance-covariance matrix. |
| STDEV.S | =STDEV.S(A2:A501) | Calculate the standard deviation required for correlation estimation. |
| PEARSON | =PEARSON(A2:A501,B2:B501) | Alternative function for calculating the Pearson correlation coefficient. |
VBA (Optional)
VBA can automate estimation of correlation matrices from simulation outputs and generate variance-covariance matrices for probabilistic sensitivity analysis.
Sources
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
- Drummond MF, et al. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
- ISPOR-SMDM Modeling Good Research Practices Task Force Reports.
- NICE. Health Technology Evaluation Manual.
Related Concepts (3)
Library
Publications
1
Parameter Estimation and Uncertainty: A Report of the ISPOR-SMDM Modeling Good Research Practices Task Force-6 — Briggs, Weinstein, Fenwick, Karnon, Sculpher & Paltiel, Task Force Report 6 ed., 2012 (Value in Health / Medical Decision Making)
Best-practice guidance on parameter estimation and the characterisation of uncertainty in decision models, covering probabilistic sensitivity analysis, distributional choices, and correlation between parameters.
Journal ArticleView source →
Frequently Asked Questions (6)
What is correlation?
A statistical measure of how closely two variables move together, ranging from negative one to positive one.
Source: Pearson 1896
What do the sign and size of a correlation indicate?
A correlation coefficient runs from minus one to plus one and summarises how closely two variables move together. A positive value means they tend to rise and fall together, a negative value that one rises as the other falls, and a value near zero that they move largely independently. The size, its distance from zero, shows how tight the relationship is, with values near the extremes indicating a strong linear association. It measures only linear co-movement, not the strength of any curved relationship. Altman and colleagues (2000) describe this measure.
Source: Altman et al. 2000
How is correlation measured?
Correlation is commonly measured by the Pearson correlation coefficient, calculated as the covariance of the two variables divided by the product of their standard deviations, which standardises it to lie between negative one and positive one. This measures the strength of their linear relationship. Rank-based measures, such as Spearman's, assess monotonic association instead. The Pearson coefficient captures linear association, so a value near zero indicates little linear relationship, though a non-linear relationship could still exist without being reflected in it.
Source: Pearson 1896
Why does correlation matter in modelling?
Correlation matters in modelling because parameters that are correlated must be sampled jointly in probabilistic analysis, since treating correlated parameters as independent would misstate the uncertainty in the results. Correlation among inputs affects the spread of the output, and ignoring it can understate or overstate uncertainty. Techniques such as Cholesky decomposition impose the correct correlation on sampled parameters. Recognising and representing correlation is therefore important for propagating joint uncertainty correctly through a model rather than assuming independence among related inputs.
Source: Briggs, Claxton & Sculpher 2006
What is the difference between correlation and causation?
Correlation measures whether two variables move together, while causation means one variable actually influences the other; a correlation can arise without causation, for instance when both variables are driven by a common third factor, or by chance. So observing correlation does not establish that one variable causes the other. This distinction matters when interpreting associations, since inferring causation from correlation alone can mislead. Establishing causation requires more than correlation, such as experimental evidence or careful control of confounding factors.
Source: Pearson 1896
What are the limitations of the correlation coefficient?
The Pearson correlation coefficient measures only linear association, so it can be near zero even when a strong non-linear relationship exists, and it is sensitive to outliers, which can inflate or deflate it. It does not imply causation, and a single coefficient can hide patterns visible in a scatter plot. It describes two variables at a time, not more complex joint structure. These limitations mean correlation is interpreted alongside plots and judgement, and non-linear or rank-based measures are used where appropriate.
Source: Pearson 1896
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 27 Oct 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/correlation
- Term code
- HE-EM-UA-015
Stable URI · Machine-readable · Resolvable · CC BY 4.0