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Repeated measures: Approaches to Analysis

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

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Repeated measures: Approaches to Analysis

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  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 1Score2Score3 1 2.83.1 4.1 25.65.7 5.1 34.34.1 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. 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 PalmitateInsulin+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

  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

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

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

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

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

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

  27. Repeated Measures in SPSS: Output –

  28. 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

  29. 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

  30. 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)

  31. 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

  32. 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…..

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

  34. 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 3rded, Open University Press, 2007. Field A. Discovering Statistics using SPSS for Windows. Sage publications, London, 2000. PuriBK. SPSS in practice. An illustrated guide. Arnold, London, 2002.

  35. Thank you for listening!

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