Concept Architecture
Concept
Theoretically, Repeated Measures Analysis is a statistical methodology used to analyse data in which multiple observations are collected from the same experimental unit over time or under multiple conditions. Because repeated observations from the same individual are correlated, standard independent-sample methods are inappropriate. Repeated measures analysis explicitly models this within-subject correlation, allowing valid estimation of treatment effects, time effects, and treatment-by-time interactions. The methodology forms the basis of longitudinal data analysis in clinical research and health economics.
Mathematically, repeated measures analysis is commonly implemented using repeated measures analysis of variance (RM-ANOVA) or, more generally, linear mixed-effects models. These models partition variation into between-subject and within-subject components while accounting for the covariance structure among repeated observations. Parameter estimation is typically performed using ordinary least squares for balanced RM-ANOVA or maximum likelihood and restricted maximum likelihood (REML) for mixed models.
In practice, repeated measures analysis is used to evaluate longitudinal outcomes measured repeatedly for each participant, such as healthcare costs, quality-adjusted life years, health-related quality of life, disease severity, or resource utilisation. In health economics, mixed-model repeated measures (MMRM) has become a standard analytical approach because it accommodates incomplete longitudinal data under the Missing At Random assumption and avoids many limitations of traditional repeated measures ANOVA.
Purpose
Used to estimate changes over time while accounting for within-subject correlation, evaluate treatment effects across repeated observations, and analyse longitudinal clinical and economic outcomes in health economic studies.
Mathematical Formulae
Primary Formula
General linear mixed repeated measures model:
Y?? = ?? + ??X?? + u? + �??
where:
- Y?? = outcome for subject i at occasion j
- ?? = intercept
- ?? = fixed-effect coefficient(s)
- X?? = explanatory variables
- u? = subject-specific random effect
- �?? = residual error
Supporting Formulae
Variance decomposition:
Var(Y) = ZGZ? + R
Intraclass Correlation Coefficient:
ICC = �?� � (�?� + ��)
Repeated measures F statistic (RM-ANOVA):
F = MS?ff?ct � MS?rror
Related Mathematical Methods
- Mixed Model Analysis
- Mixed Model Repeated Measures
- Linear Mixed Model
- Random Effects
- Repeated Measures ANOVA
- Longitudinal Methods
- Maximum Likelihood Estimation
- Restricted Maximum Likelihood
- Covariance Structure Modelling
Example
A health economic evaluation follows 300 patients receiving two alternative treatments. EQ-5D utility values are measured at baseline, 3, 6, and 12 months.
A mixed-model repeated measures analysis estimates:
Treatment effect = 0.041
95% confidence interval = 0.018 to 0.064
p = 0.001
The analysis adjusts for the correlation between repeated measurements within each patient while using all available observations, including participants with some missing follow-up measurements.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| AVERAGEIFS | =AVERAGEIFS(C:C,A:A,A2,B:B,"Month 6") | Calculate mean outcomes at each follow-up time point. |
| VAR.S | =VAR.S(C2:C301) | Estimate variability at each repeated measurement. |
| CORREL | =CORREL(BaselineRange,Month6Range) | Examine within-subject correlation between repeated measurements. |
| SUMPRODUCT | =SUMPRODUCT(Weights,Outcomes) | Calculate weighted longitudinal summaries. |
| LINEST | =LINEST(YRange,XRange,TRUE,TRUE) | Approximate repeated trend estimation for simple balanced datasets. |
VBA (Optional)
Automate preparation of longitudinal datasets, summarise repeated observations, and generate reports for repeated measures and mixed-model analyses.
Sources
- Laird NM, Ware JH. Random-Effects Models for Longitudinal Data. Biometrics. 1982.
- Fitzmaurice GM, Laird NM, Ware JH. Applied Longitudinal Analysis.
- Verbeke G, Molenberghs G. Linear Mixed Models for Longitudinal Data.
- Gueorguieva R, Krystal JH. Move Over ANOVA: Progress in Analysing Repeated-Measures Data. Archives of General Psychiatry. 2004.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
- Drummond MF, et al. Methods for the Economic Evaluation of Health Care Programmes.
- NICE Health Technology Evaluation Manual.
- ISPOR Good Practice Reports.
Related Concepts (2)
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 repeated measures analysis?
A statistical approach analysing data in which the same outcome has been measured multiple times on the same individuals, accounting for correlation.
Source: Laird & Ware 1982
Why does repeated measures analysis need special handling?
Repeated measures analysis is needed because the several readings taken on one person are correlated, so treating them as independent observations, as an ordinary analysis would, overstates how much information the data hold and understates uncertainty. It uses methods such as mixed models that explicitly account for this within-person correlation, and that can draw on partial records when some visits are missing. Handling the links between a person's own measurements is its purpose. Analysing correlated repeated readings correctly is what it does. Kirkwood and Sterne (2003) describe this.
Source: Kirkwood & Sterne 2003
Why is repeated measures analysis needed?
Repeated measures analysis is needed because measurements taken repeatedly on the same individual are correlated, violating the independence assumption of standard statistical methods, so analysing them as independent would give incorrect standard errors and misleading inference. So repeated measures analysis is needed to handle the within-individual correlation correctly, since ignoring it understates or misstates the uncertainty and can bias conclusions, which is why specialised methods that model or adjust for the correlation are used for repeated-measures data, ensuring valid estimates of change over time and of treatment or other effects from the repeated observations.
Source: Laird & Ware 1982
What methods are used in repeated measures analysis?
Methods used in repeated measures analysis include mixed effects models, which include random effects to capture the correlation and individual variation; generalised estimating equations, which estimate population-average effects while adjusting for the within-individual correlation; and repeated measures analysis of variance, an older approach requiring balanced data. So repeated measures analysis employs a range of methods that account for the correlated structure, with mixed models and generalised estimating equations preferred for their flexibility in handling unbalanced data and missing observations, which is why these modern approaches are commonly used over the more restrictive analysis of variance for repeated-measures data.
Source: Laird & Ware 1982
How does repeated measures analysis handle correlation?
Repeated measures analysis handles the correlation among an individual's measurements by modelling it, as mixed effects models do through random effects that induce within-individual correlation, or by adjusting for it, as generalised estimating equations do through a working correlation structure with robust standard errors. So repeated measures analysis handles correlation by incorporating it into the analysis rather than assuming independence, which yields valid standard errors and inference, with the correlation represented explicitly in mixed models and accounted for in estimating average effects by generalised estimating equations, the approach chosen according to whether individual-specific or population-average effects are wanted.
Source: Laird & Ware 1982
How does repeated measures analysis handle missing data?
Repeated measures analysis handles missing data, common from dropout, in various ways: likelihood-based mixed models use all available measurements and give valid results under the missing at random assumption, while other approaches may need multiple imputation or specific methods. So repeated measures analysis addresses missing data by using methods that make valid use of the observed measurements under stated assumptions, with mixed models convenient because they naturally accommodate unbalanced data and are valid under missing at random, though when missingness may not be at random, sensitivity analyses are used, since attrition can bias conclusions if mishandled.
Source: Carpenter & Kenward 2013
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 24 Dec 2025
Content version: 1.0.0
Canonical Identity
- Term code
- HE-ES-SA-181
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