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I am planing a pre-post treatment-control design study with a large number of pre-treatment measurements. I have subjects divided into a control group and a treatment group. For both groups, I will collect hourly data for one year prior to the start of the treatment and then continue collecting data for another year. This will yield approximately 9000 pre-treatment measurements and 9000 post treatment measurements for each subject.

The treatment is something that cannot be stopped once it is started, so a cross-over design could only be of the form AA/AB, which won't take advantage of the benefits of that type of design.

The psychological and bio-medical literature suggests using an ANCOVA model, where the pre-treatment data is used as a covariate in the model. Putting 9000 covariates in a model seems totally ridiculous. Also, reducing the pre-treatment data to a summary statistic doesn't take advantage of the large number of measurements.

I'm sure that this must have come up before, any ideas? References to published results would be especially helpful.

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    $\begingroup$ Is treatment randomly allocated? Is allocation concealed? Are the participants blinded to the treatment allocation? How long do you expect it will take for the treatment to have an effect? $\endgroup$ – onestop Dec 16 '10 at 22:24
  • $\begingroup$ @onestop, some good questions. I see that random allocation would have consequences for choosing a model, so let's assume random allocation, though if you have an model which uses self-selection (or ITT) into the treatment, I am very interested in that answer. Otherwise, say allocation is concealed, the participants know whether they are assigned to the control or treatment group, and the treatment should have an effect within several days, if not sooner. $\endgroup$ – Seth Dec 16 '10 at 23:05
  • $\begingroup$ @mbq Originally, the question was also tagged panel-data and mixed-model. The reason that I included these tags was because the data clearly falls into these categories. I was hoping that someone with experience using those models would have some suggestion. Economists, especially, often work with time-series panel-data data that changes as the result of some event. $\endgroup$ – Seth Dec 17 '10 at 21:49
  • $\begingroup$ Sorry, fixed. $\endgroup$ – user88 Dec 17 '10 at 21:51
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This is not a complete answer, but just a few thoughts:

  • More pre-treatment measures should increase the reliability of your measurement of baseline differences. Increasing reliability of measuring baseline differences should increase your statistical power in detecting group differences (assuming a real effect exists) using the pre-post control design.

  • 9000 pre-treatment measures is a lot. Such a design would usually imply that you are interested in the temporal dynamics of some phenomena. Nonetheless, if you are just using measurements as an indicator of baseline differences, then there would be a number of strategies for incorporating this into your model.

    • The simplest strategy would be to take the mean for each participant.
    • If there is trend in participant data, then an estimate of the individual's score just before the intervention may be more of interest.
    • Even more sophisticated would be to develop a model for each individual of what their score would be on the dependent variable following the intervention based on some projection using the pre-treatment measures. This might be more relevant if there was some form of seasonal or other systematic effect operating in different ways for different individuals.

You may also want to read this earlier question on strategies for analysing such designs.

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  • $\begingroup$ This is along the lines of what I have been thinking. I am considering running a separate multiple regression model for each subject using all of their pre-treatment data, then putting the result in as covariates in the ANCOVA. But, this seemed a lot like a multilevel model to me. I just can't think of how to structure the model. $\endgroup$ – Seth Dec 17 '10 at 21:44
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Excuse my previous post. I now see that you are not referring to 9000 different covariates.

What I have written does not apply to your situation.

Sincerest apologies.

Paul

There is a lot of discussion about matching and dimensionality reduction on pre-treatment covariates that may be worthwhile examining - i.e. propensity weighting via logistic regression and establishing balance on the pre-treatment covariates vis a vis different matching approaches.

Please refer to the following ............... http://gking.harvard.edu/matchit

This approach is easily executed in r, but the number of variables you have would be looking to use would be very unlikely to work.

Cheers Paul

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    $\begingroup$ That's why I asked if the treatment is randomly allocated - if it is then the groups would be expected to be balanced for all known and unknown covariates and matching or propensity score approaches aren't likely to be of use. $\endgroup$ – onestop Dec 17 '10 at 7:44

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