sensitivity.SensitivityResult

Result of unmeasured confounding sensitivity analysis.

Usage

sensitivity.SensitivityResult(
    outcome,
    treatment,
    observed_ate_draws,
    gamma_values,
    delta_values,
    adjusted_ate_mean,
    prob_sign_change
)

Contains the observed ATE posterior draws and adjusted ATE values for a grid of hypothetical confounder strengths (γ, δ).

The confounding model assumes a latent U with:

Effect γ on the treatment variable
Effect δ on the outcome variable
Confounding bias in the ATE = γ × δ

Parameters

outcome: str: Outcome variable name.
treatment: str: Treatment variable name.
observed_ate_draws: np.ndarray: Posterior draws of the unadjusted ATE, shape (n_draws,).
gamma_values: np.ndarray: 1D grid of γ (confounder → treatment) values.
delta_values: np.ndarray: 1D grid of δ (confounder → outcome) values.
adjusted_ate_mean: np.ndarray: Mean bias-adjusted ATE at each grid point, shape (n_gamma, n_delta).
prob_sign_change: np.ndarray: Posterior probability that the ATE sign flips at each grid point, shape (n_gamma, n_delta).

Attributes

Name	Description
observed_ate	Posterior mean of the unadjusted ATE.
observed_ate_hdi	Highest density interval of the unadjusted ATE at the default probability mass.
tipping_point	The γ × δ product that reduces the posterior mean ATE to zero.

observed_ate

Posterior mean of the unadjusted ATE.

observed_ate: float

observed_ate_hdi

Highest density interval of the unadjusted ATE at the default probability mass.

observed_ate_hdi: np.ndarray

tipping_point

The γ × δ product that reduces the posterior mean ATE to zero.

tipping_point: float

A confounder whose effects on treatment and outcome multiply to this value would exactly nullify the observed average treatment effect. The tipping point equals the observed mean ATE because adjusted ATE = observed ATE − γ × δ.

Methods

Name	Description
plot()	Contour plot of adjusted ATE vs. confounder strength.

plot()

Contour plot of adjusted ATE vs. confounder strength.

Usage

plot(ax=None, cmap="RdBu_r", n_levels=20)

Shows how the estimated ATE changes as a function of the hypothetical confounder’s effect on treatment (γ) and outcome (δ). A black contour line marks the tipping boundary where the adjusted ATE crosses zero.

Parameters

ax: matplotlib.axes.Axes | None = None: Axes to plot on. Creates a new figure if None.
cmap: str = "RdBu_r": Matplotlib colormap name (default "RdBu_r").
n_levels: int = 20: Number of filled contour levels.

Returns

matplotlib.figure.Figure: The figure containing the contour plot.