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Simpson's Paradox, Lord's Paradox, and Suppression Effects are the same phenomenon--the reversal paradox.

Tu YK, Gunnell D, Gilthorpe MS - Emerg Themes Epidemiol (2008)

Bottom Line: This article uses hypothetical scenarios to illustrate how the three paradoxes are different manifestations of one phenomenon--the reversal paradox--depending on whether the outcome and explanatory variables are categorical, continuous or a combination of both; this renders the issues and remedies for any one to be similar for all three.Understanding the concepts and theory behind these paradoxes provides insights into some controversial or contradictory research findings.These paradoxes show that prior knowledge and underlying causal theory play an important role in the statistical modelling of epidemiological data, where incorrect use of statistical models might produce consistent, replicable, yet erroneous results.

View Article: PubMed Central - HTML - PubMed

Affiliation: Biostatistics Unit, Centre for Epidemiology & Biostatistics, University of Leeds, 30/32 Hyde Terrace, Leeds, UK. y.k.tu@leeds.ac.uk

ABSTRACT
This article discusses three statistical paradoxes that pervade epidemiological research: Simpson's paradox, Lord's paradox, and suppression. These paradoxes have important implications for the interpretation of evidence from observational studies. This article uses hypothetical scenarios to illustrate how the three paradoxes are different manifestations of one phenomenon--the reversal paradox--depending on whether the outcome and explanatory variables are categorical, continuous or a combination of both; this renders the issues and remedies for any one to be similar for all three. Although the three statistical paradoxes occur in different types of variables, they share the same characteristic: the association between two variables can be reversed, diminished, or enhanced when another variable is statistically controlled for. Understanding the concepts and theory behind these paradoxes provides insights into some controversial or contradictory research findings. These paradoxes show that prior knowledge and underlying causal theory play an important role in the statistical modelling of epidemiological data, where incorrect use of statistical models might produce consistent, replicable, yet erroneous results.

No MeSH data available.


Related in: MedlinePlus

Causal models expressed as directed acyclic graphs for possible relationships between the three observed variables: birth weight (BW), current body weight (CW) and systolic blood pressure (BP). UC is an unobserved variable that affects both BW and CW. In Figure 1d, there is a back-door path from BP to BW via CW and UC, so the association between BP and BW is therefore biased. The adjustment of CW can block the backdoor path from BP to BW via UC.
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Figure 1: Causal models expressed as directed acyclic graphs for possible relationships between the three observed variables: birth weight (BW), current body weight (CW) and systolic blood pressure (BP). UC is an unobserved variable that affects both BW and CW. In Figure 1d, there is a back-door path from BP to BW via CW and UC, so the association between BP and BW is therefore biased. The adjustment of CW can block the backdoor path from BP to BW via UC.

Mentions: Using the inverse relationship between birth weight and systolic blood pressure in later life as an example, Figure 1 shows the directed acyclic graphs [9-11] for the possible relationships between the three observed variables: birth weight, current body weight and systolic blood pressure. In Figure 1a, current body weight is on the causal pathway from birth weight to systolic blood pressure, so current body weight is not a genuine confounder and should not be adjusted for. In Figure 1b, there is no relationship between birth weight and current body weight, and therefore the latter is not a confounder for the relationship between birth weight and blood pressure either. However, this model cannot explain the observed positive correlations between birth weight and current body weight in many epidemiological studies. In Figure 1c, current body weight is a confounder because it is ancestor to both birth weight and blood pressure in the directed acyclic graph [9-11]. Obviously, this scenario is implausible in reality because current body weight cannot affect birth weight. In Figure 1d, the observed positive correlation between birth weight and current body weight is due to an unobserved confounder, UC, which affects both birth weight and current body weight. Also, there is no path from birth weight and current body weight [7], i.e. if UC could be identified and measured, birth weight and current body weight would be independent, conditional on UC [12]. More complex causal diagrams for the three variables are possible by incorporating more unobserved variables in the model. However, the four scenarios in Figure 1 are sufficient for our discussion in this study, so we do not pursue them further.


Simpson's Paradox, Lord's Paradox, and Suppression Effects are the same phenomenon--the reversal paradox.

Tu YK, Gunnell D, Gilthorpe MS - Emerg Themes Epidemiol (2008)

Causal models expressed as directed acyclic graphs for possible relationships between the three observed variables: birth weight (BW), current body weight (CW) and systolic blood pressure (BP). UC is an unobserved variable that affects both BW and CW. In Figure 1d, there is a back-door path from BP to BW via CW and UC, so the association between BP and BW is therefore biased. The adjustment of CW can block the backdoor path from BP to BW via UC.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2254615&req=5

Figure 1: Causal models expressed as directed acyclic graphs for possible relationships between the three observed variables: birth weight (BW), current body weight (CW) and systolic blood pressure (BP). UC is an unobserved variable that affects both BW and CW. In Figure 1d, there is a back-door path from BP to BW via CW and UC, so the association between BP and BW is therefore biased. The adjustment of CW can block the backdoor path from BP to BW via UC.
Mentions: Using the inverse relationship between birth weight and systolic blood pressure in later life as an example, Figure 1 shows the directed acyclic graphs [9-11] for the possible relationships between the three observed variables: birth weight, current body weight and systolic blood pressure. In Figure 1a, current body weight is on the causal pathway from birth weight to systolic blood pressure, so current body weight is not a genuine confounder and should not be adjusted for. In Figure 1b, there is no relationship between birth weight and current body weight, and therefore the latter is not a confounder for the relationship between birth weight and blood pressure either. However, this model cannot explain the observed positive correlations between birth weight and current body weight in many epidemiological studies. In Figure 1c, current body weight is a confounder because it is ancestor to both birth weight and blood pressure in the directed acyclic graph [9-11]. Obviously, this scenario is implausible in reality because current body weight cannot affect birth weight. In Figure 1d, the observed positive correlation between birth weight and current body weight is due to an unobserved confounder, UC, which affects both birth weight and current body weight. Also, there is no path from birth weight and current body weight [7], i.e. if UC could be identified and measured, birth weight and current body weight would be independent, conditional on UC [12]. More complex causal diagrams for the three variables are possible by incorporating more unobserved variables in the model. However, the four scenarios in Figure 1 are sufficient for our discussion in this study, so we do not pursue them further.

Bottom Line: This article uses hypothetical scenarios to illustrate how the three paradoxes are different manifestations of one phenomenon--the reversal paradox--depending on whether the outcome and explanatory variables are categorical, continuous or a combination of both; this renders the issues and remedies for any one to be similar for all three.Understanding the concepts and theory behind these paradoxes provides insights into some controversial or contradictory research findings.These paradoxes show that prior knowledge and underlying causal theory play an important role in the statistical modelling of epidemiological data, where incorrect use of statistical models might produce consistent, replicable, yet erroneous results.

View Article: PubMed Central - HTML - PubMed

Affiliation: Biostatistics Unit, Centre for Epidemiology & Biostatistics, University of Leeds, 30/32 Hyde Terrace, Leeds, UK. y.k.tu@leeds.ac.uk

ABSTRACT
This article discusses three statistical paradoxes that pervade epidemiological research: Simpson's paradox, Lord's paradox, and suppression. These paradoxes have important implications for the interpretation of evidence from observational studies. This article uses hypothetical scenarios to illustrate how the three paradoxes are different manifestations of one phenomenon--the reversal paradox--depending on whether the outcome and explanatory variables are categorical, continuous or a combination of both; this renders the issues and remedies for any one to be similar for all three. Although the three statistical paradoxes occur in different types of variables, they share the same characteristic: the association between two variables can be reversed, diminished, or enhanced when another variable is statistically controlled for. Understanding the concepts and theory behind these paradoxes provides insights into some controversial or contradictory research findings. These paradoxes show that prior knowledge and underlying causal theory play an important role in the statistical modelling of epidemiological data, where incorrect use of statistical models might produce consistent, replicable, yet erroneous results.

No MeSH data available.


Related in: MedlinePlus