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Author: dr. ir. N van Geloven
Co-author: prof. dr. A.H. Zwinderman
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This page was translated from the Dutch-language original using AI and has not been fully reviewed. Where the two differ, the Dutch version takes precedence.

• What is meant by repeated measures?
• Why can't you use a standard regression model with repeated measures?
• What analyses are available for repeated measures?
• How can I conveniently calculate an area under the curve in SPSS when there are many repeated measures?
• How can I combine data from 4 experiments?
• References
• Additional resources
• Software tips

Repeated measures are multiple measurements of the same variable in the same person, patient, laboratory animal, or, more generally, the same observational unit. Examples:

• repetition over time: when the same measurement is performed repeatedly in a patient, for example before and after a treatment, or during a follow-up period;
• multiple locations: when measurements are taken at multiple locations in the same person's body (left and right eye, multiple sections in a biopsy, multiple slices in an MRI image);
• multiple conditions: when the same patient is measured under different conditions (e.g. two treatments or test conditions), for example in a cross-over study or when comparing raters;
• repetitions for the sake of precision: when a measurement has large within-person variation (or a large measurement error), or when, for example, a limited sample size requires greater precision for reasons of power, it can be worthwhile to take a number of separate measurements;
• (other) multilevel structures: when measurements are taken from multiple people who are part of the same group, or when it can otherwise be assumed that measurements from people within the same cluster resemble each other more than two measurements from people in a different cluster. For example: patients who have the same general practitioner (especially if the intervention was carried out per general practice) or who are treated in the same hospital often cannot be regarded as independent observations. The classic example here is pupils who have the same teacher, and teachers who in turn belong to the same school.

In a standard regression model, it is assumed that all measurements are independent of each other. With repeated measures, it is likely that two measurements from the same person resemble each other more than two measurements from different people. If that is the case, the measurements within the same person are not independent. If this dependency is not taken into account with repeated measures, the standard errors and p-values are generally (incorrectly!) too small. Moreover, the outcome of the regression analysis can even be completely wrong, as illustrated in the image below. This figure shows the observations of 12 people, and each person shows a clearly increasing trend. If the dependency of the observations is ignored, the best-fitting regression line through the total cloud of points is the orange, downward-sloping line, and this does not give a correct representation of the trend per patient.

• Simple methods: Sometimes repeated measures can be summarized in a single relevant measure. For example, you can use the measurement from just one time point or the change between two measurement points, calculate a summary measure such as the mean or the area under the curve, or analyze the time to reaching a certain threshold value of the outcome measure (survival analysis).

The simple methods use only part of the collected information, which often results in less discriminative power. On the other hand, their interpretation is potentially much more intuitive than when using more advanced methods.

• Advanced methods: There are also methods that do use all the repeated measurements and correct for the dependency of the measurements. Examples of analyses suitable for repeated measures include mixed effects models (including the repeated measures ANOVA) and generalized estimating equations (GEE).

Repeated measurements ANOVA is a specific variant of mixed effects models, specifically for continuous, normally distributed dependent variables measured at fixed and identical time points in all patients. Mixed effects models and GEE models are more flexible than the repeated measures ANOVA and are available for both continuous, normally distributed dependent variables and, for example, dichotomous dependent variables. Moreover, unlike the repeated measures ANOVA, mixed effects models can also handle a certain amount of missing values, namely when the data are missing at random.

I would like to determine the 'area under the curve' for a particular measurement over time, measured at various time points. I can't figure it out in SPSS. I need to determine about 300 of them... do you have any advice?

Within SPSS you can use 'loops' to carry out operations or recoding efficiently. You can use the following syntax, which calculates an area under the curve per patient. At the top of the document it is described how you need to have the variables set up in SPSS.

I split the experiments I carried out into 4 sessions, because it was not feasible to process all the samples at once. It now turns out that the comparison groups (different diagnoses) within each series are actually quite small, and I am wondering whether and how I could combine the data from the 4 series.

In this kind of setting, a factor correction is commonly applied. See also the reference to the paper by Ruijter [1] at the bottom of this page. You can also include a correction for 'clustering' within sessions in a statistical model, for example by using a mixed model or repeated measures ANOVA. You then treat the experiments as 'repeated measures' within a session.

1. Ruijter JM, Thygesen HH, Schoneveld OJ, Das AT, Berkhout B, and Lamers WH. Factor correction as a tool to eliminate between-session variation in replicate experiments: application to molecular biology and retrovirology. Retrovirology. 2006 Jan 6;3:2. DOI: 10.1186/1742-4690-3-2 | PMID: 16398936
2. Gueorguieva R and Krystal JH. Move over ANOVA: progress in analyzing repeated-measures data and its reflection in papers published in the Archives of General Psychiatry. Arch Gen Psychiatry. 2004 Mar;61(3):310-7. DOI: 10.1001/archpsyc.61.3.310 | PMID: 14993119
3. West BT. Analyzing longitudinal data with the linear mixed models procedure in SPSS. Eval Health Prof. 2009 Sep;32(3):207-28. DOI: 10.1177/0163278709338554 | PMID: 19679634

• This post by Jonathan Bartlett about Odds ratios, collapsibility, marginal vs. conditional, GEE vs GLMMs explains the difference between the GEE and GLMM (mixed model) approaches for binary outcomes.
• The analysis factor - The Repeated and Random Statements in Mixed Models for Repeated Measures information on the distinction between the repeated and random statements in SPSS mixed.
• The analysis factor information on the different approaches for repeated measures: repeated measurements ANOVA, marginal model, mixed model.
• Robin Beaumont Heath Informatics course material Freely usable course material on linear mixed models with explanation of specification in both SPSS and R, see weeks 6, 7 and 8. Includes accompanying Youtube instructional videos.

• GLLAMM A family of functions (freely downloadable) in Stata, offering options for modeling repeatedly measured non-continuous outcome measures (dichotomous, ordinal, etc).
• SuperMix A standalone program suitable for modeling repeatedly measured non-continuous outcome measures (dichotomous, ordinal, etc).

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