1. Repeated measures: Approaches to Analysis
Peter T. Donnan
Professor of Epidemiology and Biostatistics

2. Objectives of session Understand what is meant by repeated measures
Be able to set out data in required format
Carry out mixed model analyses with continuous outcome in SPSS
Interpret the output

3. Repeated Measures Repeated Measures arise when:
In trials where baseline and several measurement of primary outcome
Example - Trial of Chronic Rhinosinusitis
Treatment usual care vs 2 weeks oral steroids
Measurements at 0, 2 , 10, 28 weeks

4. General Principles Battery of methods to analyse Repeated Measures:
Repeated use of significance testing at multiple time points
ANOVA - ‘a dangerously wrong method’ - David Finney
MANOVA
Multi-level models / mixed models

5. Significance testing at all time points
Probably most common – multiple t-tests
Least valid!
Sometimes account for multiple testing by adjusting p-value i.e. 0.05/k with k tests
Assumes that aim of study is to show significant difference at every time point
Most studies aim to show OVERALL difference between treatments and /or reaching therapeutic target quicker
PRIMARY HYPOTHESIS IS GLOBAL

6. Repeated Measures: Summary Measures
Post treatment means
Mean change (post – baseline)
ANCOVA or Multiple regression account for baseline as covariate
Slope of change
Maximum value – with multiple endpoints select highest value and compare across treatments
Area under the curve – difference
Time to reach a target or peak

7. Type of Analyses – Compare Slopes
Advice only
Pedometer
Controls β1
Difference in slopes as summary measure
e.g. β1-β2
Activity β2 β3
Baseline
3-months
Compare slopes which summarise change

8. Type of Analyses – Area under the curve
Advice only
Pedometer
Controls
Difference in Area between treatment slopes as summary measure
Activity
Baseline
3-months
6-months

9. Simple approach
Basically just an extension of analysis of variance (ANOVA)
Pairing or matching of measurements on same unit needs to be taken into account
Method is General Linear Model for continuous measures and adjusts tests for correlation

10. Simple approach
But simple approach can only use COMPLETE CASE analysis where say wk 0 50, wk 2 47, wk10 36, wk 28 30
Then analysis is on 30
Assumes data is MCAR
Better approach is MIXED MODEL which only assumes MAR and uses all data

11. Organisation of data (Simple Approach)
Generally each unit in one row and repeated measures in separate columns
Unit Score 1 Score2 Score ….

12. Repeated Measures in SPSS: Set factor and number of levels
Within subject factor
Within subject factor levels
Within subject factor name

13. Repeated Measures in SPSS: Enter columns of repeated measures
Use arrow to enter each repeated measure column
Between subject factor column

14. Repeated Measures in SPSS:
Select options
Use arrow to select display of means and Bonferroni corrected comparisons
Select other options

15. Repeated Measures in SPSS:
Select options
Select a plot of means of each within subject treatment

16. Repeated Measures in SPSS:
Output - Mean glucose uptake
Means for four treatments and 95% CI
1 = Basal; 2 = Insulin;
3 = Palmitate; 4 = Insulin+Palmitate

17. Repeated Measures in SPSS:
Output – Plot of Mean glucose uptake
Basal Insulin Palmitate Insulin+Palmitate

18. Repeated Measures in SPSS: Output – Comparisons of Mean glucose uptake
Comparison of means with Bonferroni correction
1 = Basal; 2 = Insulin;
3 = Palmitate; 4 = Insulin+Palmitate

19. Repeated Measures: Conclusion
Energy intake significantly higher with insulin compared to all other treatments
Addition of palmitate removes this effect

20. Organisation of data (Mixed Model)
Note most other programs and Mixed Model analyses require ONE row per measurement
Unit
Score 1
2.8
3.1
4.1 2
5.6
5.7
5.1 3
4.3
Etc…….

21. Repeated Measures in SPSS
Mixed Model in SPSS is:
Mixed Model
Linear
Hence can ONLY be used for continuous outcomes.
For binary need other Software e.g. SAS

23. Repeated Measures in SPSS: Mixed: Set within subject factor
Within subject factor name
Repeated Within subject factor

24. Repeated Measures in SPSS: Enter columns of repeated measures
Use arrow to enter subjects and repeated measure column
Choose covariance type = AR (1)

25. Repeated Measures in SPSS:
Select options
Add dependent
Treatment factor
And covariates
Select other options

26. Repeated Measures in SPSS:
Select options
Add effects as fixed
And Main Effects

27. Repeated Measures in SPSS:
Output -
Overall test for treatment p = 0.024

28. Repeated Measures in SPSS:
Output –

29. Mixed Model Repeated Measures:Conclusion
Use of Mixed Models ensures all data used assuming data is MAR and so more efficient in presence of missing data (if MAR) than the simple repeated measures
Other software e.g. SAS can also handle binary outcome data

30. Sample size for repeated Measures
Number in each arm =
Where r = number of post treatment measures
p = number of pre-treatment measures often 1
Frison&Pocock Stats in Med1992; 11:

31. Sample size for repeated Measures
Number in each arm =
Where σ = between treatment variance
δ = difference in treatment means
ρ = pairwise correlation (often 0.5 – 0.7)

32. Sample size for repeated Measures
Efficiency increase with number of measurements (r)
(zα +zβ)2 = 7.84 for 5% sig and 80% power
Methods assumes compound symmetry – often wrong but reasonable for sample size

33. Example: Sample size for repeated Measures
For r = 3 post-measures, correlation=0.7, p=1,
(zα +zβ)2 = 7.84 for 5% sig. and 80% power
Say δ=0.5σ then…..

34. Example: Sample size for repeated Measures
Which gives n = 19 in each arm with 80% power and 5% significance level

35. References
Repeated Measures in Clinical Trials: Analysis using mean summary statistics and its implications for design. Statist Med 1992; 11:
Field A. A bluffers guide to …Sphericity.
J Educational Statistics 13(3):
Pallant J. SPSS Survival Manual 3rd ed, Open University Press, 2007.
Field A. Discovering Statistics using SPSS for Windows. Sage publications, London, 2000.
Puri BK. SPSS in practice. An illustrated guide. Arnold, London, 2002.

36. Contemplating statistical analysis

37. Thank you
for
listening!