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The role of causal reasoning in understanding Simpson's paradox, Lord's paradox, and the suppression effect: covariate selection in the analysis of observational studies.

Arah OA - Emerg Themes Epidemiol (2008)

Bottom Line: They conclude that all three simply reiterate the occurrence of a change in the association of any two variables when a third variable is statistically controlled for.At the heart of the phenomenon of change in magnitude, with or without reversal of effect estimate, is the question of which to use: the unadjusted (combined table) or adjusted (sub-table) estimate.It cannot be overemphasized that although these paradoxes reveal the perils of using statistical criteria to guide causal analysis, they hold neither the explanations of the phenomenon they depict nor the pointers on how to avoid them.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Social Medicine, Academic Medical Center, University of Amsterdam, Amsterdam, The Netherlands. o.a.arah@amc.uva.nl

ABSTRACT
Tu et al present an analysis of the equivalence of three paradoxes, namely, Simpson's, Lord's, and the suppression phenomena. They conclude that all three simply reiterate the occurrence of a change in the association of any two variables when a third variable is statistically controlled for. This is not surprising because reversal or change in magnitude is common in conditional analysis. At the heart of the phenomenon of change in magnitude, with or without reversal of effect estimate, is the question of which to use: the unadjusted (combined table) or adjusted (sub-table) estimate. Hence, Simpson's paradox and related phenomena are a problem of covariate selection and adjustment (when to adjust or not) in the causal analysis of non-experimental data. It cannot be overemphasized that although these paradoxes reveal the perils of using statistical criteria to guide causal analysis, they hold neither the explanations of the phenomenon they depict nor the pointers on how to avoid them. The explanations and solutions lie in causal reasoning which relies on background knowledge, not statistical criteria.

No MeSH data available.


Related in: MedlinePlus

DAG showing a scenario where birth weight (BW) has a causal effect on and shares a common cause – current weight (CW) – with blood pressure (BP). That is, the relationship between BW and BP is confounded by CW.
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Figure 2: DAG showing a scenario where birth weight (BW) has a causal effect on and shares a common cause – current weight (CW) – with blood pressure (BP). That is, the relationship between BW and BP is confounded by CW.

Mentions: Now, suppose there are no other unmeasured covariates given the DAGs in Figures 1 to 7. If Figure 1 is the true state of affairs, to estimate the total effect of BW on BP, the unadjusted analysis will suffice. If, however, Figure 2 or 3 applies, then the adjusted (that is conditional on CW) is needed to estimate the total effect of BW on BP. This is because conditioning on CW will block the back-door BW to BP: BW←CW→BP in Figure 2 or BW←U→CW→BP in Figure 3. The reader could by now have doubts about the correctness of Figure 2 where a later observation CW is a confounder of the effect of BW on BP since one could argue that, by occurring after BW, CW could not be seen as a common cause of both BW and BP. (See Hernán et al [8] for an accessible defence of the structural approach to confounding and selection bias using DAGs.) Nonetheless, while temporality seemingly excludes CW as a confounder in Figure 2, it does not exclude CW from ever being part of a confounding path as seen in Figure 3. Both BW and CW are more likely to be the result of a common cause (U), possibly genetic. Based on background knowledge and common sense, Figure 3 is more plausible than 2. Therefore, temporality cannot be used to judge whether a variable is a confounder, part of a sufficient subset of covariates needed to block a backdoor, or not [5].


The role of causal reasoning in understanding Simpson's paradox, Lord's paradox, and the suppression effect: covariate selection in the analysis of observational studies.

Arah OA - Emerg Themes Epidemiol (2008)

DAG showing a scenario where birth weight (BW) has a causal effect on and shares a common cause – current weight (CW) – with blood pressure (BP). That is, the relationship between BW and BP is confounded by CW.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2266743&req=5

Figure 2: DAG showing a scenario where birth weight (BW) has a causal effect on and shares a common cause – current weight (CW) – with blood pressure (BP). That is, the relationship between BW and BP is confounded by CW.
Mentions: Now, suppose there are no other unmeasured covariates given the DAGs in Figures 1 to 7. If Figure 1 is the true state of affairs, to estimate the total effect of BW on BP, the unadjusted analysis will suffice. If, however, Figure 2 or 3 applies, then the adjusted (that is conditional on CW) is needed to estimate the total effect of BW on BP. This is because conditioning on CW will block the back-door BW to BP: BW←CW→BP in Figure 2 or BW←U→CW→BP in Figure 3. The reader could by now have doubts about the correctness of Figure 2 where a later observation CW is a confounder of the effect of BW on BP since one could argue that, by occurring after BW, CW could not be seen as a common cause of both BW and BP. (See Hernán et al [8] for an accessible defence of the structural approach to confounding and selection bias using DAGs.) Nonetheless, while temporality seemingly excludes CW as a confounder in Figure 2, it does not exclude CW from ever being part of a confounding path as seen in Figure 3. Both BW and CW are more likely to be the result of a common cause (U), possibly genetic. Based on background knowledge and common sense, Figure 3 is more plausible than 2. Therefore, temporality cannot be used to judge whether a variable is a confounder, part of a sufficient subset of covariates needed to block a backdoor, or not [5].

Bottom Line: They conclude that all three simply reiterate the occurrence of a change in the association of any two variables when a third variable is statistically controlled for.At the heart of the phenomenon of change in magnitude, with or without reversal of effect estimate, is the question of which to use: the unadjusted (combined table) or adjusted (sub-table) estimate.It cannot be overemphasized that although these paradoxes reveal the perils of using statistical criteria to guide causal analysis, they hold neither the explanations of the phenomenon they depict nor the pointers on how to avoid them.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Social Medicine, Academic Medical Center, University of Amsterdam, Amsterdam, The Netherlands. o.a.arah@amc.uva.nl

ABSTRACT
Tu et al present an analysis of the equivalence of three paradoxes, namely, Simpson's, Lord's, and the suppression phenomena. They conclude that all three simply reiterate the occurrence of a change in the association of any two variables when a third variable is statistically controlled for. This is not surprising because reversal or change in magnitude is common in conditional analysis. At the heart of the phenomenon of change in magnitude, with or without reversal of effect estimate, is the question of which to use: the unadjusted (combined table) or adjusted (sub-table) estimate. Hence, Simpson's paradox and related phenomena are a problem of covariate selection and adjustment (when to adjust or not) in the causal analysis of non-experimental data. It cannot be overemphasized that although these paradoxes reveal the perils of using statistical criteria to guide causal analysis, they hold neither the explanations of the phenomenon they depict nor the pointers on how to avoid them. The explanations and solutions lie in causal reasoning which relies on background knowledge, not statistical criteria.

No MeSH data available.


Related in: MedlinePlus