Re: st: Estimating Independent Contribution of Each Alzheimer's Risk Factor

["Austin Nichols" <austinnichols@gmail.com>]

Dear  William Rodman Shankle:
Part 1 (Data) below presents an interesting problem in meta-analysis,
about which I know only a little, but I don't think Part 2 (Method)
helps you at all.
Suppose you have 81 studies, each of which has nine coefficients of a
possible 41, and you satisfy some rank condition  (the overlap of
coefficients across studies is sufficient to identify all population
parameters).  You can treat the 32 coefficients not included in any
given study as constrained to be zero, but that does not solve the
problem that the remaining nine coefficients suffer from omitted
variable bias.  There is no one/zero dichotomy that I see here--you
want to use the estimated effects from each study somehow.
I am guessing there is a nice Bayesian approach, or a very messy
pseudo maximum likelihood [see Gourieroux, C., Monfort, A., and
Trognon, A. (1984) Pseudomaximum likelihood methods: theory.
Econometrika, 52, 681--700.] version of meta-analysis that might
work... but I don't know it.
Perhaps someone else will chime in with an elegant answer.
--Austin

ps. OTOH, if you don't think there is any omitted variable bias, then
I guess you can run separate meta-analyses for each subset of studies
with the relevant set of coefficient estimates.

On 7/6/06, William Rodman Shankle <rshankle@mccare.com> wrote:
> Dear Statalisters,
> I would appreciate any knowledge whether the following method estimates
> the independent effect of each AD risk factor
> 1.  Data:
>     a. 81 studies measured the relative risk ratio of AD (Y, the
> dependent variable).
>     b. Among these 81 studies, 41 risk factors (X, the independent
> variables) were found make significant contribution to AD relative risk.
>     c. Each study measured only a subset of the 41 risk factors.
>     d. One therefore does not know, from any single study, what are the
> independent contributions of each AD risk factor.
>
> 2. Method:
>     a. Treat the 81 studies as 81 rows of a matrix.  Each row is
> characterized by the AD relative risk ratio, Y.
>     b. Treat the 41 AD risk factors, X, as the columns of this matrix.
>     c. For each study (row),  put a "1" in all columns where the risk
> factors were measured, and put a "0" in all columns where the risk
> factors were not measured.
>     d. This gives an 81 by 41 binary matrix.
>     d. Apply matrix algebra, Y = B*X to estimate the independent
> coefficients, B, of each AD risk factor
>     e. I think this method is equivalent to a multivariate linear
> regression model.
>
> Are the estimated coefficients, B, truly independent of each other?
> If not, are there any suggestions about making them more independent?
>
> Thank you for your knowledge,
> Sincerely,
> Rod Shankle
>
> --
> William Rodman Shankle, MS MD
> Neurologist Specialized in Alzheimer's Disease and Related Disorders
> Research Fellow, Cognitive Sciences, UC Irvine
> Chief Medical Officer, Medical Care Corporation
> Office: 949 833 2383
> Facsimile: 949 838 0153
> Address: 19782 Macarthur Blvd, Suite 310, Irvine, CA 92612
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