PStrata

PStrata fits Bayesian principal stratification models using Stan. It supports a wide variety of models, priors, and assumptions to provide flexibility for causal inference in the presence of post-treatment confounding.

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

Installation

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

Overview

Let \(Z\) denote the assigned treatment, \(D\) denote the post-randomization intermediate variable, \(X\) denote the covariates and \(Y\) denote the outcome. Define \(S = (D(0), D(1))\) as the principal stratum.

PStrata requires specification of two models:

• S-model: a multinomial model for the distribution of principal strata given covariates \[\log \frac{p(S = s\mid X)}{p(S = s_0 \mid X)} = X \beta^S.\]

• Y-model: a generalized linear model for the outcome specific to a principal stratum and treatment, given the covariates \[\mathbb{E}[Y \mid X, S, Z] = g^{-1}(X \beta_{s, z}^Y).\]

Assumptions

• Monotonicity: assumes \(D(0)\leq D(1)\), ruling out the existence of principal stratum \(S = (1, 0)\). In PStrata, users explicitly specify all principal strata that are assumed to exist, allowing more flexibility than the standard monotonicity assumption.

• Exclusion restriction (ER): for principal stratum \(S\) where \(D(0) = D(1)\), assumes \(p(Y \mid X, S, Z) = p(Y \mid X, S)\).

Example

Normal outcome

Consider fitting a Bayesian principal stratification model on sim_data_normal, with intercept-only S-model and Y-model. The Y-model uses a Gaussian family with identity link. We assume monotonicity and exclusion restriction on both \(S = (0, 0)\) and \(S = (1, 1)\).

library(PStrata)

obj <- PStrata(
    S.formula = Z + D ~ 1,
    Y.formula = Y ~ 1,
    Y.family = gaussian(link = "identity"),
    data = sim_data_normal,
    strata = c(n = "00*", c = "01", a = "11*"),
    prior_intercept = prior_normal(0, 1),
    prior_sigma = prior_inv_gamma(1),
    chains = 4, warmup = 500, iter = 1000
)

The strata argument specifies the assumed principal strata. The * suffix denotes that the exclusion restriction is applied to that stratum. Names (e.g., n, c, a for never-taker, complier, always-taker) are optional.

Print obj for an overview of estimated stratum proportions. Use summary(obj) for quantiles and confidence intervals.

obj
summary(obj)

Outcome estimation and contrasts

To obtain estimated mean effects by principal stratum and treatment arm:

res <- PSOutcome(obj)
summary(res, "data.frame")
plot(res)

To compute stratum-specific treatment effects (\(Y(1) - Y(0)\)):

cont <- PSContrast(res, Z = TRUE)
summary(cont, "data.frame")
plot(cont)

Survival outcome

PStrata also supports survival outcomes with Cox proportional hazards models:

obj <- PStrata(
    S.formula = Z + D ~ 1,
    Y.formula = survival(time, status, method = "Cox") ~ 1,
    data = sim_data_Cox,
    strata = c(n = "00*", c = "01", a = "11*"),
    prior_intercept = prior_normal(0, 1),
    chains = 4, warmup = 500, iter = 1000
)

res <- PSOutcome(obj)
cont <- PSContrast(res, Z = TRUE)
plot(cont)

Key Functions

Prior distributions

PStrata provides a set of prior distribution functions:

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

License

GPL (>= 2)