International Journal of Epidemiology 2002;31:163-165
© International Epidemiological Association 2002
Theory and Methods |
Fallibility in estimating direct effects
a Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, MD, USA.
b Department of Epidemiology, Harvard School of Public Health, MA, USA.
Dr Stephen Cole, Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, 615 N Wolfe St E-7139 Baltimore, MD 21205, USA. E-mail: scole{at}jhsph.edu
Abstract
We use causal graphs and a partly hypothetical example from the Physicians' Health Study to explain why a common standard method for quantifying direct effects (i.e. stratifying on the intermediate variable) may be flawed. Estimating direct effects without bias requires that two assumptions hold, namely the absence of unmeasured confounding for (1) exposure and outcome, and (2) the intermediate variable and outcome. Recommendations include collecting and incorporating potential confounders for the causal effect of the mediator on the outcome, as well as the causal effect of the exposure on the outcome, and clearly stating the additional assumption that there is no unmeasured confounding for the causal effect of the mediator on the outcome.
Keywords Causal inference, direct effect, intermediate variable, risk ratio
Accepted 11 July 2001
Epidemiologists often try to identify specific pathways through which an exposure may affect an endpoint. One standard method used to examine a potential pathway from an exposure E through a measured intermediate variable M to an endpoint D is to stratify the measure of effect between E and D by M. The residual association after adjustment for the posited intermediate variable is then interpreted as the direct effect of exposure on the endpoint through pathways other than that pathway marked by the intermediate variable.
Following Robins1 and Robins and Greenland,2 we define the direct effect of E on D controlling for M as the causal effect of E on D when the M value of everybody in the population is physically set to a predetermined value. Therefore, there are as many direct effects as levels of M, and hence we generally refer in plural to the direct effects of E on D. Robins1 and Robins and Greenland2 demonstrated that the standard method described above does not generally provide an unbiased estimate of the direct effects of exposure. Using a hypothetical example, Poole and Kaufman3 further demonstrated the inadequacy of this standard method. Below, we revisit this issue using directed acyclic graphs,4–6 and an example that appends two hypothetical variables to data from the Physicians' Health Study.7
Example
The Physicians' Health Study (PHS) was a randomized double blind 2 x 2 factorial placebo-controlled trial of 22 071 US male physicians assigned to aspirin and ß-carotene for the primary prevention of cardiovascular disease and cancer.7 The aspirin component of PHS was stopped in January 1988 after an average of 5 years of follow-up, due primarily to the emergence of a 44% reduction in risk of myocardial infarction (MI) among those randomized to aspirin compared to placebo. Let E = 1 represent randomization to aspirin and E = 0 randomization to placebo. Likewise, let D = 1 represent diagnosis of myocardial infarction (MI) during the defined period of follow-up, with all subjects free of such a diagnosis at the start of follow-up. Let M = 1 represent a hypothetical indicator of high platelet aggregation measured without error after allocation to aspirin, but before possible diagnosis of MI. For simplicity, we will assume that M is a dichotomous variable throughout.
Our goal is to estimate the direct effect of aspirin on MI when everybody is treated in such a way that his or her platelet aggregation level is kept low, and similarly when platelet aggregation is kept high. Note that an unambiguous definition of direct effects requires detailed specification of the method by which platelet aggregation levels are physically set. For simplicity, we will assume throughout that such a method exists and is generally accepted, although this is an issue that would require discussion among subject-matter experts.
Because of randomization, the crude risk ratio RRED of 0.6 (Table 1
) has, in principle, a causal interpretation indicating that aspirin exposure decreases the risk of MI. Imagine two investigators, one of who hypothesizes that the effect of exposure to aspirin causes the endpoint solely through reduced platelet aggregation (i.e. no direct effects of E on D). We may depict this hypothesis using a directed acyclic graph,
|
|
| ((1)) |
If graph (1)
represented the true state of nature, standard adjustment (stratification or regression) for M would leave no pathway from E to D (i.e. E would not be a cause of D within strata of M) and therefore the stratum-specific risk ratios RRED|M=m (m = 0, 1) and the Mantel-Haenszel summary risk ratio RRED|M would be 1. The second investigator agrees that aspirin use directly effects platelet aggregation but hypothesizes that the effect of aspirin on risk of MI goes through some other undetermined pathway not mediated by platelet aggregation (M), thereby proposing an alternative graph,
|
| ((2)) |
Under graph (2), adjustment for M would not alter the crude risk ratio RRED. Of course, one could hypothesize more complex alternate worlds where the effect of aspirin is both mediated through platelet aggregation and has a residual direct effect (possibly mediated through its anti-inflammatory properties). The partly hypothetical data from Table 2, with Mantel-Haenszel RRED|M = 0.6, apparently supports the second investigator's hypothesis. A naïve interpretation of this RR could lead to the conclusion that E exerts a direct protection on D after adjusting for M. We explain below why this interpretation is incorrect for this example.
|
The true causal graph, unknown to both investigators, is
|
| ((3)) |
is consistent with the first investigator's hypothesis, but she did not consider the existence of U. Recall that the genotype U, or any other pre-randomization variable, is not associated with aspirin assignment due to randomization. A cursory glance at causal graph (3) may leave one with the impression that the RRED|M should equal 1, not 0.6. However, it can be shown using the theory of directed acyclic graphs that stratifying on M will induce a spurious (non-causal) association between E and D because (1) E predicts M, and (2) the causal effect of M on D is confounded by U (refs5,8,9 for general explanations of causal graphs geared towards epidemiologists). An intuitive understanding may be gleaned from the following. First, among people with high platelet aggregation (M = 1), those randomized to aspirin will be more likely to harbour the predisposing genotype U (since the cause of their high platelet aggregation cannot be due to the absence of aspirin). Similarly, among people with low platelet aggregation (M = 0), those randomized to placebo will be more likely to lack the genotype U. Thus within both strata of M, there is a positive association between U and E (RRUEU|M=m > 1 for m = 0, 1). Second, U is inversely associated with D (RRUD|M=m = 0.1 for m = 0, 1). Given these two conditions, and an understanding of the directionality of confounding, an inverse association between E and D is generally expected after conditioning on M. The magnitude of this spurious association will depend upon the associations between the unmeasured genotype and platelet aggregation, and between the genotype and MI, which were relatively strong in this example (RRUM = 2.7 and RRUD = 0.2). As our example shows, this spurious association may appear even if E has no direct effect on D. We consider confounding to be present for the causal effect of an exposure A on an outcome B when there exists a common cause of A and B.9 In summary, we would expect a spurious association between E and D whenever (a) there is confounding for the effect of M on D (e.g. due to their common cause U), and (b) E predicts M. Note that M does not have to be on a causal pathway between E and D for the spurious association to occur.
One way to avoid this spurious association is to stratify on U in addition to M. Since this is a partly hypothetical example, we can stratify on both U and M and obtain a Mantel-Haenszel RRED|UM = 1.0 (Table 3). Under our causal graph (3), RRED|UM has a simple causal interpretation as the direct effect of E on D within levels of both U and M. If the direct effects varied across the four strata defined by U and M, one would likely present the four direct effects separately. Alternatively, one may wish to calculate an average causal direct effect (by pooling over levels of U and M).6 In real world applications U would remain unobserved and therefore estimation of RRED|MU would be impossible.
|
When U is difficult or impossible to measure, one could remove the spurious association by stratifying on any measured variable C that is in the causal pathway between U and M (or between U and D), for example
|
| ((4)) |
Note that stratifying on either U or C in data generated from graph (4) eliminates confounding of the effect of M on D.5 But if C itself is affected by exposure, for example,
|
| ((5)) |
,then no standard method (stratification or regression) can estimate the direct effects of interest without bias. Therefore, in cases where either U or C are affected by exposure E, a more general analytical framework for direct effects estimation is needed, such as Robins' non-parametric (g-formula1,10) or semi-parametric (direct effect nested structural models,11 marginal structural models12) causal methods. As long as either U or C is measured and there is no model misspecification, these methods provide estimates that can be causally interpreted as the direct effect of E on D controlling for M.
Conclusion
Estimating direct effects requires the absence of unmeasured confounding for the effect of both the exposure and the intermediate variable on the outcome. If both of these conditions do not hold then no method is able to provide unbiased estimates the direct effects of exposure. Unfortunately, these assumptions of no unmeasured confounding are not testable given observed data. The directed acyclic graphs we presented are overly simplistic depictions of an often-complex world. However, understanding the assumptions necessary for correct estimation of direct effects in such simple worlds is prerequisite to any extension towards more realistic scenarios.
A recommendation to practising epidemiologists who wish to estimate direct effects of exposure is threefold. First, at the study planning stage collect potential confounders for the mediator-outcome association, as well as the exposure-outcome association. Second, at the study analysis stage, incorporate these additional variables (using standard or causal methods, as needed) in an attempt to correctly control for both paths of confounding. In particular, causal methods are generally required when one needs to adjust for variables affected by the exposure. Third, when communicating research results, clearly state and examine the additional assumption that there is no unmeasured confounding for the causal effect of the mediator on the outcome.
Acknowledgments
We thank Drs James Robins, Sander Greenland and Nancy Cook, as well as three anonymous reviewers for helpful suggestions and comments. Dr Cole was partly supported by the US National Institute of Allergy and Infectious Diseases by means of the data coordinating centers for the Multicenter AIDS Cohort (U01-Al-35043) and Women's Interagency HIV (U01-Al-42590) studies.
References
1 Robins JM. A new approach to causal inference in mortality studies with a sustained exposure period: application to the healthy worker survivor effect. Mathematical Modeling 1986;7:1393–512.
2 Robins JM, Greenland S. Identifiability and exchangeability for direct and indirect effects. Epidemiology 1992;3:143–55.[Web of Science][Medline]
3 Poole C, Kaufman JS. What does standard adjustment for downstream mediators tell us about social effect pathways? Am J Epidemiol 2000;151:S52.
4
Pearl J. Causal diagrams for empirical research. Biometrika 1995;82: 669–710.
5 Greenland S, Pearl J, Robins JM. Causal diagrams for epidemiologic research. Epidemiology 1999;10:37–48.[CrossRef][Web of Science][Medline]
6 Pearl J. Causality. New York: Cambridge, 2000.
7 Final report on the aspirin component of the ongoing Physicians' Health Study. Steering Committee of the Physicians' Health Study Research Group. N Engl J Med 1989;321:129–35.[Abstract]
8 Robins JM. Data, design, and background knowledge in etiologic inference. Epidemiology 2001;12:313–20.[CrossRef][Web of Science][Medline]
9 Hernán MA, Hernandez-Diaz S, Werler MM, Mitchell AA. Causal knowledge as a prerequisite for confounding evaluation: an application to birth defects epidemiology. Am J Epidemiol 2001;In press.
10 Robins J. The control of confounding by intermediate variables. Stat Med 1989;8:679–701.[Web of Science][Medline]
11 Robins JM. Testing and estimation of direct effects by reparameterizing directed acyclic graphs with structural nested models. In: Glymour C, Cooper G (eds). Computation, Causation, and Discovery. Menlo Park, CA: AAAI Press/The MIT Press, 1999, pp.349–405.
12 Robins JM, Hernán MA, Brumback B. Marginal structural models and causal inference in epidemiology. Epidemiology 2000;11:550–60.[CrossRef][Web of Science][Medline]
CiteULike 
Connotea 
Del.icio.us What's this?
This article has been cited by other articles:
|
|
 |
|
  D. M. Hafeman "Proportion Explained": A Causal Interpretation for Standard Measures of Indirect Effect? Am. J. Epidemiol., December 1, 2009; 170(11): 1443 - 1448. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
S. R. Cole, L. P. Jacobson, P. C. Tien, L. Kingsley, J. S. Chmiel, and K. Anastos Using Marginal Structural Measurement-Error Models to Estimate the Long-term Effect of Antiretroviral Therapy on Incident AIDS or Death Am. J. Epidemiol., November 24, 2009; (2009) kwp329v1. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 S. R Cole, R. W Platt, E. F Schisterman, H. Chu, D. Westreich, D. Richardson, and C. Poole Illustrating bias due to conditioning on a collider Int. J. Epidemiol., November 19, 2009; (2009) dyp334v1. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 A. H. Auchincloss, A. V. D. Roux, M. S. Mujahid, M. Shen, A. G. Bertoni, and M. R. Carnethon Neighborhood Resources for Physical Activity and Healthy Foods and Incidence of Type 2 Diabetes Mellitus: The Multi-Ethnic Study of Atherosclerosis Arch Intern Med, October 12, 2009; 169(18): 1698 - 1704. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 G D. Datta, B A Neville, I Kawachi, N S Datta, and C C Earle Marital status and survival following bladder cancer J Epidemiol Community Health, October 1, 2009; 63(10): 807 - 813. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 L. H. Mortensen, F. Diderichsen, G. D. Smith, and A. M. N. Andersen The social gradient in birthweight at term: quantification of the mediating role of maternal smoking and body mass index Hum. Reprod., October 1, 2009; 24(10): 2629 - 2635. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
V. Skalicka, F. van Lenthe, C. Bambra, S. Krokstad, and J. Mackenbach Material, psychosocial, behavioural and biomedical factors in the explanation of relative socio-economic inequalities in mortality: evidence from the HUNT study Int. J. Epidemiol., October 1, 2009; 38(5): 1272 - 1284. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
D. M Hafeman and S. Schwartz Opening the Black Box: a motivation for the assessment of mediation Int. J. Epidemiol., June 1, 2009; 38(3): 838 - 845. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. P Fox, D. R Brooks, L. Kuhn, G. Aldrovandi, M. Sinkala, C. Kankasa, R. Horsburgh, and D. M Thea Role of breastfeeding cessation in mediating the relationship between maternal HIV disease stage and increased child mortality among HIV-exposed uninfected children Int. J. Epidemiol., April 1, 2009; 38(2): 569 - 576. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
E. B. Loucks, J. W. Lynch, L. Pilote, R. Fuhrer, N. D. Almeida, H. Richard, G. Agha, J. M. Murabito, and E. J. Benjamin Life-Course Socioeconomic Position and Incidence of Coronary Heart Disease: The Framingham Offspring Study Am. J. Epidemiol., April 1, 2009; 169(7): 829 - 836. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. Tobias, T. Blakely, D. Matheson, K. Rasanathan, and J. Atkinson Changing trends in indigenous inequalities in mortality: lessons from New Zealand Int. J. Epidemiol., March 30, 2009; (2009) dyp156v1. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M Richards, C Power, and A Sacker Paths to literacy and numeracy problems: evidence from two British birth cohorts J Epidemiol Community Health, March 1, 2009; 63(3): 239 - 244. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 S. Wacholder, N. Chatterjee, and N. Caporaso Intermediacy and Gene-Environment Interaction: The Example of CHRNA5-A3 Region, Smoking, Nicotine Dependence, and Lung Cancer J Natl Cancer Inst, November 5, 2008; 100(21): 1488 - 1491. [Full Text] [PDF]
|
|
|
|
|
|
A V D. Roux Next steps in understanding the multilevel determinants of health J Epidemiol Community Health, November 1, 2008; 62(11): 957 - 959. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
F I. Gunasekara, K Carter, and T Blakely Glossary for econometrics and epidemiology J Epidemiol Community Health, October 1, 2008; 62(10): 858 - 861. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
N L Fleischer and A V D. Roux Using directed acyclic graphs to guide analyses of neighbourhood health effects: an introduction J Epidemiol Community Health, September 1, 2008; 62(9): 842 - 846. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 H. Zhang, L. A. Garcia Rodriguez, and S. Hernandez-Diaz Antibiotic Use and the Risk of Lung Cancer Cancer Epidemiol. Biomarkers Prev., June 1, 2008; 17(6): 1308 - 1315. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. S. Mujahid, A. V. D. Roux, M. Shen, D. Gowda, B. Sanchez, S. Shea, D. R. Jacobs Jr., and S. A. Jackson Relation between Neighborhood Environments and Obesity in the Multi-Ethnic Study of Atherosclerosis Am. J. Epidemiol., June 1, 2008; 167(11): 1349 - 1357. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 M. Avendano and M. M. Glymour Stroke Disparities in Older Americans: Is Wealth a More Powerful Indicator of Risk Than Income and Education? Stroke, May 1, 2008; 39(5): 1533 - 1540. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
Y. C. Cohen, K. S. Liu, N. L. Heyden, A. D. Carides, K. M. Anderson, A. G. Daifotis, and P. H. Gann Detection Bias Due to the Effect of Finasteride on Prostate Volume: A Modeling Approach for Analysis of the Prostate Cancer Prevention Trial J Natl Cancer Inst, September 19, 2007; 99(18): 1366 - 1374. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. M. Glymour, M. Avendano, and L. F. Berkman Is the 'Stroke Belt' Worn From Childhood?: Risk of First Stroke and State of Residence in Childhood and Adulthood Stroke, September 1, 2007; 38(9): 2415 - 2421. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 N. Pearce, H. Checkoway, and D. Kriebel Bias in occupational epidemiology studies Occup. Environ. Med., August 1, 2007; 64(8): 562 - 568. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
I. Delbaere, S. Vansteelandt, D. De Bacquer, H. Verstraelen, J. Gerris, P. De Sutter, and M. Temmerman Should we adjust for gestational age when analysing birth weights? The use of z-scores revisited Hum. Reprod., August 1, 2007; 22(8): 2080 - 2083. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
S. R. Cole, M. A. Hernan, K. Anastos, B. D. Jamieson, and J. M. Robins Determining the Effect of Highly Active Antiretroviral Therapy on Changes in Human Immunodeficiency Virus Type 1 RNA Viral Load using a Marginal Structural Left-censored Mean Model Am. J. Epidemiol., July 15, 2007; 166(2): 219 - 227. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M M. Glymour Commentary: Selected samples and nebulous measures: some methodological difficulties in life-course epidemiology Int. J. Epidemiol., June 1, 2007; 36(3): 566 - 568. [Full Text] [PDF]
|
|
|
|
 |
|
 M.-J. A. Brion, S. D. Leary, G. D. Smith, and A. R. Ness Similar Associations of Parental Prenatal Smoking Suggest Child Blood Pressure Is Not Influenced by Intrauterine Effects Hypertension, June 1, 2007; 49(6): 1422 - 1428. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
H Lopez-Gatell, S. Cole, N. Hessol, A. French, R. Greenblatt, S Landesman, S Preston-Martin, and K Anastos Effect of Tuberculosis on the Survival of Women Infected with Human Immunodeficiency Virus Am. J. Epidemiol., May 15, 2007; 165(10): 1134 - 1142. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
N. E. Caporaso Integrative Study Designs--Next Step in the Evolution of Molecular Epidemiology? Cancer Epidemiol. Biomarkers Prev., March 1, 2007; 16(3): 365 - 366. [Full Text] [PDF]
|
|
|
|
|
|
A. H. Auchincloss, A. V. Diez Roux, D. G. Brown, E. S. O'Meara, and T. E. Raghunathan Association of Insulin Resistance with Distance to Wealthy Areas: The Multi-Ethnic Study of Atherosclerosis Am. J. Epidemiol., February 15, 2007; 165(4): 389 - 397. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
S. Hernandez-Diaz, E. F. Schisterman, and M. A. Hernan The Birth Weight "Paradox" Uncovered? Am. J. Epidemiol., December 1, 2006; 164(11): 1115 - 1120. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 L. A. Stevens, T. Greene, and A. S. Levey Surrogate End Points for Clinical Trials of Kidney Disease Progression Clin. J. Am. Soc. Nephrol., July 1, 2006; 1(4): 874 - 884. [Full Text] [PDF]
|
|
|
|
|
|
O. Klungsoyr, J. F. Nygard, T. Sorensen, and I. Sandanger Cigarette Smoking and Incidence of First Depressive Episode: An 11-Year, Population-based Follow-up Study Am. J. Epidemiol., March 1, 2006; 163(5): 421 - 432. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 R. C. Thurston, L. D. Kubzansky, I. Kawachi, and L. F. Berkman Do Depression and Anxiety Mediate the Link Between Educational Attainment and CHD? Psychosom Med, January 1, 2006; 68(1): 25 - 32. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
B. L. De Stavola, D. Nitsch, I. dos Santos Silva, V. McCormack, R. Hardy, V. Mann, T. J. Cole, S. Morton, and D. A. Leon Statistical Issues in Life Course Epidemiology Am. J. Epidemiol., January 1, 2006; 163(1): 84 - 96. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
L. M. Bodnar, R. B. Ness, G. F. Harger, and J. M. Roberts Inflammation and Triglycerides Partially Mediate the Effect of Prepregnancy Body Mass Index on the Risk of Preeclampsia Am. J. Epidemiol., December 15, 2005; 162(12): 1198 - 1206. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
T. Blakely and N. Wilson The contribution of smoking to inequalities in mortality by education varies over time and by sex: two national cohort studies, 1981-84 and 1996-99 Int. J. Epidemiol., October 1, 2005; 34(5): 1054 - 1062. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
S. R. Cole, M. A. Hernan, J. B. Margolick, M. H. Cohen, and J. M. Robins Marginal Structural Models for Estimating the Effect of Highly Active Antiretroviral Therapy Initiation on CD4 Cell Count Am. J. Epidemiol., September 1, 2005; 162(5): 471 - 478. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
C. J. Newschaffer and S. R. Cole Invited Commentary: Risk Factors for Autism--Perinatal Factors, Parental Psychiatric History, and Socioeconomic Status Am. J. Epidemiol., May 15, 2005; 161(10): 926 - 928. [Full Text] [PDF]
|
|
|
|
|
|
A. V Diez Roux Commentary: Estimating and understanding area health effects Int. J. Epidemiol., April 1, 2005; 34(2): 284 - 285. [Full Text] [PDF]
|
|
|
|
|
|
N. J. S. Christenfeld, R. P. Sloan, D. Carroll, and S. Greenland Risk Factors, Confounding, and the Illusion of Statistical Control Psychosom Med, November 1, 2004; 66(6): 868 - 875. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
T. Blakely, I. Kawachi, J. Atkinson, and J. Fawcett Income and mortality: the shape of the association and confounding New Zealand Census-Mortality Study, 1981-1999 Int. J. Epidemiol., August 1, 2004; 33(4): 874 - 883. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 A. V. Diez Roux The Study of Group-Level Factors in Epidemiology: Rethinking Variables, Study Designs, and Analytical Approaches Epidemiol. Rev., July 1, 2004; 26(1): 104 - 111. [Full Text] [PDF]
|
|
|
|
|
|
N Wilson, G Thomson, M Tobias, and T Blakely How much downside? Quantifying the relative harm from tobacco taxation J Epidemiol Community Health, June 1, 2004; 58(6): 451 - 454. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
S. R. Cole, M. A. Hernan, J. M. Robins, K. Anastos, J. Chmiel, R. Detels, C. Ervin, J. Feldman, R. Greenblatt, L. Kingsley, et al. Effect of Highly Active Antiretroviral Therapy on Time to Acquired Immunodeficiency Syndrome or Death using Marginal Structural Models Am. J. Epidemiol., October 1, 2003; 158(7): 687 - 694. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
S. Greenland and B. Brumback An overview of relations among causal modelling methods Int. J. Epidemiol., October 1, 2002; 31(5): 1030 - 1037. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
F. Mendez, A. Munoz, G. Carrasquilla, D. Jurado, M. Arevalo-Herrera, J. F. Cortese, and C. V. Plowe Determinants of Treatment Response to Sulfadoxine-Pyrimethamine and Subsequent Transmission Potential in Falciparum Malaria Am. J. Epidemiol., August 1, 2002; 156(3): 230 - 238. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
T. Blakely Commentary: Estimating direct and indirect effects--fallible in theory, but in the real world? Int. J. Epidemiol., February 1, 2002; 31(1): 166 - 167. [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||