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Mediation Analysis for Life Course Studies

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Pathways to Health

Part of the book series: SpringerBriefs in Population Studies ((BRIEFSPOPULAT))

Abstract

The main aim of life course epidemiology is to elucidate the processes that link early life factors to later life health. Mediation analysis plays an important role in these investigations since it offers the potential to use empirical data and statistical tools to separate the influence of an exposure on an outcome into effects through and around potential mediators. In this chapter, we have attempted to give a thorough but accessible introduction to causal mediation analysis and how it relates to Structural Equation Modelling (SEM). In particular we have reviewed the assumptions implicit in the traditional approach for the desired interpretation of mediation effects to be justified, and how many of these are relaxed when adopting the more flexible counterfactual-based approach. We have highlighted particular aspects, such as intermediate confounding and survival outcomes, which are particularly pertinent in life course investigations.

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Notes

  1. 1.

    Note that T represents matrix transposition, so that \(\mathbf {C}\) is \((p\times 1)\) even though \((C_1,C_2,\ldots ,C_p)\) is a (\(1\times p\)) row vector. This will be useful for writing regression equations later. Also note that, for now, an informal notion of “confounding” is adopted, but see Sect. 1.2.2.3 for the formal definition.

  2. 2.

    One important subtlety that we do not consider further in this chapter is that an alternative partitioning of the total effect in terms of alternative definitions of natural effects is given by \(\text {TCE}= E\left\{ Y\left( 1,M(1)\right) \right\} - E\left\{ Y\left( 0,M(1)\right) \right\} \; + \; E\left\{ Y\left( 0,M(1)\right) \right\} - E\left\{ Y\left( 0,M(0)\right) \right\} \). In other words, the definitions of NDE and NIE given above are not unique. Indeed, reversing the coding of X leads in general to direct and indirect effects of different magnitudes (not just different signs), which is somewhat unpleasing. This was acknowledged when the first definitions were given Robins and Greenland (1992), and much has been written about it since; see, for example, (Daniel, De Stavola, Cousens, & Vansteelandt, 2015; VanderWeele, 2013).

  3. 3.

    Note that the definitions given here are not exactly the same as those originally given by VanderWeele et al. (2014), but rather are the closely-related definitions given by Vansteelandt and Daniel (2016).

  4. 4.

    This is since we are using approaches that deal with confounding by adjustment/weighting etc, rather than approaches that rely on having measured instrumental variables Burgess (2015).

  5. 5.

    Note that the mathematical representation of this assumption makes it clear that in fact unmeasured common causes of X and M (i.e. \(V_3\) in Fig. 1.5), which would constitute a form of unmeasured confounding of X and Y, is not prohibited by this assumption.

  6. 6.

    Note that although it may appear more complicated, we are only using the identity \(E(A)=\sum _bE(A|B=b)\text {Pr}(B=b)\), except now that we condition on X and \(\mathbf {C}\) throughout. In other words, we are using \(E(A|C)=\sum _bE(A|B=b,C)\text {Pr}(B=b|C)\) with \(C=\{X,\mathbf {C}\}\), \(A=Y(x,m)\) and \(B=\mathbf {L}\).

  7. 7.

    Although note that identical results would be obtained using the product method were we to use a linear probability model for the binary mediator.

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  1. Department of Medical Statistics, Centre for Statistical Methodology, London School of Hygiene and Tropical Medicine, London, UK

    Rhian M. Daniel & Bianca L. De Stavola

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Daniel, R.M., De Stavola, B.L. (2019). Mediation Analysis for Life Course Studies. In: Pathways to Health. SpringerBriefs in Population Studies. Springer, Dordrecht. https://doi.org/10.1007/978-94-024-1707-4_1

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