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Subject: Fw: Data Clarification for Glymour et al 2005

From: Maria Glymour <mglymour@hsph.harvard.edu>

To: David Svendsgaard/RTP/USEPA/US@EPA

Date: 09/05/2012 11:39 AM

Subject: Re: Negative bias when adjusting for baseline and health status has changed prior to exposure

Sent by: mglymour@gmail.com

Hi David,

I agree. In general (there are exceptions) collider bias (i.e. the

association between E and U induced by conditioning on function95 if

the DAG is: E-->function95<--U ) will be negative if E and U both

positively affect M but positive if the effects of E and U on M are of

opposite signs (as in your 2nd example). The direction of the net

bias induced by adjusting for baseline cognition in this example is

the product of the sign of the collider bias and the sign of the

effect of U on the outcome. So yes, you can get the sign of net bias

in horse racing to go either way, if you flip the sign of

E-->function95 or U-->function95 or U-->Y.

I haven't looked back at the original paper but we may well have not

been clear about that. Certainly I did not consider the situation in

which education was associated with worse baseline cognitive function!

But regardless we should not have claimed that this type of bias will

always be negative regardless of the direction of the other effects.

In non-linear models, or if you restrict to a single stratum of

function95, you can also get the bias to go in unexpected directions.

Therefore, you cannot conclusively predict the direction of bias

without a bit more specificity on the underlying causal structure.

Thanks for the interesting question.

All best,

Maria

Maria Glymour, ScD

Assistant Professor

Department of Society, Human Development, and Health

Harvard School of Public Health

677 Huntington Avenue, Kresge 617 | Boston, MA 02115

phone: (617) 432-7454 | fax: (617) 432-3755

http://tinyurl.com/GlymourAppointments/

http://www.hsph.harvard.edu/faculty/maria-glymour/

..............................................................................

.

On Wed, Sep 5, 2012 at 10:09 AM, David Svendsgaard

<Svendsgaard.David@epamail.epa.gov> wrote:

> Hi

>

> Congratulations on an important paper. However, you report a negative bias

> when I think the bias is in the opposite direction of the effect of

> education on function95.

>

> I used the STATA code you provided for figure 4 of Glymour et al (2005)

>
> I changed the effect of education so that it is negative (see below), and 

found a

> positive bias when using baseline adjustment.

>

> This indicates to me that if the expected effects of prior exposure and

> exposure during the longitudinal study have the same sign, then

> the exposure effect is underestimated.

>

> Do you agree?

>

> Sincerely,

>

> David

>

> David J Svendsgaard, PhD

> Biostatistician

> EPA/ORD/NCEA/RTP, Mail Drop B-243-01

> Research Triangle Park, NC 27711

> Phone (919) 541-4186

> Fax (919) 541-1818

......................................................................

Original article:

http://dx.doi.org/10.1093/aje/kwi187

Letter to the editor:

http://dx.doi.org/10.1093/aje/kwj358

Am J Epidemiol 2006;164:1138–1139.

Reply to Letter to the editor:

http://dx.doi.org/10.1093/aje/kwj360

Am J Epidemiol 2006;164:1139–1140.

Reference to Code (Web-only Appendix / Supplemental Material; from the Reply:

http://aje.oxfordjournals.org/content/164/11/1139/suppl/DC1

"They may also be useful for understanding the issue of statistical power raised in the 

letter (1).

For an example of STATA code (StataCorp LP, College Station, Texas) that can be used 

to generate data 

following the causal structure of the DAGs presented in our paper (2), please refer to the 

Web appendix."

> "The code below generates a data set to demonstrate bias due to 

horse-racing,

> i.e. when there is an unmeasured cause of decline that influences both 

the baseline

> function and the change experienced over the follow-up period (similar 

to Figure 4 in the

> original paper)."

>

> "Fig4Sim.do

> set obs 10000

> gen education=invnorm(uniform())

> gen unmz_causes=invnorm(uniform())

> gen function95=.5*education+.5* unmz_causes+.7*invnorm(uniform())

> gen change95_98=.5*unmz_causes+.85*invnorm(uniform())

> reg change95_98 education
> reg change95_98 education function95

> drop education unmz_causes function95 change95_98"

>

..............................................................................

................

> When Changed sign of education:

>

> set obs 10000

> gen education=invnorm(uniform())

> gen unmz_causes=invnorm(uniform())

> gen function95=-.5*education+.5* unmz_causes+.7*invnorm(uniform())

> gen change95_98=.5*unmz_causes+.85*invnorm(uniform())

> reg change95_98 education

> reg change95_98 education function95

> drop education unmz_causes function95 change95_98

--