Confounding and effect modification: distribution and measure

This paper revisits the properties of and relationships between confounding and effect modification. The topic has of course received attention in the past (Miettinen, 1974; Greenland and Morgenstern, 1989; Geng and Li, 2002; Sturmer et al., 2006; Rothman et al., 2008). Here, I would like to revisit it in light of insights that can be drawn from the causal inference literature and also with an eye towards a further distinction that can be drawn concerning how these two epidemiologic concepts relate both to overall distributions and to specific measures. The paper describes how both confounding and effect modification may be defined so as to make reference to an entire distribution of potential outcomes or so as to reference a specific measure. The paper then also considers (i) the conditionality of both concepts, (ii) the relation of both concepts to study design, (iii) that both concepts are properties of the population, (iv) that both concepts are relative with respect to exposure and the outcome, (v) implications that hold between confounding and effect modification and (vi) the relation of both concepts to statistical models. The paper concludes by discussing a few points concerning how relations between confounding and effect modification, as they relate to both distribution and measure, are relevant for data analysis and interpretation.

[1]  T. VanderWeele.  The Sign of the Bias of Unmeasured Confounding , 2008, Biometrics.

[2]  I. Shpitser,et al.  A New Criterion for Confounder Selection , 2011, Biometrics.

[3]  Richard M Martin,et al.  Effects of prolonged and exclusive breastfeeding on child height, weight, adiposity, and blood pressure at age 6.5 y: evidence from a large randomized trial. , 2007, The American journal of clinical nutrition.

[4]  S Greenland,et al.  Randomization, Statistics, and Causal Inference , 1990, Epidemiology.

[5]  N. Jewell,et al.  Some surprising results about covariate adjustment in logistic regression models , 1991 .

[6]  Z. Geng,et al.  Conditions for Non‐confounding and Collapsibility without Knowledge of Completely Constructed Causal Diagrams , 2002 .

[7]  C. Charig,et al.  Comparison of treatment of renal calculi by open surgery, percutaneous nephrolithotomy, and extracorporeal shockwave lithotripsy. , 1986, British medical journal.

[8]  T. VanderWeele,et al.  Interpretation of Subgroup Analyses in Randomized Trials: Heterogeneity Versus Secondary Interventions , 2011, Annals of Internal Medicine.

[9]  J. Robins,et al.  Marginal Structural Models and Causal Inference in Epidemiology , 2000, Epidemiology.

[10]  G. Leung,et al.  Does breastfeeding protect against childhood overweight? Hong Kong's 'Children of 1997' birth cohort. , 2010, International journal of epidemiology.

[11]  Timothy L. Lash,et al.  Applying Quantitative Bias Analysis to Epidemiologic Data , 2009, Statistics for Biology and Health.

[12]  K J Rothman,et al.  Epidemiologic methods in clinical trials , 1977, Cancer.

[13]  L. Fisher,et al.  Matching and unrelatedness. , 1974, American journal of epidemiology.

[14]  S. Cole,et al.  Illustrating bias due to conditioning on a collider. , 2010, International journal of epidemiology.

[15]  Onyebuchi A Arah,et al.  Bias Formulas for Sensitivity Analysis of Unmeasured Confounding for General Outcomes, Treatments, and Confounders , 2011, Epidemiology.

[16]  J. Robins.  Estimation of the time-dependent accelerated failure time model in the presence of confounding factors , 1992 .

[17]  J. Pearl,et al.  Confounding and Collapsibility in Causal Inference , 1999 .

[18]  D B Rubin,et al.  Practical implications of modes of statistical inference for causal effects and the critical role of the assignment mechanism. , 1991, Biometrics.