Simple Repeated measures Peter T. Donnan Professor of Epidemiology and Biostatistics Statistics for Health Research

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 simple analyses in SPSS Carry out simple analyses in SPSS Interpret the output Interpret the output

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

Examples of Repeated Measures Measuring glucose uptake by cells at different time points, under different stimuli, etc. 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 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 Implementing weight loss intervention and measuring weight at different time points

Analysis of Repeated Measures T-test at each time point very common – multiple t-tests T-test at each time point very common – multiple t-tests Least valid analysis! Least valid analysis! Primary hypothesis is usually a single test of overall effect Primary hypothesis is usually a single test of overall effect By testing at each time point we are increasing the type I error 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 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! If we keep testing we will eventually find a significant result!

Repeated Measures Could perform t-test at each time point

Analysis of Repeated Measures 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 Known as the Bonferoni correction Known as the Bonferoni correction Multiple tests assumes that aim of study is to show significant difference at every time point 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 Most studies aim to show OVERALL difference between treatments and /or reaching therapeutic target quicker PRIMARY HYPOTHESIS IS GLOBAL PRIMARY HYPOTHESIS IS GLOBAL

Simple general 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

Organisation of data (1) Generally each unit in one row and repeated measures in separate columns Unit Score 1Score2Score ….

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

BasalInsulinPalmitateInsul+PalmCell type Exper …..……12 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

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

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

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

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

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

Mauchley’s Sphericity test Sphericity refers to the issue 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. It is an assumption of SPSS Repeated Measures i.e. s 2 a-b ~ s 2 a-c ~ s 2 a-d ~ s 2 b-c ~ s 2 b-d ~ s 2 c-d

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

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

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

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

Repeated Measures in SPSS: Output – Pedometer Trial 0 = Control; 1 = Pedometer+advice Factor 1 – time baseline, 3 mnths, 9 mnths Pedometer Group * factor1 Measure: Physical Activity Pedometer factor1 Mean Std. Error 95%CI group Lower Upper a a a a. Based on modified population marginal mean. Pedometer Group * factor1 Measure: Physical Activity Pedometer factor1 Mean Std. Error 95%CI group Lower Upper a a a a. Based on modified population marginal mean.

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

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

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

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

References Field A. A bluffers guide to …Sphericity. J Educational Statistics 13(3): Pallant J. SPSS Survival Manual 3 rd ed, Open University Press, Field A. Discovering Statistics using SPSS for Windows. Sage publications, London, Foster JJ. Data Analysis using SPSS for Windows (Versions 8 – 10). Sage publications, London, Puri BK. SPSS in practice. An illustrated guide. Arnold, London, 2002.

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

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

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