So far in this course we have dealt entirely with the evolution of characters that are controlled by simple Mendelian inheritance at a single locus. There are notes on the course website about gametic disequilibrium and how allele frequencies change at two loci simultaneously, but we didn’t discuss them. In every example we’ve considered we’ve imagined that we could understand something about evolution by examining the evolution of a single gene. That’s the domain of classical population genetics. For the next few weeks we’re going to be exploring a field that’s actually older than classical population genetics, although the approach we’ll be taking to it involves the use of population genetic machinery. If you know a little about the history of evolutionary biology, you may know that after the rediscovery of Mendel’s work in 1900 there was a heated debate between the “biometricians” (e.g., Galton and Pearson) and the “Mendelians” (e.g., de Vries, Correns, Bateson, and Morgan). Biometricians asserted that the really important variation in evolution didn’t follow Mendelian rules. Height, weight, skin color, and similar traits seemed to

Human biochemical genetics

The 11th edition of Harrison's Principles of Internal Medicine welcomes Anthony Fauci to its editorial staff, in addition to more than 85 new contributors. While the organization of the book is similar to previous editions, major emphasis has been placed on disorders that affect multiple organ systems. Important advances in genetics, immunology, and oncology are emphasized. Many chapters of the book have been rewritten and describe major advances in internal medicine. Subjects that received only a paragraph or two of attention in previous editions are now covered in entire chapters. Among the chapters that have been extensively revised are the chapters on infections in the compromised host, on skin rashes in infections, on many of the viral infections, including cytomegalovirus and Epstein-Barr virus, on sexually transmitted diseases, on diabetes mellitus, on disorders of bone and mineral metabolism, and on lymphadenopathy and splenomegaly. The major revisions in these chapters and many

Harrison's Principles of Internal Medicine

Secret History: Return of the Black Death Channel 4, 7-8pm In 1348 the Black Death swept through London, killing people within days of the appearance of their first symptoms. Exactly how many died, and why, has long been a mystery. This Secret History documentary follows experts as they pick through the evidence and reveal why the plague killed on such a scale. And they ask, what might be coming next?

Medscape

Background: The number of Mendelian randomization analyses including large numbers of genetic variants is rapidly increasing. This is due to the proliferation of genome-wide association studies, and the desire to obtain more precise estimates of causal effects. However, some genetic variants may not be valid instrumental variables, in particular due to them having more than one proximal phenotypic correlate (pleiotropy).

Methods: We view Mendelian randomization with multiple instruments as a meta-analysis, and show that bias caused by pleiotropy can be regarded as analogous to small study bias. Causal estimates using each instrument can be displayed visually by a funnel plot to assess potential asymmetry. Egger regression, a tool to detect small study bias in meta-analysis, can be adapted to test for bias from pleiotropy, and the slope coefficient from Egger regression provides an estimate of the causal effect. Under the assumption that the association of each genetic variant with the exposure is independent of the pleiotropic effect of the variant (not via the exposure), Egger’s test gives a valid test of the null causal hypothesis and a consistent causal effect estimate even when all the genetic variants are invalid instrumental variables.

Results: We illustrate the use of this approach by re-analysing two published Mendelian randomization studies of the causal effect of height on lung function, and the causal effect of blood pressure on coronary artery disease risk. The conservative nature of this approach is illustrated with these examples.

Conclusions: An adaption of Egger regression (which we call MR-Egger) can detect some violations of the standard instrumental variable assumptions, and provide an effect estimate which is not subject to these violations. The approach provides a sensitivity analysis for the robustness of the findings from a Mendelian randomization investigation.

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Mendelian randomization with invalid instruments: effect estimation and bias detection through Egger regression

We investigate conditions sufficient for identification of average treatment effects using instrumental variables. First we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect. We then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument. Finally we derive the probability limit of the standard IV estimator under these conditions. It is seen to be a weighted average of local average treatment effects.

Evolution and Rationality Some Recent Game-Theoretic Results. Identification and Estimation of Local Average Treatment Effects

Sensitivity analysis is useful in assessing how robust an association is to potential unmeasured or uncontrolled confounding. This article introduces a new measure called the "E-value," which is related to the evidence for causality in observational studies that are potentially subject to confounding. The E-value is defined as the minimum strength of association, on the risk ratio scale, that an unmeasured confounder would need to have with both the treatment and the outcome to fully explain away a specific treatment-outcome association, conditional on the measured covariates. A large E-value implies that considerable unmeasured confounding would be needed to explain away an effect estimate. A small E-value implies little unmeasured confounding would be needed to explain away an effect estimate. The authors propose that in all observational studies intended to produce evidence for causality, the E-value be reported or some other sensitivity analysis be used. They suggest calculating the E-value for both the observed association estimate (after adjustments for measured confounders) and the limit of the confidence interval closest to the null. If this were to become standard practice, the ability of the scientific community to assess evidence from observational studies would improve considerably, and ultimately, science would be strengthened.

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Sensitivity Analysis in Observational Research: Introducing the E-Value

Mediation analysis is a useful and widely employed approach to studies in the field of psychology and in the social and biomedical sciences. The contributions of this article are several-fold. First we seek to bring the developments in mediation analysis for nonlinear models within the counterfactual framework to the psychology audience in an accessible format and compare the sorts of inferences about mediation that are possible in the presence of exposure-mediator interaction when using a counterfactual versus the standard statistical approach. Second, the work by VanderWeele and Vansteelandt (2009, 2010) is extended here to allow for dichotomous mediators and count outcomes. Third, we provide SAS and SPSS macros to implement all of these mediation analysis techniques automatically, and we compare the types of inferences about mediation that are allowed by a variety of software macros.

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Mediation analysis allowing for exposure-mediator interactions and causal interpretation: theoretical assumptions and implementation with SAS and SPSS macros.

This article provides an overview of recent developments in mediation analysis, that is, analyses used to assess the relative magnitude of different pathways and mechanisms by which an exposure may affect an outcome. Traditional approaches to mediation in the biomedical and social sciences are described. Attention is given to the confounding assumptions required for a causal interpretation of direct and indirect effect estimates. Methods from the causal inference literature to conduct mediation in the presence of exposure-mediator interactions, binary outcomes, binary mediators, and case-control study designs are presented. Sensitivity analysis techniques for unmeasured confounding and measurement error are introduced. Discussion is given to extensions to time-to-event outcomes and multiple mediators. Further flexible modeling strategies arising from the precise counterfactual definitions of direct and indirect effects are also described. The focus throughout is on methodology that is easily implementable...

https://www.annualreviews.org/doi/pdf/10.1146/annurev-publhealth-032315-021402

Mediation Analysis: A Practitioner's Guide

Authors often do not give sufficient information to draw conclusions about the size and statistical significance of interaction on the additive and multiplicative scales. To improve this, we provide four steps, template tables and examples. We distinguish two cases: when the causal effect of intervening on one exposure, across strata of another factor, is of interest (‘effect modification’); and when the causal effect of intervening on two exposures is of interest (‘interaction’).

Assume we study whether X modifies the effect of A on D, where A, X and D are dichotomous. We propose presenting: (i) relative risks (RRs), odds ratios (ORs) or risk differences (RDs) for each (A, X) stratum with a single reference category taken as the stratum with the lowest risk of D; (ii) RRs, ORs or RDs for A within strata of X; (iii) interaction measures on additive and multiplicative scales; (iv) the A–D confounders adjusted for.

Assume we study the interaction between A and B on D, where A, B and D are dichotomous. Steps (i) and (iii) are similar to presenting effect modification. (ii) Present RRs, ORs or RDs for A within strata of B and for B within strata of A. (iv) List the A–D and B–D confounders adjusted for.

These four pieces of information will provide a reader the information needed to assess effect modification or interaction. The presentation can be further enriched when exposures have multiple categories. Our proposal hopefully encourages researchers to present effect modification and interaction analyses in as informative a manner as possible.

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Recommendations for presenting analyses of effect modification and interaction

PART I: MEDIATION ANALYSIS Chapter 1. Explanation and Mechanism Chapter 2. Mediation: Introduction and Regression-Based Approaches Chapter 3. Sensitivity Analysis for Mediation Chapter 4. Mediation Analysis with Survival Data Chapter 5. Multiple Mediators Chapter 6. Mediation Analysis with Time-Varying Exposures and Mediators Chapter 7. Selected Topics in Mediation Analysis Chapter 8. Other Topics Related to Intermediates PART II: INTERACTION ANALYSIS Chapter 9. An Introduction to Interaction Analysis Chapter 10. Mechanistic Interaction Chapter 11. Bias Analysis for Interactions Chapter 12. Interaction in Genetics: Independence and Boosting Power Chapter 13. Power and Sample-Size Calculations for Interaction Analysis PART III: SYNTHESIS AND SPILLOVER EFFECTS Chapter 14. A Unification of Mediation and Interaction Chapter 15. Social Interactions and Spillover Effects Chapter 16. Mediation and Interaction: Future and Context Appendix. Technical Details and Proofs References

Tyler J. VanderWeele

Papers

Sensitivity Analysis in Observational Research: Introducing the E-Value

Mediation analysis allowing for exposure-mediator interactions and causal interpretation: theoretical assumptions and implementation with SAS and SPSS macros.

Mediation Analysis: A Practitioner's Guide

Recommendations for presenting analyses of effect modification and interaction

Explanation in Causal Inference: Methods for Mediation and Interaction