PStrata

PStrata fits Bayesian principal stratification models using Stan. It supports a wide variety of outcome families, link functions, priors, and customizable monotonicity / exclusion-restriction assumptions for causal inference in the presence of post-treatment confounding.

See Liu and Li (2023) arXiv:2304.02740 for methodological details.

Installation

# Install from GitHub
devtools::install_github("LauBok/PStrata")

PStrata compiles models with Stan via rstan, so a working C++ toolchain is required (Rtools on Windows, Xcode command-line tools on macOS). See the RStan Getting Started guide.

Overview

Let Z denote the assigned treatment, D the post-randomization intermediate variable, X the covariates and Y the outcome. The principal stratum is S = (D(0), D(1)). PStrata specifies two models:

• S-model — a multinomial (softmax) model for the principal stratum given covariates: log p(S=s | X) / p(S=s0 | X) = X beta^S.
• Y-model — a generalized linear (or survival) model for the outcome, specific to a principal stratum and treatment arm: E[Y | X, S, Z] = g^{-1}(X beta_{s,z}^Y).

Assumptions

• Monotonicity — you explicitly list every principal stratum assumed to exist via the strata argument; any stratum you omit (e.g. defiers "10") is ruled out. This is more flexible than a fixed monotonicity assumption.
• Exclusion restriction (ER) — for a stratum where D(0) = D(1), the outcome distribution does not depend on Z. Strata under ER are named in the ER argument.

Workflow

Step	Function	Purpose
1	PStrataModel()	Specify the model symbolically (no data needed)
2	fit()	Build data, generate Stan code, run MCMC
3	estimate()	Extract posterior potential outcomes per stratum × arm
4	contrast()	Compute causal effects (e.g. Y(1) - Y(0))

print(), summary(), plot(), diagnostics(), and stancode() are available on the fitted object.

Example

Normal outcome

Fit an intercept-only model on sim_data_normal (non-compliance: never-takers, compliers, always-takers) under monotonicity, with exclusion restriction on never-takers and always-takers.

library(PStrata)

model <- PStrataModel(
  S.formula = Z + D ~ 1,
  Y.formula = Y ~ 1,
  Y.family  = gaussian(link = "identity"),
  strata    = c(n = "00", c = "01", a = "11"),
  ER        = c("n", "a"),
  prior_intercept = prior_normal(0, 1),
  prior_sigma     = prior_inv_gamma(1)
)
summary(model)   # algebraic description of the specified model

ps_fit <- fit(model, data = sim_data_normal,
              chains = 4, warmup = 500, iter = 1000)
ps_fit            # stratum proportions + mean outcome per group
summary(ps_fit)   # posterior intervals for all parameters
diagnostics(ps_fit)

Each stratum is a string of D values, one digit per treatment arm: "00" = never-taker, "01" = complier, "11" = always-taker. Names (n, c, a) are optional. Multiple post-randomization variables use | (e.g. "00|01") or the list-of-lists form.

Potential outcomes and contrasts

est <- estimate(ps_fit)        # E[Y(z) | S = s] by stratum and arm
summary(est, "data.frame")
plot(est)

ctr <- contrast(ps_fit, Z = TRUE)   # treatment effect Y(1) - Y(0) per stratum
summary(ctr, "data.frame")
plot(ctr)

Survival outcome

Time-to-event outcomes use Y.family = survival("Cox") (Weibull-Cox) or survival("AFT") (log-normal AFT). The outcome formula carries the event indicator: time + status ~ X.

model_s <- PStrataModel(
  S.formula = Z + D ~ 1,
  Y.formula = Y + delta ~ 1,
  Y.family  = survival("Cox"),
  strata    = c(n = "00", c = "01", a = "11"),
  ER        = c("n", "a"),
  prior_intercept = prior_normal(0, 1)
)
ps_fit_s <- fit(model_s, data = sim_data_Cox,
                chains = 4, warmup = 500, iter = 1000)

# Survival probability (or type = "RACE" for restricted average causal effect)
est_s <- estimate(ps_fit_s, type = "probability")
plot(est_s)

ctr_s <- contrast(ps_fit_s, Z = TRUE)
plot(ctr_s)

Outcome families

gaussian, binomial, Gamma, poisson, inverse.gaussian (standard stats::family objects with their usual links), plus survival("Cox") and survival("AFT").

Binary-outcome principal stratification is weakly identified at small sample sizes / short chains; use enough data and MCMC iterations (e.g. chains = 4, iter = 2000) and check diagnostics() for convergence.

Prior distributions

prior_normal(), prior_t(), prior_cauchy(), prior_logistic(), prior_lasso(), prior_exponential(), prior_gamma(), prior_inv_gamma(), prior_chisq(), prior_inv_chisq(), prior_weibull(), prior_flat().

Assign them through the PStrataModel() arguments prior_intercept, prior_coefficient, prior_sigma, prior_alpha, prior_lambda, prior_theta.

Key functions

Function	Description
PStrataModel()	Specify a principal stratification model
fit()	Fit the model via Stan MCMC
estimate()	Posterior potential outcomes by stratum × arm
contrast()	Causal-effect contrasts (strata, arms, time)
diagnostics()	MCMC convergence diagnostics
make_stancode() / stancode()	Inspect the generated Stan program
survival()	Family constructor for time-to-event outcomes

Datasets

sim_data_normal (Gaussian outcome, non-compliance) and sim_data_Cox (survival outcome) are bundled for illustration.

License

GPL (>= 2)