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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 depicting each variable pair – BW/CW, CW/BP, or BW/BP – as being connected only by an unmeasured common cause (U1, U2 or U3 respectively).
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Figure 5: DAG depicting each variable pair – BW/CW, CW/BP, or BW/BP – as being connected only by an unmeasured common cause (U1, U2 or U3 respectively).

Mentions: Figure 4 presents a scenario where the unadjusted effect of BW on BP is the correct estimate since CW is a collider (that is, without conditioning, it already acts as a blocker) in the DAG depicting two unobserved common causes of BW and CW and of CW and BP. This scenario is closely related to that in Figure 5 where BW has no effect on, but shares an unobserved common cause (U3) with, BP. In all scenarios, our choice of which (unadjusted or adjusted) estimate to use is not based on the magnitude or direction of the estimate but on the governing causal relations. Put this way, Simpson's paradox becomes a problem of covariate adjustment (when to adjust or not) in the causal analysis of non-experimental or observational data. The paradox arises due to the causal interpretation of the observation that the proportion of a given level of BW is evidence for making an educated guess of the proportion of a given BP level in an observed sample if the status of the third related covariate CW is unknown [5]. What we really want to answer is "Does BW cause BP?", not "Does observing BW allow us to predict BP?".


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 depicting each variable pair – BW/CW, CW/BP, or BW/BP – as being connected only by an unmeasured common cause (U1, U2 or U3 respectively).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 5: DAG depicting each variable pair – BW/CW, CW/BP, or BW/BP – as being connected only by an unmeasured common cause (U1, U2 or U3 respectively).
Mentions: Figure 4 presents a scenario where the unadjusted effect of BW on BP is the correct estimate since CW is a collider (that is, without conditioning, it already acts as a blocker) in the DAG depicting two unobserved common causes of BW and CW and of CW and BP. This scenario is closely related to that in Figure 5 where BW has no effect on, but shares an unobserved common cause (U3) with, BP. In all scenarios, our choice of which (unadjusted or adjusted) estimate to use is not based on the magnitude or direction of the estimate but on the governing causal relations. Put this way, Simpson's paradox becomes a problem of covariate adjustment (when to adjust or not) in the causal analysis of non-experimental or observational data. The paradox arises due to the causal interpretation of the observation that the proportion of a given level of BW is evidence for making an educated guess of the proportion of a given BP level in an observed sample if the status of the third related covariate CW is unknown [5]. What we really want to answer is "Does BW cause BP?", not "Does observing BW allow us to predict BP?".

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