Relationship between mediation analysis and the structured life course approach

Abstract Many questions in life course epidemiology involve mediation and/or interaction because of the long latency period between exposures and outcomes. In this paper, we explore how mediation analysis (based on counterfactual theory and implemented using conventional regression approaches) links with a structured approach to selecting life course hypotheses. Using theory and simulated data, we show how the alternative life course hypotheses assessed in the structured life course approach correspond to different combinations of mediation and interaction parameters. For example, an early life critical period model corresponds to a direct effect of the early life exposure, but no indirect effect via the mediator and no interaction between the early life exposure and the mediator. We also compare these methods using an illustrative real-data example using data on parental occupational social class (early life exposure), own adult occupational social class (mediator) and physical capability (outcome).

The pure indirect effect can only be non-zero if Y 01 -Y 00 ≠ 0, which happens under the adult critical adulthood, accumulation, decreasing social class and ever exposed models. Therefore a pure indirect effect will show in these models provided that M 1 -M 0 ≠ 0, i.e.
there is an association between exposure and mediator.
The reference interaction will be non-zero if Y 11 -Y 10 -Y 01 + Y 00 ≠ 0, under the reasonable assumption that M 0 ≠ 0. Therefore the increasing social class, decreasing social class, always exposed and ever exposed models will show a reference interaction.
The mediated interaction can only be non-zero if Y 11 -Y 10 -Y 01 + Y 00 ≠ 0, which occurs under the increasing social class, decreasing social class, always exposed and ever exposed models. Therefore a mediated interaction will show in these models provided that The total indirect effect is TIE = PIE + INT med . In general, this will be non-zero if PIE and/or INT med are non-zero. Therefore a total indirect effect will show in the critical adulthood, accumulation, increasing social class and always exposed models, provided that M 1 -M 0 ≠ 0. However, in the decreasing social class and ever exposed models, we have Y 11 -Y 10 = 0 and hence PIE = -INT med , so a total indirect effect will not show in these models in spite of having non-zero PIE and non-zero INT med .
To consider the conventional direct and indirect effects in mediation analysis, we switch from counterfactuals to regression models. Suppose then that the outcome can be modelled by the linear model with interaction: where E(ε) = 0 and ε is independent of the binary X and M. The seven life course models in Box 2 can be summarized by the relationships of the regression parameters β, γ and δ: Decreasing social class β = 0, γ = -δ ≠ 0 Always exposed β = 0, γ = 0, δ ≠ 0 The conventional Direct Effect is the regression coefficient of Y on X, adjusted for M. This can be calculated using a standard formula: The covariances with the outcome are cov(X,Y) = cov(X, α + βX + γM + δXM + ε) = cov(X,α) + cov(X,βX) + cov(X,γM) + cov(X,δXM) + cov(X,ε) The coefficient for δ is (1-E(X))E(XM)(E(X)-E(XM)), which once again cannot be zero if all combinations of X and M occur with non-zero probability. The indirect effect will always be zero unless cov(X,M) ≠ 0, i.e. there is an association between exposure and mediator. Again ignoring chance cancellation, it is simpler to show the models in which the indirect effect is zero. This is only certain to occur when γ = 0 and δ= 0. Only in the early critical period model will this occur and there be no Indirect Effect.

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Some life course models can be thought of as a combination of simpler models. For instance a 'sensitive period' hypothesis can be thought of as a combination of a critical period and accumulation models. Should such a model be identified, all effects that are non-zero in the component models could be considered to be non-zero in the identified compound model.
There is the possibility that the effects of the separate component models may cancel each other out by chance.