Estimation of controlled direct effects in time‐varying treatments using structural nested mean models: application to a primary prevention trial for coronary events with pravastatin

Abstract

For the estimation of controlled direct effects (i.e., direct effects controlling intermediates that are set at a fixed level for all members of the population) without bias, two fundamental assumptions must hold: the absence of unmeasured confounding factors for treatment and outcome and for intermediate variables and outcome. Even if these assumptions hold, one would nonetheless fail to estimate direct effects using standard methods, for example, stratification or regression modeling, when the treatment influences confounding factors. For such situations, the sequential g-estimation method for structural nested mean models has been developed for estimating controlled direct effects in point-treatment situations. In this study, we demonstrate that this method can be applied to longitudinal data with time-varying treatments and repeatedly measured intermediate variables. We sequentially estimate the parameters in two structural nested mean models: one for a repeatedly measured intermediate and the other one for direct effects of a time-varying treatment. The method was applied to data from a large primary prevention trial for coronary events, in which pravastatin was used to lower the cholesterol levels in patients with moderate hypercholesterolemia.

Understanding Marginal Structural Models for Time-Varying Exposures: Pitfalls and Tips

“…We can also consider E[Y 1,0 ] − E[Y 0,0 ], which is referred to as the "controlled direct effect of A 1 while A 2 set at 0." [65][66][67] Note that joint exposure (A 1 , A 2 ) can affect not only outcome Y, but also L 2 (by A 1 ), which is measured after exposure initiation. Under the implausible assumption of no effect of (the part of ) exposure on (the part of ) the following confounders, the effect of (A 1 , A 2 ) can solely be seen as a multivalued exposure at a single time-point; as shown earlier, a1;a2 ] if the corresponding exchangeability assumptions for point-exposure hold.…”

“…There is a relevant method other than the g-formula and inverse probability weighting that requires essentially the same assumptions to estimate causal effects of time-varying exposures: gestimation. 15,18,[38][39][40][41]51,67 Like the relation of marginal structural modeling and inverse probability weighting, g-estimation is a method to estimate the parameters of structural nested models. Structural nested models and g-estimation indeed have attractive statistical properties (eg, robustness, efficiency, and flexible parameterization), which successfully work within Robins' causal "interventionism" framework with minimal conditions.…”

“…The average causal effect of exposure on outcome may be defined as any contrast between counterfactual expectations E[ ]; eg, E[ Y 1,1 ] − E[ Y 0,0 ]. We can also consider E[ Y 1,0 ] − E[ Y 0,0 ], which is referred to as the “controlled direct effect of A 1 while A 2 set at 0.” 65 – 67 …”

Mediational g-formula for time-varying treatment and repeated-measured multiple mediators: Application to atorvastatin’s effect on cardiovascular disease via cholesterol lowering and anti-inflammatory actions in elderly type 2 diabetics

“…Similar results including other statin drugs were observed in the previous causal analyses. 15 , 24 This apparent underestimation may be attributable to the loss of information of the mediators because many patients were subjected to laboratory testing only once per year; as cholesterol level is considered to have underlying time-continuous dynamic system, the models for mediators could be elaborated to incorporate continuous stochastic process, possibly based on more granular measurements. 36 , 40 , 41 Furthermore, there was no preventive effect via the second mediator in our case study, the white blood cell counts, which was expected to represent anti-inflammatory action.…”

Importance of the lipid‐related pathways in the association between statins, mortality, and cardiovascular disease risk: The Multi‐Ethnic Study of Atherosclerosis

“…However, typical trials where only the treatment is randomized are susceptible to yield biased estimates of the importance of intermediate pathways, unless appropriate control is made for potential confounders and causal mediation analyses are conducted . We are aware of only 1 study that used such causal mediation methods to quantify the importance of the cholesterol pathway in the effect of statins …”