Assessing Proximal, Distal, and Mediated Causal Excursion Effects for Micro-Randomized Trials

Provides methods to analyze micro-randomized trials (MRTs) with binary treatment options. Supports four types of analyses: (1) proximal causal excursion effects, including weighted and centered least squares (WCLS) for continuous proximal outcomes by Boruvka et al. (2018) and the estimator for marginal excursion effect (EMEE) for binary proximal outcomes by Qian et al. (2021) ; (2) distal causal excursion effects (DCEE) for continuous distal outcomes using a two-stage estimator by Qian (2025) ; (3) mediated causal excursion effects (MCEE) for continuous distal outcomes, estimating natural direct and indirect excursion effects in the presence of time-varying mediators by Qian (2025) ; and (4) standardized proximal effect size estimation for continuous proximal outcomes, generalizing the approach in Luers et al. (2019) to allow adjustment for baseline and time-varying covariates for improved efficiency.

MRTAnalysis

The MRTAnalysis package provides functions to conduct post-study analyses of Micro-Randomized Trials (MRTs), focusing on estimating causal excursion effects.

• Proximal outcomes (measured shortly after each treatment decision point):

  • wcls(): Primary analysis for continuous proximal outcomes. Implements weighted and centered least squares (the $k=1$ special case of Boruvka et al., 2018).
  • emee(): Primary analysis for binary proximal outcomes. Implements the estimator for marginal excursion effect (the $\Delta=1$ special case of Qian et al., 2021).
  • emee2(): Variant of emee(), centering treatment in the residual term. Basis for the sample size calculator in MRTSampleSizeBinary.

• Distal outcomes (measured once at end of study):

  • dcee(): Exploratory analysis for distal causal excursion effects in MRTs (Qian et al. 2025). Supports linear models and machine-learning learners (lm, gam, random forest, ranger, SuperLearner) with optional cross-fitting.

• Mediated effects through time-varying mediators to distal outcomes:

  • mcee(): Exploratory analysis for mediated causal excursion effects in MRTs, estimating natural direct excursion effects (NDEE) and natural indirect excursion effects (NIEE) through time-varying mediators. Supports GLM, GAM, random forest, ranger, and SuperLearner learners for fitting nuisance parameters.

• Standardized proximal effect size (continuous proximal outcomes only):

  • calculate_mrt_effect_size(): Standardized proximal effect size estimation for continuous proximal outcomes, with optional smoothing and bootstrap CIs.

Installation

You can install the package from CRAN:

install.packages("MRTAnalysis")

Usage

See vignettes for detailed examples:

library(MRTAnalysis)

# Proximal outcome analysis (continuous)
fit1 <- wcls(
  data = data_mimicHeartSteps,
  id = "userid", outcome = "logstep_30min",
  treatment = "intervention", rand_prob = 0.6,
  moderator_formula = ~1,
  control_formula = ~logstep_pre30min,
  availability = "avail"
)
summary(fit1)

# Distal outcome analysis
fit2 <- dcee(
  data = data_distal_continuous,
  id = "userid", outcome = "Y",
  treatment = "A", rand_prob = "prob_A",
  moderator_formula = ~1,
  control_formula = ~X,
  availability = "avail",
  control_reg_method = "lm"
)
summary(fit2)

# Mediation with distal outcome
fit3 <- mcee(
  data = data_time_varying_mediator_distal_outcome,
  id = "id", dp = "dp",
  outcome = "Y", treatment = "A", mediator = "M",
  availability = "I", rand_prob = "p_A",
  time_varying_effect_form = ~1,                # constant effects over time
  control_formula_with_mediator = ~ dp + M + X, # adjustment set
  control_reg_method = "glm"
)
summary(fit3)

# Standardized proximal effect size (continuous proximal outcomes only)
data("data_example_for_standardized_effect")
ans_ci <- calculate_mrt_effect_size(
  data = data_example_for_standardized_effect,
  id = "id",
  outcome = "outcome",
  treatment = "treatment",
  time = "decision_point",
  rand_prob = "prob_treatment",
  availability = "availability",
  covariates = "covariate1",
  do_bootstrap = TRUE,
  boot_replications = 100
)
# Note: use at least 1000 bootstrap replications for stable CIs.
summary(ans_ci)
plot(ans_ci)

References

• Boruvka, A., Almirall, D., Witkiewitz, K., & Murphy, S. A. (2018). Assessing time-varying causal effect moderation in mobile health. Journal of the American Statistical Association, 113(523), 1112–1121. doi:10.1080/01621459.2017.1305274

• Qian, T., Yoo, H., Klasnja, P., Almirall, D., & Murphy, S. A. (2021). Estimating time-varying causal excursion effects in mobile health with binary outcomes. Biometrika, 108(3), 507–527. doi:10.1093/biomet/asaa070

• Qian, T. (2025). Distal causal excursion effects: modeling long-term effects of time-varying treatments in micro-randomized trials. Biometrics, 81(4), ujaf134.

• Qian, T. (2025). Dynamic Causal Mediation Analysis for Intensive Longitudinal Data. arXiv:2506.20027.

• Luers, B., Klasnja, P., & Murphy, S. (2019). Standardized effect sizes for preventive mobile health interventions in micro-randomized trials. Prevention Science, 20(1), 100–109.