Causal Mediation Analysis for Estimating Interventional Effects Mapped to a Target Trial
intro.RmdBackground
Causal mediation analysis methods are commonly used in research studies to explore the causal pathways linking exposures to outcomes. Traditional mediation analysis aims to decompose the total effect of an exposure on an outcome into the natural direct and indirect effects, with the natural indirect effect capturing the exposure effect acting through the mediator. However, the goal of research studies, especially in health and medical research, is often to elucidate the extent to which hypothetical interventions targeting mediators could counter exposure effects. This suggests that a shift in focus is warranted, from effect decomposition to explicitly evaluating hypothetical mediator interventions that may inform future policy, practice and intervention development.
Interventional effects (VanderWeele, Vansteelandt, and Robins 2014) are mediation estimands that are more aligned with this interventional focus while addressing key identifiability challenges associated with natural effects (Robins and Greenland 1992). Indeed, interventional effects have been shown to implicitly emulate effects in target trials (Hernán and Robins 2016) assessing the impact of distributional shifts in mediators (Moreno-Betancur and Carlin 2018). Based on this concept, Moreno-Betancur et al. (2021) proposed definitions of interventional effects that map explicitly to a target trial assessing hypothetical mediator interventions of specific interest, making them particularly useful for policy-relevant evaluations in applied research as illustrated in several published examples (Dashti et al. 2022; Goldfeld et al. 2023; Afshar et al. 2024).
Interventional effects: definition and estimation methods
Moreno-Betancur et al. (2021) provided
definitions for interventional effects based on three types of
hypothetical mediator interventions. In this vignette, we describe these
estimands and their corresponding mediator interventions, as implemented
in the medRCT R package. The type of mediator intervention
can be specified using the argument intervention_type. The
default, intervention_type = "all", estimates all three
types of interventional effects, which are:
shift_all:
This estimand corresponds to an intervention that shifts the joint distribution of all mediators in the exposed to match the corresponding distribution in the unexposed.shift_k:
This estimand corresponds to an intervention that shifts the distribution of a specific mediator in the exposed to match the corresponding distribution in the unexposed, independent of and without considering flow-on effects on other mediators.shift_k_order:
This estimand corresponds to an intervention that shifts the distribution of a specific mediator in the exposed to match the corresponding distribution in the unexposed, while considering flow-on effects on causally descendant mediators.
medRCT estimates interventional effects based on these
interventions using a Monte Carlo simulation-based g-computation
approach, as described by Vansteelandt and Daniel
(2017). The number of Monte Carlo simulations can be specified
using the argument mcsim, allowing users to balance
computational efficiency and estimation accuracy. The default number of
Monte Carlo simulations used is 200. Additionally, medRCT
automatically removes records with missing data for any of the analysis
variables, performing a complete-case analysis.
Getting started with medRCT: Estimating interventional
effects
The medRCT package is designed to handle complex
mediation settings involving multiple interrelated
mediators and intermediate confounders
(exposure-induced mediator-outcome confounders). It supports a range of
variable types. Specifically, it supports categorical
exposures with two or more levels (Levels
2). For the outcome variable, medRCT
supports both binary and continuous
outcomes. Additionally, it supports any number of mediators. Each
mediator, including those not of primary interest
(i.e., intermediate confounders), can be either
binary or continuous. Any number and
type of baseline confounders are supported. This makes
the package suitable for a broad range of real-world applications in
epidemiology, public health, and social science research.
We begin by illustrating how to estimate the three different types of
interventional effects in the presence of multiple mediators and
intermediate confounders. Such intermediate confounders can be specified
using the argument intermediate_confs. We consider the
following example using simulated data inspired by a case study within
the Longitudinal Study of Australian Children (LSAC) (Goldfeld et al. 2023). Specifically, we aim to
estimate the difference in expected outcome (risk of mental health
problems) under exposure (low socioeconomic position) with versus
without a hypothetical intervention that individually shifts the
distribution of each mediator (parental mental health and preschool
attendance) to the levels in the unexposed, while accounting for
baseline confounders, an intermediate (exposure-induced)
mediator-outcome confounder and correlations amongst mediators.
library(medRCT)
#> medRCT: Causal mediation analysis estimating interventional effects mapped to a target trial
#> Note: When setting intervention_type = 'shift_k_order', the order of the mediators as specified
#> in the 'mediators' argument is important.
# Set a seed for reproducibility
set.seed(2025)
# Display the first few rows of the dataset
head(LSACdata)
#> child_sex child_atsi mat_cob mat_engl mat_age sep fam_stress parent_mh
#> 1 0 1 0 0 1 0 0 0
#> 2 NA 0 0 0 NA 0 NA NA
#> 3 NA 0 0 0 NA 0 NA NA
#> 4 NA 0 0 0 NA 0 NA NA
#> 5 1 0 0 0 1 1 0 0
#> 6 1 0 0 0 1 0 1 1
#> preschool_att child_mh child_SDQscore
#> 1 1 0 8.924660
#> 2 0 0 7.349826
#> 3 0 1 12.824643
#> 4 0 0 6.611369
#> 5 0 1 10.329341
#> 6 0 1 13.552515
# Define confounders for the analysis
confounders <- c("child_sex", "child_atsi", "mat_cob", "mat_engl", "mat_age")
# Define intermediate confounders
intermediate_confs <- "fam_stress"
# Estimate interventional indirect effects
med_res <- medRCT(
dat = LSACdata,
exposure = "sep",
outcome = "child_mh",
mediators = c("parent_mh", "preschool_att"),
intermediate_confs = intermediate_confs,
confounders = confounders,
interactions_XC = "all",
intervention_type = "all",
bootstrap = TRUE,
boot_args = list(R = 100, stype = "i", ci.type = "norm"),
mcsim = 200
)
#> Conducting complete case analysis, 2499 observations were excluded due to missing data.
# Summarise the results
summary(med_res)
#>
#> Estimated interventional indirect effect:
#>
#> Estimate Std. Error CI Lower CI Upper
#> IIE_1 (p_trt - p_1) 0.012233 0.003988 0.004156 0.019787
#> IIE_2 (p_trt - p_2) 0.000284 0.002492 -0.004544 0.005224
#> IIE_all (p_trt - p_all) 0.012192 0.004735 0.002680 0.021243
#> IIE_1_prime (p_trt - p_1_prime) 0.013044 0.004151 0.004521 0.020794
#> TCE (p_trt - p_ctr) 0.129132 0.024456 0.082318 0.178184
#> p-value
#> IIE_1 (p_trt - p_1) 0.0022
#> IIE_2 (p_trt - p_2) 0.9092
#> IIE_all (p_trt - p_all) 0.0100
#> IIE_1_prime (p_trt - p_1_prime) 0.0017
#> TCE (p_trt - p_ctr) 1.3e-07
#>
#> Estimated interventional direct effect:
#>
#> Estimate Std. Error CI Lower CI Upper p-value
#> IDE_1 (p_1 - p_ctr) 0.1169 0.0246 0.0700 0.1666 2.1e-06
#> IDE_2 (p_2 - p_ctr) 0.1288 0.0243 0.0823 0.1775 1.1e-07
#> IDE_all (p_all - p_ctr) 0.1169 0.0245 0.0703 0.1663 1.8e-06
#> IDE_1_prime (p_1_prime - p_ctr) 0.1161 0.0247 0.0692 0.1660 2.6e-06
#>
#> Estimated expected outcome in each trial arm:
#>
#> Estimate Std. Error CI Lower CI Upper p-value
#> p_1 0.3300 0.0225 0.2868 0.3751 <2e-16
#> p_2 0.3419 0.0220 0.2994 0.3858 <2e-16
#> p_all 0.3300 0.0224 0.2871 0.3748 <2e-16
#> p_ctr 0.2131 0.0100 0.1930 0.2323 <2e-16
#> p_trt 0.3422 0.0222 0.2994 0.3864 <2e-16
#> p_1_prime 0.3292 0.0226 0.2860 0.3745 <2e-16
#>
#> Sample Size: 2608
#>
#> Simulations: 200
In the summary table:
IIE_allis the estimated interventional indirect effect when applying the hypothetical intervention specified byshift_all. A hypothetical intervention improving both the mental health of parents of children and preschool attendance in low socioeconomic position to the levels in those with high socioeconomic position could potentially prevent 1 per 100 cases of child mental health problems.IIE_kis the estimated interventional indirect effect when applying the hypothetical intervention described byshift_kto a specific mediatork. A hypothetical intervention improving the mental health of parents of children (IIE_1) in low socioeconomic position to the levels in those with high socioeconomic position could potentially prevent 1 per 100 cases of child mental health problems. Meanwhile, the effect of a hypothetical intervention on preschool attendance (IIE_2) is negligible.IIE_k_primeis the estimated interventional indirect effect for a specific mediatork, accounting for the flow-on effects on its descendant mediators under the hypothetical intervention described byshift_k_order. A hypothetical intervention improving the mental health of parents of children (IIE_1_prime) in low socioeconomic position to the levels in those with high socioeconomic position, while accounting for flow-on effects on preschool attendance, could potentially prevent 1 per 100 cases of child mental health problems.TCEis the estimated total causal effect.
Specifying interactions with interactions_XC
The argument interactions_XC in medRCT
allows users to specify two-way interactions amongst exposure and
baseline confounders. Of note, the algorithm automatically includes all
two-way interactions between the exposure, mediators, and intermediate
confounders. These interaction terms are fixed and cannot be modified by
the user.
Default option:
- By default,
interactions_XC = "all"includes all two-way interactions between the exposure and baseline confounders, while baseline confounder-baseline confounder interactions are excluded.
Removing interactions:
- Setting
interactions_XC = "none"removes all two-way interactions involving the exposure and baseline confounders.
Custom interactions:
-
Custom specification: Users can manually specify
interaction terms by providing the model formula in the format
interactions_XC = "exposure:confounder1 + exposure:confounder2". This option provides full control over interaction terms between the exposure and baseline confounders in the model, enabling customisation for specific research questions.
Special cases
Analysis without intermediate confounders
If there are no intermediate confounders in the
analysis, set the argument
intermediate_confs = NULL when calling the
medRCT function, as described in the following example:
med_res <- medRCT(
dat = LSACdata,
exposure = "sep",
outcome = "child_mh",
mediators = c("parent_mh", "preschool_att"),
intermediate_confs = intermediate_confs,
confounders = confounders,
interactions_XC = "all",
intervention_type = "all",
intermediate_confs = NULL,
bootstrap = TRUE,
boot_args = list(R = 100, stype = "i", ci.type = "norm"),
mcsim = 200
)Single mediator case:
If there is only one mediator, only the
intervention_type shift_k can
be estimated, as the other options (shift_all and
shift_k_order) require multiple mediators
to define meaningful interventional effects.
Causal ordering for the estimation of the estimand
shift_k_order:
When estimating the estimand shift_k_order, the
order of mediators specified in the argument
mediators is important, as it defines the
causal ordering among the mediators. This ordering
determines the causal descendants for the mediator of
interest, providing essential information for accounting for
flow-on effects after the hypothetical intervention. Specifying
an incorrect mediator ordering may result in biased
estimates for the estimand shift_k_order.
Model assessment
We have developed a Shiny application for convenient model assessment, which can be launched using the command:
medRCT_shiny(dat = data)Before conducting the mediation analysis, users are encouraged to assess the models fitted by the algorithm using this Shiny application. The Shiny app aims to provide a user-friendly interface to review model summaries and identify potential warnings and errors, ensuring that the models are appropriately specified before proceeding with the analysis. If issues with model fitting are detected, users are encouraged to adjust the exposure-confounder interaction term as needed. However, mediators or confounders must not be selected based on model fitting results.
In the Shiny application, after specifying the relevant arguments and
clicking the Run medRCT models button, the app will fit all
regression models required by the medRCT algorithm and
generate detailed summaries for each model. These summaries support
model assessment, allowing users to identify potential issues with
fitting what are usually richly-specified models.
Additionally, any warnings or error
messages encountered during the model fitting process are
highlighted in the app. By offering a user-friendly interface and
diagnostic tool, our Shiny app streamlines the model assessment process
for the medRCT algorithm, facilitating transparent and
comprehensive model assessment.