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From |
David Airey <david.airey@Vanderbilt.Edu> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Tue, 6 Nov 2007 10:54:08 -0600 |

This might be off topic, but I liked a recent paper by Senn:

Senn S (2006) Change from baseline and analysis of covariance revisited. Statist. Med. 2006; 25:4334–4344

The case for preferring analysis of covariance (ANCOVA) to the simple analysis of change scores (SACS) has often been made. Nevertheless, claims continue to be made that analysis of covariance is biased if the groups are not equal at baseline. If the required equality were in expectation only, this would permit the use of ANCOVA in randomized clinical trials but not in observational studies. The discussion is related to Lord’s paradox. In this note, it is shown, however that it is not a necessary condition for groups to be equal at baseline, not even in expectation, for ANCOVA to provide unbiased estimates of treatment effects. It is also shown that although many situations can be envisaged where ANCOVA is biased it is very difﬁcult to imagine circumstances under which SACS would then be unbiased and a causal interpretation could be made.

On Nov 5, 2007, at 10:50 PM, Joseph Coveney wrote:

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

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-- David C. Airey, Ph.D. Pharmacology Research Assistant Professor Center for Human Genetics Research Member Department of Pharmacology School of Medicine Vanderbilt University Rm 8158A Bldg MR3 465 21st Avenue South Nashville, TN 37232-8548 TEL (615) 936-1510 FAX (615) 936-3747 EMAIL david.airey@vanderbilt.edu URL http://people.vanderbilt.edu/~david.c.airey/dca_cv.pdf URL http://www.vanderbilt.edu/pharmacology * * 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/

**References**:**Re: st: MANCOVA versus Zellner's SUR***From:*"Joseph Coveney" <jcoveney@bigplanet.com>

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