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 Interpret the output

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

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

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

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

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

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

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

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

Organisation of data (Simple Approach) Generally each unit in one row and repeated measures in separate columns Unit Score 1 Score2 Score3 1 2.8 3.1 4.1 2 5.6 5.7 5.1 3 4.3 4.1 5.4 ….

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

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

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

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

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

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

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

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

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…….

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

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

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

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

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

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

Repeated Measures in SPSS: Output –

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

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

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)

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  

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…..    

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

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 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.

Contemplating statistical analysis

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