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

3. Repeated Measures Repeated Measures arise when: In trials where baseline and several measurement of primary outcome In trials where baseline and several measurement of primary outcome Example - Trial of Chronic Rhinosinusitis Example - Trial of Chronic Rhinosinusitis Treatment usual care vs 2 weeks oral steroids Treatment usual care vs 2 weeks oral steroids Measurements at 0, 2, 10, 28 weeks 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 Repeated use of significance testing at multiple time points ANOVA - ANOVA - ‘a dangerously wrong method’ - David Finney MANOVA MANOVA Multi-level models / mixed models Multi-level models / mixed models

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

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

7. Type of Analyses – Compare Slopes Compare slopes which summarise change Activity Baseline3-months Difference in slopes as summary measure e.g. β 1 -β 2 Advice only Pedometer Controls β1β1 β2β2 β3β3

8. Type of Analyses – Area under the curve Activity Baseline3-months Difference in Area between treatment slopes as summary measure Advice only Pedometer Controls 6-months

9. Simple approach Basically just an extension of analysis of variance (ANOVA) Basically just an extension of analysis of variance (ANOVA) Pairing or matching of measurements on same unit needs to be taken into account 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 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 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 Then analysis is on 30 Assumes data is MCAR Assumes data is MCAR Better approach is MIXED MODEL which only assumes MAR and uses all data 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 1Score2Score3 1 2.8 3.1 4.1 2 5.6 5.7 5.1 3 4.3 4.1 5.4 ….

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

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

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 Energy intake significantly higher with insulin compared to all other treatments Addition of palmitate removes this effect 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 UnitScore 12.8 13.1 14.1 25.6 25.7 25.1 34.3 Etc…….

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

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

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

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 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 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: 1685-1704

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) (z α +z β ) 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, (z α +z β ) 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: 1685-1704. Field A. A bluffers guide to …Sphericity. J Educational Statistics 13(3): 215-226. Pallant J. SPSS Survival Manual 3 rd 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. Thank you forlistening!