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Controversies in Statistical Science
Published in Mark Chang, John Balser, Jim Roach, Robin Bliss, Innovative Strategies, Statistical Solutions and Simulations for Modern Clinical Trials, 2019
Mark Chang, John Balser, Jim Roach, Robin Bliss
Simpson’s paradox is not uncommon if we continue slicing the data into more categories until the paradox appears. In a worldwide drug development program, for example, a drug can appear to be effective globally while its effects in different countries or regions may be very different. The question is how should such a drug be used in different countries or regions?
Biostatistics: Issues in study design, analysis, and reporting
Published in Stephen W. Gutkin, Writing High-Quality Medical Publications, 2018
The classic pedagogical example of Simpson’s Paradox is the well-documented rise in the incidence of lung cancer, which correlated with increases in sales of automobiles, in the 1950s. Simpson’s Paradox results because of a failure to recognize and control for covariates, often in epidemiologic research. A covariate may influence predictive relationships between exposures (e.g., treatments) and outcomes (e.g., disease events). In the aforementioned example, the covariate was an increased incidence of cigarette smoking, which paralleled the rise in car sales, during the 1950s. Performing an ANCOVA to control for cigarette smoking would largely abolish or neutralize the spurious association between car sales and lung cancer.
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Published in Filomena Pereira-Maxwell, Medical Statistics, 2018
An extreme type of bias that may occur when the evaluation of an exposure effect does not take into account an important confounding factor. Simpson’s paradox may cause crude estimates of effect to show the oppositedirection to that of adjusted estimates (which are obtained after stratification). The spurious association is due to the fact that a common cause creates the association between exposure and outcome. HERNAN, CLAYTON & KEIDING (2011) commented that Simpson’s intent in highlighting this phenomenon was less to point out the resulting confounding effect, and more to point out the fact that fallacies in defining a causal structure for the problem at hand will result in oddities and distortions. Box S.1 provides an illustrative example (although not conclusive regarding the effectiveness of the treatment in question). See JULIOUS & MULLEE (1994) for further illustration. Cf. non-collapsibility.
Unique Pakistani gut microbiota highlights population-specific microbiota signatures of type 2 diabetes mellitus
Published in Gut Microbes, 2022
Afshan Saleem, Aamer Ikram, Evgenia Dikareva, Emilia Lahtinen, Dollwin Matharu, Anne-Maria Pajari, Willem M. de Vos, Fariha Hasan, Anne Salonen, Ching Jian
Microbiota α-diversity (observed richness and Shannon diversity index) was estimated using the vegan package.84 Overall microbiota structure was assessed by principal coordinate analysis (PCoA) based on β-diversity computed using the Bray-Curtis dissimilarity matrix, representing the compositional dissimilarity between samples or groups. Significant differences between groups were tested using nonparametric multivariate analysis of variance (PERMANOVA).84 The associations between continuous or categorical variables and β-diversity were calculated using the envfit function in the vegan package,84 and P values were determined using 999 permutations. Associations between relative abundances of bacterial taxa and other measurements were assessed using Spearman’s correlation and visualized by the R package circlize.85 The R package Simpsons was additionally employed to ensure the absence of Simpson’s paradox that misleads the interpretation of correlative analysis.86
Modernizing the Bradford Hill criteria for assessing causal relationships in observational data
Published in Critical Reviews in Toxicology, 2018
In some data sets, the sign of an association between a predictor and a response variable can be reversed, e.g. from a significant positive association to a significant negative association, depending on modeling choices about which other variables to include in a regression model or condition on in stratified analyses. This occurs for PM2.5 and response in the data set in Figure 1 if heart attack rather than heart disease is used as the response variable (Cox 2017b). Simpson’s Paradox, in which aggregating over levels of a discrete covariate reverses the direction of an association that holds within each level (i.e. conditioned on any level), illustrates the malleability of the concept of a positive association. Because the strengths and directions of exposure–response associations often depend on such details of modeling assumptions and choices, “There is a growing consensus in economics, political science, statistics, and other fields that the associational or regression approach to inferring causal relations – on the basis of adjustment with observable confounders – is unreliable in many settings” (Dominici et al. 2014).
The Effect of CS Administration or an R-Optimized Alternative on Potential Projective Material in Rorschach Responses From Six Studies and a Meta-Analysis of Their Findings
Published in Journal of Personality Assessment, 2020
Gregory J. Meyer, Abufazel Hosseininasab, Donald J. Viglione, Joni L. Mihura, Ety Berant, Ana Cristina Resende, Jennifer Reese
Further, as Bravata and Olkin (2001) documented, pooling results across types of studies could generate several named statistical fallacies or paradoxes (e.g., ecological fallacy, Simpson’s paradox). These include observing instances of spurious seeming findings (i.e., false effects) or the converse of observing null seeming findings that obscure genuine differences. For instance, false effects might emerge if a study of children and a study of adults have an overall mean difference in R, even though neither study has differences in R due to method of administration. Paradoxical results are avoided by retaining each study’s distinctiveness and instead using weighed meta-analytic procedures to combine effects across studies (Bravata & Olkin, 2001).