**Date Published:** May 06, 2018

**Publisher:** Oxford University Press

**Author(s):** Ruth H Keogh, Rhian M Daniel, Tyler J VanderWeele, Stijn Vansteelandt.

http://doi.org/10.1093/aje/kwx311

**Abstract**

**Estimation of causal effects of time-varying exposures using longitudinal data is a common problem in epidemiology. When there are time-varying confounders, which may include past outcomes, affected by prior exposure, standard regression methods can lead to bias. Methods such as inverse probability weighted estimation of marginal structural models have been developed to address this problem. However, in this paper we show how standard regression methods can be used, even in the presence of time-dependent confounding, to estimate the total effect of an exposure on a subsequent outcome by controlling appropriately for prior exposures, outcomes, and time-varying covariates. We refer to the resulting estimation approach as sequential conditional mean models (SCMMs), which can be fitted using generalized estimating equations. We outline this approach and describe how including propensity score adjustment is advantageous. We compare the causal effects being estimated using SCMMs and marginal structural models, and we compare the two approaches using simulations. SCMMs enable more precise inferences, with greater robustness against model misspecification via propensity score adjustment, and easily accommodate continuous exposures and interactions. A new test for direct effects of past exposures on a subsequent outcome is described.**

**Partial Text**

SCMMs give insight into total exposure effects. However, it is useful to understand whether earlier exposures directly affect a subsequent outcome other than via intermediate exposures. Focusing on Figure 1B, we outline a test for the existence of any direct effect of Xt−1 on Yt, except that mediated through Xt. This long-term direct effect is represented by unblocked pathways from Xt−1 to Yt that do not pass through Xt.

We used simulation studies to compare SCMMs with IPW estimation of MSMs for the short-term effect of a binary exposure Xt on a continuous outcome Yt, and to assess the performance of the test for long-term direct effects. Data were simulated according to Figure 1A, using n=200 individuals observed at T=5 visits (simulation scenario 1). To further assess the test for long-term direct effects we generated data under a second scenario in which there is no direct effect of Xt−1 on Yt (δY=0 in model (14)), represented by a modification of Figure 1A with the arrows from Xt−1 to Yt removed (simulation scenario 2). See Web Appendix 2 for details.

We have shown how standard regression methods using SCMMs can be used to estimate total effects of a time-varying exposure on a subsequent outcome by controlling for confounding by prior exposures, outcomes, and time-varying covariates. We compared this with IPW estimation of MSMs, which handles time-varying confounding when estimating joint effects but which can also be used to estimate total effects. Other methods for estimating joint effects include g-estimation and g-computation (see Daniel et al. (3) for an overview), which have not been used extensively in practice (24–26). There is a close connection between SCMMs and structural nested mean models (SNMMs) (26), in which a parametric model is specified for the causal effect of interest among people receiving a given level of treatment (e.g., g{E(Y(x¯t−1,1)|X¯t=x¯t,L¯t)}−g{E(Y(x¯t−1,0)|X¯t=x¯t,L¯t)}). In linear models, our propensity score adjusted estimates are equivalent to efficient g-estimates in a SNMM for short-term effects (27). When the remaining long-term direct effects are of interest, estimation in linear SNMMs becomes more involved, but it is still feasible using standard software (27, 28).

Source:

http://doi.org/10.1093/aje/kwx311