Causal Inference in a Longitudinal Transitioning State Environment

Implements Sequential Doubly Robust (SDR) and infinite-dimensional Targeted Maximum Likelihood (iTMLE) estimators for longitudinal modified treatment policies in settings with transitioning states, such as ICU, ward, or emergency department care episodes. Treatment is permitted in active states and becomes structurally inapplicable after a state transition (e.g. discharge or death). Supports asymmetric g- and Q-model regularisation, k-fold cross-fitting, and pluggable SuperLearner ensembles. Includes specialised SuperLearner wrappers (SL.tgt.* and SL.tmle_* families) for the iTMLE targeting step, which pass the logit offset as a covariate column to preserve correct subsetting during SuperLearner cross-validation. Methods based on Diaz et al. (2021) and Luedtke et al. (2017) .

CausalState

CausalState provides Sequential Doubly Robust (SDR) and infinite-dimensional Targeted Maximum Likelihood (iTMLE) estimators for longitudinal modified treatment policies (MTPs) in care-episode settings where patients can transition irreversibly out of an active state – for example, ICU discharge or in-hospital death.

The distinctive feature of the package is that the MTP can shift the transition dynamics themselves, not only the terminal outcome. A policy that shortens ICU stay changes both when patients leave and what outcomes they experience after leaving; CausalState handles both simultaneously.

Problem setting

The estimators apply when:

• Data are in long format, one row per patient per time point, with rows present only while the patient is in the active state.
• At each time point a patient can remain, discharge (alive exit), or die (dead exit); no return to the active state is possible.
• The treatment policy of interest is a modified treatment policy (MTP): a data-adaptive shift of the observed treatment rather than a static intervention.
• Interest is in the mean counterfactual outcome under the MTP, estimated from observational or trial data.

The practical limit on follow-up length is the number of patients still in the active state at each time point: as patients exit, the risk set shrinks and model fits become unstable. Cumulative density-ratio products also compound across time, so both considerations favour shorter episodes.

Estimators

Both estimators are sequentially doubly robust (2^K-robust, Luedtke et al. 2017): consistent whenever, at each time point, either the treatment model or the outcome model is correctly specified.

qreg() is a pure Q-recursion plug-in (no update, no DR guarantees) included as a weight-independent sensitivity check.

Workflow

density_ratio()  ->  sdr() / itmle() / qreg()

density_ratio() must run first. It fits per-time-point treatment classification models, computes the instantaneous density ratios r_t = dP~(A_t|H_t) / dP(A_t|H_t), and packages them with fold assignments that the downstream estimators inherit. Running it once and passing the result to multiple estimators is the intended pattern.

Quick example

library(CausalState)
library(SuperLearner)

# --- 1. Define the policy -------------------------------------------------
# Soft upward shift: nudge treatment probability up by 0.3, capped at 1
policy_up <- function(D_block, t, a_names) {
  out <- D_block[, ..a_names, drop = FALSE]
  out[[a_names[1]]] <- pmin(D_block[[a_names[1]]] + 0.3, 1)
  out
}

# --- 2. Density ratios ----------------------------------------------------
sl_lib <- c("SL.mean", "SL.glm")   # replace with richer library in practice

wr <- density_ratio(
  df              = patient_data,   # long-format data frame
  a_names         = "A",
  tmax            = 7L,
  baseline        = c("age", "sex"),
  tv_names        = c("L1", "L2"),
  sl_g            = sl_lib,
  k               = 5L,
  inner_v         = 5L,
  v               = 5L,
  seed            = 1L,
  id              = "id",
  time            = "time",
  policy_spec_fun = policy_up
)

# --- 3a. SDR estimate -----------------------------------------------------
res_sdr <- sdr(
  df              = patient_data,
  weight_object   = wr,
  tmax            = 7L,
  id              = "id", time = "time",
  alive           = "alive", in_state = "in_state",
  y               = "Y",
  baseline        = c("age", "sex"),
  tv_names        = c("L1", "L2"),
  a_names         = "A",
  sl_remain       = sl_lib, sl_death = sl_lib,
  sl_recursive    = sl_lib, sl_y = sl_lib,
  outcome_family  = "binomial",
  k               = 5L, inner_v = 5L,
  seed            = 1L,
  policy_spec_fun = policy_up
)

cat(sprintf("SDR:   psi = %.3f  SE = %.3f  95%% CI [%.3f, %.3f]\n",
            res_sdr$psi, res_sdr$se, res_sdr$ci[1], res_sdr$ci[2]))

# --- 3b. iTMLE estimate ---------------------------------------------------
res_itmle <- itmle(
  df              = patient_data,
  weight_object   = wr,
  tmax            = 7L,
  id              = "id", time = "time",
  alive           = "alive", in_state = "in_state",
  y               = "Y",
  baseline        = c("age", "sex"),
  tv_names        = c("L1", "L2"),
  a_names         = "A",
  sl_remain       = sl_lib, sl_death = sl_lib,
  sl_recursive    = sl_lib, sl_y = sl_lib,
  sl_target       = sl_tmle,
  outcome_family  = "binomial",
  k               = 5L, inner_v = 5L,
  seed            = 1L,
  policy_spec_fun = policy_up
)

cat(sprintf("iTMLE: psi = %.3f  SE = %.3f  95%% CI [%.3f, %.3f]\n",
            res_itmle$psi, res_itmle$se, res_itmle$ci[1], res_itmle$ci[2]))

# --- 4. Risk difference ---------------------------------------------------
ctr <- contrast(res_sdr, res_sdr_nat)   # intervention vs natural course
ctr$RD; ctr$ci_RD

Key design choices

Separate learner stacks per regression. Each regression component (g, Q at each time point, the terminal outcome) accepts its own SuperLearner library, allowing independent tuning across the pipeline.

Uniform clipping. Every SL prediction across the entire pipeline (g and Q models at every time point) is clipped to [bounds, 1-bounds] using the same bounds parameter (default 1e-5). The only exception is the Wu-Benkeser direct density-ratio metalearner, which clips in density-ratio space via dr_floor – see vignette("wb-metalearner").

Weight reuse. density_ratio() is designed to be run once and shared across sdr(), itmle(), and qreg(). Trimming is applied globally at consumption time, so all estimators that share a weight object operate on identically trimmed weights and produce directly comparable estimates.

Parallelism via mclapply. Process-level parallelism is available at the fold level (parallel = TRUE) and within-fold regression level (reg_workers). Does not work on Windows. Set BLAS and learner thread counts to 1 when enabling process-level parallelism to avoid oversubscription.

Installation

# install.packages("remotes")
remotes::install_github("sebastiaan-blank/CausalState")

Getting started

See vignette("getting-started") for a complete worked example with a simulated ICU dataset, including data structure, policy definition, SuperLearner library choices, and diagnostics.

Citation

Blank S (2026). CausalState: SDR and iTMLE for State-Aware Longitudinal
Modified Treatment Policies. R package version 0.9.0.
https://github.com/sebastiaan-blank/CausalState

References

Diaz I, Williams N, Hoffman KL, Schenck EJ (2021). Nonparametric Causal Effects Based on Longitudinal Modified Treatment Policies. JASA 118(542):846-857. doi:10.1080/01621459.2021.1955691.

Luedtke AR, Sofrygin O, van der Laan MJ, Carone M (2017). Sequential Double Robustness in Right-Censored Longitudinal Models. arXiv:1705.02459.

Rotnitzky A, Robins J, Babino L (2017). On the multiply robust estimation of the mean of the g-functional. arXiv:1705.08582.

Wu C, Benkeser D (2024). Nonparametric Efficient Estimation of Marginal Structural Models using Targeted Machine Learning. arXiv:2408.10847.

Williams NT, Diaz I (2023). lmtp: An R package for estimating the causal effects of modified treatment policies. Observational Studies.

Bang H, Robins JM (2005). Doubly robust estimation in missing data and causal inference models. Biometrics 61(4):962-973.

Haneuse S, Rotnitzky A (2013). Estimation of the effect of interventions that modify the received treatment. Statistics in Medicine 32(30):5260-5277.

Diaz Munoz I, van der Laan MJ (2012). Population intervention causal effects based on stochastic interventions. Biometrics 68(2):541-549.

License

AGPL-3. See LICENSE.md for details.