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

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.

Predicting response to a cognitive–behavioral approach to treating low back pain: Secondary analysis of the BeST data set

“…Initially we identified potential predictors of outcome using univariate ana- lyses, followed by a more formal approach of forward stepwise selection (model 3). The stepwise selection process does not identify the same predictors as that from the univariate analyses, as some covariates either become significant or insignificant in the presence of other covariates during the modeling process (35).…”

Serum 25-Hydroxyvitamin D Level and Kidney Function Decline in a Swiss General Adult Population

“…To take into account the effect of baseline albuminuria and eGFR on the association of 25(OH)D and kidney outcomes, models were further adjusted for baseline albuminuria and eGFR. Because it is not clear whether change in eGFR should be adjusted for baseline eGFR (28)(29)(30), models of change in eGFR without and with adjustment for the initial eGFR value are presented. De Boer and colleagues could not consider the effect of baseline albuminuria on the associations of 25(OH)D with change in eGFR (9).…”

“…Indeed, if 25(OH)D influences kidney function through mechanisms including glomerular filtration, baseline eGFR would lie in the causal pathway of the relation between 25(OH)D and rapid eGFR decline. Because of mathematical coupling and reversal paradox, experts have warned against adjusting for the initial value when modeling change in the value (28)(29)(30)39). Conversely, adjusting for baseline eGFR may better reflect the biology.…”

Metabolic Syndrome and Prevalent Any-site, Prostate, Breast and Colon Cancers in the U.S. Adult Population: NHANES 1999-2010

“…Once more, while the general pattern crude analyses was suggestive of a relationship between number of MetS clusters and any-site cancer, these associations were almost entirely reversed by age, a phenomenon known as Simpson's paradox [34][35][36]. Cancer risk progressively increases with age and may be linked to age-related increases in susceptibility to carcinogens, hormonal imbalance, immunologic dysfunction, and decreased capacity for cell repair/apoptosis [37].…”