data_binary

Baseline model:
$$\log E\{Y_{t+1} \mid A_t = 0, I_t = 1\} =
 \alpha_0 + \alpha_1 \cdot \mathrm{time} / \mathrm{total\_T}
 + \alpha_2 \cdot \mathbf{1}(\mathrm{time} &gt; \mathrm{total\_T}/2).$$
Treatment effect model:
$$\log RR_t = \beta_0 + \beta_1 \cdot \mathrm{time} / \mathrm{total\_T}.$$
Randomization probabilities $p_t$ cycle over 0.3, 0.5, 0.7 (with repetition).
Availability is exogenous at 0.8 for all time points.

datasets

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) <doi:10.1080/01621459.2017.1305274> and the estimator for marginal excursion effect (EMEE) for binary proximal outcomes by Qian et al. (2021) <doi:10.1093/biomet/asaa070>; (2) distal causal excursion effects (DCEE) for continuous distal outcomes using a two-stage estimator by Qian (2025) <doi:10.1093/biomtc/ujaf134>; (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) <doi:10.48550/arXiv.2506.20027>; and (4) standardized proximal effect size estimation for continuous proximal outcomes, generalizing the approach in Luers et al. (2019) <doi:10.1007/s11121-017-0862-5> to allow adjustment for baseline and time-varying covariates for improved efficiency.

Tianchen Qian

MRTAnalysis

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

Shaolin Xiang

Zhaoxi Cheng

Xinyi Song

John Dziak

Audrey Boruvka

data_binary function

A data frame with 3000 observations and 10 variables:<dl>
 <dt>userid</dt>
<dd>Individual id number.</dd> <dt>time</dt>
<dd>Decision point index.</dd> <dt>time_var1</dt>
<dd>Time-varying covariate 1, the \"standardized time in study\",
 defined as the current decision point index divided by the total number
 of decision points.</dd> <dt>time_var2</dt>
<dd>Time-varying covariate 2, indicator of \"the second half of the study\",
 defined as whether the current decision point index is greater than the total number
 of decision points divided by 2.</dd> <dt>Y</dt>
<dd>Binary proximal outcome.</dd> <dt>A</dt>
<dd>Treatment assignment: whether the intervention is randomized to be delivered (=1)
 or not (=0) at the current decision point.</dd> <dt>rand_prob</dt>
<dd>Randomization probability $P(A=1)$ for the current decision point.</dd> <dt>avail</dt>
<dd>Availability indicator (=1 available, =0 not available) at the current decision point.</dd>
</dl>

Format

A synthetic data set of an MRT with binary proximal outcomes — data_binary

A data frame with 3000 observations and 10 variables:<dl>
 <dt>userid</dt>
<dd>Individual id number.</dd>

 <dt>time</dt>
<dd>Decision point index.</dd>

 <dt>time_var1</dt>
<dd>Time-varying covariate 1, the \"standardized time in study\",
 defined as the current decision point index divided by the total number
 of decision points.</dd>

 <dt>time_var2</dt>
<dd>Time-varying covariate 2, indicator of \"the second half of the study\",
 defined as whether the current decision point index is greater than the total number
 of decision points divided by 2.</dd>

 <dt>Y</dt>
<dd>Binary proximal outcome.</dd>

 <dt>A</dt>
<dd>Treatment assignment: whether the intervention is randomized to be delivered (=1)
 or not (=0) at the current decision point.</dd>

 <dt>rand_prob</dt>
<dd>Randomization probability $P(A=1)$ for the current decision point.</dd>

 <dt>avail</dt>
<dd>Availability indicator (=1 available, =0 not available) at the current decision point.</dd>


</dl>

data_binary: A synthetic data set of an MRT with binary proximal outcomes

Description

Usage

Arguments

Format