Repeated measures are response outcomes measured on the same experimental unit. Usually, these measurements are made over a period of time, such as blood pressure measured once a week for a month. However, repeated measures can also refer to multiple measurements on an experimental unit, such as left- and right-eye visual acuity.
The experimental units are most often called subjects. The repeated measures for the same subject are correlated, and this correlation must be taken into account in an analysis. You must specify a covariance structure for the repeated measurements of an individual subject, and the same covariance structure is then used for all subjects.
For example, consider a clinical trial comparing several antihypertensive medications for optimal treatment of mild hypertension. The response variable is systolic blood pressure (SBP) measured at 3, 6, and 9 months on a total of 128 subjects in the treatment group and 230 subjects in the placebo (or control) group. Other variables include Clinic, Person, Treatment, and SBPbl.
Clinic: Clinical center (4 levels)
Person: Subject in the trial (358 levels)
SBP3: Systolic blood pressure at the 3-month visit
SBP6: Systolic blood pressure at the 6-month visit
SBP9: Systolic blood pressure at the 9-month visit
SBLbl: Baseline blood pressure at 0 months
Treatment: Treatment group (2 levels)
Since the clinical trials data was recorded in an Excel spreadsheet, you can open the data by selecting File > Open, changing File Type to "Microsoft Excel Spreadsheet," and opening bpmult.xls.
Figure 1: BPMULT Data Set in the Data Table
The data contain several blood pressure measurements for each subject in the clinical trial in a single observation. However, for the repeated measurements task in the Analyst Application, your data must be structured with a single repeated measurement per observation for each subject. You can create a new Data Table with this structure by performing the Stack Columns task.
Figure 2: Stack Columns Dialog
The new stacked data set will contain each blood pressure measurement as a separate observation identified by a source variable indicating the visit. Select Data > Stack Columns, highlight SBP3, SBP6, and SBP9 in the candidate list, and designate the variables as stack columns by clicking Stack. Type "SBP" in the Stacked Column box, "VST" in the Source Column box, and click Ok. To open the new stacked columns data set in the Data Table, right-click on the data set in the Project Tree and select Open.
The data set now contains an observation corresponding to each visit for each subject. The variable SBP contains blood pressure at time of visit, and VST denotes the month of visit with three distinct character values: SBP3, SPB6, and SBP9. However, the values of VST must be numeric to include it as a covariate in the repeated measures analysis. A numeric variable can be created using the recode values facility.
Figure 3: Recode Values Dialog
To recode the VST variable, select Data > Transform > Recode Values, specify VST as the column to recode, name the new column VISIT, click on numeric to create a numeric variable, and click Ok. The next dialog contains a table listing each unique value of VST as well as cells for you to type the recoded value. In these cells, type 3 in the cell next to SBP3, 6 next to SBP6, 9 next to SBP9, and click Ok.
Figure 4: Stacked BPMULT Data
Repeated Measures Analysis
Using the repeated measures task, you can assess the relationship between systolic blood pressure and treatment, clinic, the treatment by clinic interaction, visit, and baseline blood pressure. You can specify that the repeated measures analysis utilize a compound symmetry covariance structure, where VST defines the repeated measures and PERSON defines individual subjects.
To perform a repeated measures analysis, select Statistics > ANOVA > Repeated Measures. In the main window, specify SBP as the dependent variable, Clinic, Treatment, VST, and Person as class variables, and SBPbl and VISIT as quantitative variables. Click on Model and specify Person as the variable uniquely defining subjects by highlighting the variable in the Independent list and clicking Add. On the model tab, highlight Treatment, Clinic, VISIT, and SBPbl and click Add to specify the effects in the model; then CTRL click on Treatment and Clinic in the Independent list and click on Cross to specify the Treatment*Clinic interaction. On the repeated tab, specify VST as the repeated variable by highlighting it and clicking Add. Click OK twice to run the analysis.
Figure 5: Repeated Measures analysis results
The Covariance Parameter Estimates table provides the estimate of the residual variance = 80.6 and the compound symmetry = 58.2. The Type III Tests table provides the tests for each effect in the model. For example, there is significant evidence of differences in blood pressure across clinics based on an F statistic of 5.65 and p-value of 0.0009.