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

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.