To : Cc: Bcc: 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/

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. 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 belo w**  ), 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

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### 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 ), p lease 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 function 9 5 > drop education unmz

_ causes function95 change95

_ 98" >

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> **W hen Changed sign of educatio**  **n :**  > > 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

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