An Introduction to Causal Inference

Pearl, Judea

doi:10.2202/1557-4679.1203

Cited by 458 publications

(344 citation statements)

References 115 publications

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“…However, when these assumptions are not met, the sum of direct and indirect effect does not give the total effect, i.e., c / = ab + c . A counterfactual definition guarantees the correct allocation of the total effect into direct and indirect effects (Pearl, 2010): a (natural) direct effect is the difference in Y of a change in Z, when M is kept at the value it would have had if Z had not changed. A (natural) indirect effect is the effect (on Y) of a change in M when Z is kept constant.…”

Section: Introductionmentioning

confidence: 99%

Mediation analysis to estimate direct and indirect milk losses due to clinical mastitis in dairy cattle

Detilleux

Kastelic

Barkema

2015

Preventive Veterinary Medicine

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a b s t r a c tMilk losses associated with mastitis can be attributed to either effects of pathogens per se (i.e., direct losses) or effects of the immune response triggered by intramammary infection (indirect losses). The distinction is important in terms of mastitis prevention and treatment. Regardless, the number of pathogens is often unknown (particularly in field studies), making it difficult to estimate direct losses, whereas indirect losses can be approximated by measuring the association between increased somatic cell count (SCC) and milk production. An alternative is to perform a mediation analysis in which changes in milk yield are allocated into their direct and indirect components. We applied this method on data for clinical mastitis, milk and SCC test-day recordings, results of bacteriological cultures (Escherichia coli, Staphylococcus aureus, Streptococcus uberis, coagulase-negative staphylococci, Streptococcus dysgalactiae, and streptococci other than Strep. dysgalactiae and Strep. uberis), and cow characteristics. Following a diagnosis of clinical mastitis, the cow was treated and changes (increase or decrease) in milk production before and after a diagnosis were interpreted counterfactually. On a daily basis, indirect changes, mediated by SCC increase, were significantly different from zero for all bacterial species, with a milk yield decrease (ranging among species from 4 to 33 g and mediated by an increase of 1000 SCC/mL/day) before and a daily milk increase (ranging among species from 2 to 12 g and mediated by a decrease of 1000 SCC/mL/day) after detection. Direct changes, not mediated by SCC, were only different from zero for coagulase-negative staphylococci before diagnosis (72 g per day). We concluded that mixed structural equation models were useful to estimate direct and indirect effects of the presence of clinical mastitis on milk yield.

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Section: Introductionmentioning

confidence: 99%

Mediation analysis to estimate direct and indirect milk losses due to clinical mastitis in dairy cattle

Detilleux

Kastelic

Barkema

2015

Preventive Veterinary Medicine

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“…1 Several methods already exist that can be used to evaluate interventions within complex contexts. [19][20][21][22][23][24][25][26] For example, the UK's Medical Research Council has produced guidance on natural experimental evaluations, 27 studies in which the differences between experimental and control contexts are not determined by researchers, but result from policy or other interventions outside their control. Statistical methods, such as interrupted time-series analysis, can be used effectively to evaluate the impacts of such interventions over time, 28 and simulation approaches, such as agent-based modelling, can integrate diverse evidence sources, allow for non-independence and feedback, and simulate emergence.…”

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confidence: 99%

The need for a complex systems model of evidence for public health

et al. 2017

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Despite major investment in both research and policy, many pressing contemporary public health challenges remain. To date, the evidence underpinning responses to these challenges has largely been generated by tools and methods that were developed to answer questions about the effectiveness of clinical interventions, and as such are grounded in linear models of cause and effect. Identification, implementation, and evaluation of effective responses to major public health challenges require a wider set of approaches 1,2 and a focus on complex systems. 3,4 A complex systems model of public health conceptualises poor health and health inequalities as outcomes of a multitude of interdependent elements within a connected whole. These elements affect each other in sometimes subtle ways, with changes potentially reverberating throughout the system. 5 A complex systems approach uses a broad spectrum of methods to design, implement, and evaluate interventions for changing these systems to improve public health.Complex systems are defined by several properties, including emergence, feedback, and adaptation. 3 Emergence describes the properties of a complex system that cannot be directly predicted from the elements within it and are more than just the sum of its parts. For example, the changing distribution of obesity across the population can be conceptualised as an emergent property of the food, employment, transport, economic, and other systems that shape the energy intake and expenditure of individuals. Feedback describes the situation in which a change reinforces or balances further change. For example, if a smoking ban in public places reduces the visibility and convenience of smoking, and this makes it less appealing, fewer young people might then start smoking, further reducing its visibility, and so on in a reinforcing loop. Adaptation refers to adjustments in behaviour in response to interventions, such as a tobacco company lowering the price of cigarettes in response to a public smoking ban.Rhetoric urging complex systems approaches to public health is only rarely operationalised in ways that generate relevant evidence or effective policies. 1,6 Public health problems that emerge as a property of a complex system cannot necessarily be solved with a simple, single intervention, but the interacting factors within the system can potentially be reshaped to generate a more desirable set of outcomes. 7,8 Achievement of meaningful impacts on complex multicausal problems, like obesity, requires more than single interventions, such as traffic light food labelling or exercise on prescription, many of which require high levels of individual agency, have low reach and impact, and tend to widen health inequalities. 9-11 Shifts within multiple elements across the many systems that influence obesity are required, some of which might only have small effects on individuals but can drive large changes when aggregated at population level. 12 Although randomised controlled trials of individual-level interventions are relatively strai...

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“…Moreover, the formula is readily estimable by regression. Owing to its generality and ubiquity, I have referred to this expression as the "Mediation Formula" (Pearl, 2009(Pearl, , 2010.…”

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confidence: 99%

The Causal Mediation Formula—A Guide to the Assessment of Pathways and Mechanisms

2012

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Recent advances in causal inference have given rise to a general and easy-to-use formula for assessing the extent to which the effect of one variable on another is mediated by a third. This so-called Mediation Formula is applicable to nonlinear models with both discrete and continuous variables, and permits the evaluation of path-specific effects with minimal assumptions regarding the data-generating process. We demonstrate the use of the Mediation Formula in simple examples and illustrate why parametric methods of analysis yield distorted results, even when parameters are known precisely. We stress the importance of distinguishing between the necessary and sufficient interpretations of "mediated-effect" and show how to estimate the two components in nonlinear systems with continuous and categorical variables.

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An Introduction to Causal Inference

Cited by 458 publications

References 115 publications

Mediation analysis to estimate direct and indirect milk losses due to clinical mastitis in dairy cattle

Mediation analysis to estimate direct and indirect milk losses due to clinical mastitis in dairy cattle

The need for a complex systems model of evidence for public health

The Causal Mediation Formula—A Guide to the Assessment of Pathways and Mechanisms

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