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From |
"Joseph Coveney" <jcoveney@bigplanet.com> |

To |
"Statalist" <statalist@hsphsun2.harvard.edu> |

Subject |
Re: st: MANCOVA versus Zellner's SUR |

Date |
Tue, 6 Nov 2007 13:50:16 +0900 |

Phil Schumm wrote: Focusing for a moment on just one outcome, your options are essentially (1) an analysis of the change scores, or (2) regression of the outcome on the treatment indicator and the baseline value. Option (2) can give inconsistent estimates of the treatment effect due to measurement error in y_1 unless your treatment assignment is randomized (e.g., Allison 1990), which you indicated is the case here. The advantage of (2) is that it is more efficient (as you point out), and yields a result that is often of direct interest (i.e., the difference between treatment groups in the mean value of y_2 for a given *observed* value of y_1). There was a thread in the American Statistician on these issues a while back; Laird (1983) is a good entry point. Once you have a model for each outcome that you feel comfortable with, you can then think about estimating them jointly either to increase efficiency and/or to permit joint tests (e.g., to construct a single test of treatment effect for both outcomes). Certainly - sureg- provides one reasonable approach for doing this. Your other approach -- multivariate regression in which both outcomes are regressed on both sets of baseline values -- strikes me as unjustifiable, unless you are really interested in the effects of the baseline value of one measure on the post-treatment value of the other. Of course, if you are really interested in this, then you also need to consider the effect that measurement error in the baseline values may have on your analysis. Personally, whenever I've been faced with an analysis of pre/post data, I've always started by considering several specific models for the measurement process and for the effect(s) of the treatment (e.g., homogeneous versus heterogeneous, dependent on the baseline value of the outcome, etc.), and tried to figure out what the implications of these were for different analyses. There's a limit to what you can do in terms of estimation with only a single pre and post measurement, of course, but I have still found this exercise to be helpful. The papers cited here (and their references) provide several good examples of what I am talking about. -------------------------------------------------------------------------------- Thanks again, Phil, for the follow-up. I'll see if I can get my hands on a copy of the Allison paper. You make several good points. The study will be conducted in a so-called government-regulated environment. The analysis must be specified in detail in writing in advance, and so there isn't much opportunity after the data are in hand to find a model to be comfortable with. In accordance with the study's primary objective, the primary analysis is geared toward hypothesis testing instead of estimation. The use of the response variable at baseline as a covariate is solely utilitarian, to increase efficiency. (Of course, should the treatment null hypothesis be rejected, a natural question arises as to the nature of the effect, and answering that will involve estimation.) I'm with you in having reservations about including both responses as covariates in a multivariate regression. But it might help thinking about it not as involving a regression left_after upon right_before and vice versa, but rather as regressing a response vector upon a vector of predictors--the latter happens to include baseline responses among the other predictors shared by each element of the response vector. I still like -sureg-, though. But client's love to see that "exact" that you'll get in the -manova- printout, and don't like any fiddling with the denominator degrees of freedom after -sureg-. I know that when there is randomized assignment to treatment group the expectation is zero for the correlation between the baseline covariate and treatment. But I was concerned that a finite-sample realization as a given study will have a nonzero correlation, in practice. Simulations with univariate regressions have been reassuring, though, in that there hasn't been any discernable association between realized correlation coefficient and regression-coefficient attenuation in sample sizes of 50 per treatment group. It seems that a pretest response as a covariate doesn't behave like an errors-in-variables predictor, that, because the source of errors for the response is the same before and after, the errors can be assigned entirely to the posttest response. Joseph Coveney * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: MANCOVA versus Zellner's SUR***From:*David Airey <david.airey@Vanderbilt.Edu>

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