Bootstrap for repeated measures data

[MarieBernadette]

I am interested in running bootstrap for the mean estimate of repeated measures data. I came across the following SAS document by David Cassell which presents effective ways of running bootstrap for IID data. In the article it is mentioned that there are non-naïve version of bootstrap for repeated measure data however after a survey of the web I could not find any other SAS article on the topic. 

Can anyone provide me with some insight on how to proceed?

Thank you.

[Rick_SAS]

What is the statistic of interest? Is this a one-way ANOVA design with repeated measures or something else?

The resampling can be efficient in the SAS/IML matrix language. Do you plan on using SAS/IML, or are you intending to use the DATA step?

In general, your bootstrap resampling should mimic the sampling design that collected the original data. Along with the statistic of interest, a description of your data would be helpful.

Here's an example:

Each of N subjects has his blood pressure taken every day for 5 days. In a simple bootstrap, you could do the following:

1. Center the data by subtracting the overall mean from each measurement.  (In an ANOVA, you would subtract the group means.)

2. The residuals are what you should bootstrap. 

3. Sample N subjects with replacement. Each subject contains 5 data points. Add those residual values to the overall mean or relevant group mean.

4. Compute the statistic of interest.

5. Go to (3) and repeat a large number of times. 

[MarieBernadette]

Thank you for the response. The design setting for the experiment I am working with is as follows:

A group of subjects were asked to complete a task in two different sites (A and B). Sites A and B differs mainly in terms of terrain.

Vitals  (blood pressure and breathing rate) of each subjects were taken during the completion of the task. At a given site, each subject was asked to traverse the site and repeated the same task 4 times. Hence each subject has four measurements of blood pressure and four measurement of breathing rate in a day. The experiment was repeated for 3 days in each site. 

I am interested in comparing the distribution of the vital means for site A and B that is I wish to conduct a one-way repeated measure ANOVA with site as the between subject factor and time as the within subject factor for each vital.

I do not want to make any distribution assumption about the vital means and was therefore looking to use the bootstrap method to reveal the distribution of the two means ( for site A and site B).

Thank you

[Rick_SAS]

So the same subjects repeated at each site?  Then if there were N subjects you should:

1. Select a subject at random with replacement.

2. Get their scores (all reps at both sites).

3. Repeat from 1 until a bootstrap sample of N subjects obtains.

4. Compute the test statistic for the repeated measure ANOVA.on the bootstrap sample

5. Repeat from 1 until B samples obtained and B test statistics calculated.

6. Use the bootstrap distribution of the test statistics to determine confidence intervals, standard errors, p values, etc

[MarieBernadette]

Thank you very much this is very helpful.