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Simple Repeated measures

Statistics for Health Research. Simple Repeated measures. 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 simple analyses in SPSS Interpret the output.

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Simple Repeated measures

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  1. Statistics for Health Research Simple Repeated measures 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 simple analyses in SPSS Interpret the output

  3. Repeated Measures Repeated Measures arise when: Measuring the same experimental unit (cell, rat, patient) on a number of occasions Standard analysis of variance not valid as assumes independent measures Essentially measurements are paired or correlated

  4. Examples of Repeated Measures Measuring glucose uptake by cells at different time points, under different stimuli, etc. Measuring cholesterol in a randomised controlled trial of a new statin at 3, 6 and 12 months Implementing weight loss intervention and measuring weight at different time points

  5. Analysis of Repeated Measures T-test at each time point very common – multiple t-tests Least valid analysis! Primary hypothesis is usually a single test of overall effect By testing at each time point we are increasing the type I error P=0.05 means that we would reject the null hypothesis incorrectly on 1 in 20 occasions If we keep testing we will eventually find a significant result!

  6. Repeated Measures Could perform t-test at each time point

  7. Analysis of Repeated Measures Sometimes account for multiple testing by adjusting p-value i.e. 0.05/k with k tests Known as the Bonferoni correction Multiple 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

  8. Simple general 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

  9. Organisation of data (1) 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 ….

  10. Organisation of data (2) Note most other programs and later analyses require ONE row per measurement

  11. Glucose uptake of two cell types (liver and muscle). Each cell challenged with four different ‘treatments’ Data given in ‘Glucose uptake.sav’ Note: cell type is a fixed BETWEEN CELL factor ‘Treatments’ are REPEATED WITHIN CELL factors

  12. Repeated Measures in SPSS Simplest method in SPSS is: General Linear Model Repeated Measures Note many other methods in SPSS – Mixed Models described on day 4

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

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

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

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

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

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

  19. 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

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

  21. Mauchley’sSphericity test Sphericity refers to the issue of the similarity (homogeneity) of variances in the differences between treatments Think of it as an extension to assumption in ANOVA of similar variances It is an assumption of SPSS Repeated Measures i.e. s2a-b ~ s2a-c ~ s2a-d ~ s2b-c ~ s2b-d ~ s2c-d

  22. Meeting conditions of repeated measures: Mauchly Sphericity Test P-value for test of Sphericity Significant so need to correct F test by multiplying degrees of freedom by Greenhouse-Geisser epsilon

  23. Meeting conditions of repeated measures: Use corrected p-value if significant non-sphericity Output gives four different tests Overall test of differences between treatments within subjects: Use Greenhouse-Geisser corrected p-value

  24. Alternatives When Sphericity is not met an alternative to the correction factors is to use MANOVA Unfortunately this has less power than the Repeated Measures analysis demonstrated and so should generally be avoided

  25. Repeated Measures in SPSS: Output – Pedometer Trial • Randomised controlled trial in sedentary elderly women • Three groups Pedometer+advice, Advice only, Control • Physical activity measured on three occasions • 1 – baseline; • 2 - 3 mnths; • 3 – 9 mnths

  26. Repeated Measures in SPSS: Output – Pedometer Trial Pedometer Group * factor1 Measure: Physical Activity Pedometer factor1 Mean Std. Error 95%CI group Lower Upper .00 1 126792 4665 117578 136006 2 133619 5089 123568 143669 3 128766 4969 118952 138580 1.00 1 141138a 6520 128262 154015 2 147371a 7111 133326 161417 3 136059a 6944 122344 149773 a. Based on modified population marginal mean. 0 = Control; 1 = Pedometer+advice Factor 1 – time baseline, 3 mnths, 9 mnths

  27. Repeated Measures in SPSS: Output – Plot of Mean Activity over time

  28. Repeated Measures in SPSS: Output – Tests of significance Not quite significant!

  29. Repeated Measures:Conclusion Activity increased with pedometer + advice but rise was greatest in Advice only group

  30. Repeated Measures:Conclusion Simple repeated measures is useful analysis for overall effect Avoid multiple testing at each time point Check assumption of Sphericity Use adjusted Greenhouse-Geisser or Huynh-Feldt adjustment if sphericity not met Later demonstrate mixed model

  31. References 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. Foster JJ. Data Analysis using SPSS for Windows (Versions 8 – 10). Sage publications, London, 2001. Puri BK. SPSS in practice. An illustrated guide. Arnold, London, 2002.

  32. Repeated Measures: Practical in SPSS Previous analysis lumped all cells together Two types: liver and muscle 1) Repeat the analysis separately for each cell type 2) Then compare results from two types in single analysis Is cell type within subject or between subject factor?

  33. Repeated Measures: Practical in SPSS Hint - To do separate analysis by cell type use: Data Select Cases (If celltype = 1 or 2) OR Data Split file (compare groups by celltype)

  34. Repeated Measures: Practical in SPSSSPSS Study database.sav Trial of pedometers in elderly sedentary women Try repeated measures of Accelerometer trial data Baseline, 3 months and 9 months AccelVM1a, AccelVM2, AccelVM3 Trial arms Ran_grp (1,2,3) Try adjusting for Age, StairsDifficult, SIMD

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