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CausalSpline

Overview

CausalSpline estimates nonlinear causal dose-response functions for continuous treatments using spline-based methods under standard causal assumptions (unconfoundedness + positivity).

Most causal inference tools assume a linear treatment effect:

\[Y = \beta_0 + \beta_1 T + \gamma X + \varepsilon\]

Real policy and health problems often violate this: dosage effects, thresholds, diminishing returns, and non-monotone relationships are common. CausalSpline models the exposure-response curve nonparametrically:

\[E[Y(t)] = \beta_0 + f(T)\]

where \(f(T)\) is a natural cubic spline or B-spline, estimated via IPW, G-computation, or doubly-robust methods.

Installation

# CRAN
install.packages("CausalSpline")

# Development version
remotes::install_github("causalfragility-lab/CausalSpline")

Quick Example

library(CausalSpline)

# Simulate data with a threshold effect
set.seed(42)
dat <- simulate_dose_response(n = 500, dgp = "threshold", confounding = 0.6)

# Fit causal dose-response curve via IPW
fit <- causal_spline(
  Y ~ T | X1 + X2 + X3,   # outcome ~ treatment | confounders
  data        = dat,
  method      = "ipw",
  df_exposure = 5
)

summary(fit)
plot(fit)

# G-computation alternative
fit_gc <- causal_spline(Y ~ T | X1 + X2 + X3, data = dat,
                        method = "gcomp", df_exposure = 5)

# Doubly robust estimation
fit_dr <- causal_spline(Y ~ T | X1 + X2 + X3, data = dat,
                        method = "dr", df_exposure = 5)

# Predict at specific treatment values
predict(fit_gc, newt = c(3, 5, 7), se_fit = TRUE)

# Check positivity / overlap
check_overlap(dat$T, fit$weights)

Fragility Diagnostics

A key feature of CausalSpline is geometric fragility diagnostics — tools for evaluating the structural stability of the estimated dose-response curve across treatment levels.

# Slope-based fragility (identifies flat / weak-effect regions)
fc_slope <- fragility_curve(fit, type = "inverse_slope")
plot(fc_slope)

# Curvature-based fragility (identifies thresholds and turning points)
fc_curv <- fragility_curve(fit, type = "curvature_ratio")
plot(fc_curv)

# Regional fragility summary over a policy-relevant interval
region_fragility(fit, a = 3, b = 6, type = "curvature_ratio")

These diagnostics complement traditional sensitivity analyses by examining the internal geometric stability of the causal function — where is the estimated relationship flat, rapidly changing, or structurally ambiguous?

Supported Methods

Method	`method =`	Consistent if …
Inverse Probability Weighting	`"ipw"`	GPS model correct
G-computation	`"gcomp"`	Outcome model correct
Doubly Robust (AIPW)	`"dr"`	At least one model correct

Supported DGPs (for Simulation)

simulate_dose_response(dgp = "threshold")   # flat region then linear rise
simulate_dose_response(dgp = "diminishing") # concave / diminishing returns
simulate_dose_response(dgp = "nonmonotone") # inverted-U / hump shape
simulate_dose_response(dgp = "linear")      # linear baseline
simulate_dose_response(dgp = "sinusoidal")  # oscillatory / complex shape

Key Functions

Function	Description
`causal_spline()`	Estimate the causal dose-response curve
`fragility_curve()`	Compute local geometric fragility diagnostics
`region_fragility()`	Regional fragility summary over treatment intervals
`gradient_curve()`	First and second derivatives of the estimated curve
`dose_response_curve()`	Extract the dose-response data frame
`predict()`	Predict E[Y(t)] at new treatment values
`check_overlap()`	Overlap / positivity diagnostics (ESS, weight plot)
`simulate_dose_response()`	Simulate nonlinear dose-response datasets

Relationship to MultiSpline

CausalSpline is the causal extension of MultiSpline. While MultiSpline fits multivariate spline regressions for prediction, CausalSpline:

Incorporates the generalised propensity score for causal identification
Targets the marginal structural mean \(E[Y(t)]\), not the conditional mean
Provides doubly-robust estimation
Includes positivity diagnostics (ESS, weight trimming)
Adds geometric fragility diagnostics with no precedent in existing packages

References

Hirano, K., & Imbens, G. W. (2004). The propensity score with continuous treatments. In Applied Bayesian Modeling and Causal Inference from Incomplete-Data Perspectives (pp. 73–84). Wiley.
Imbens, G. W. (2000). The role of the propensity score in estimating dose-response functions. Biometrika, 87(3), 706–710.
Robins, J. M., Hernán, M. A., & Brumback, B. (2000). Marginal structural models and causal inference in epidemiology. Epidemiology, 11(5), 550–560.
Flores, C. A., Flores-Lagunes, A., Gonzalez, A., & Neumann, T. C. (2012). Estimating the effects of length of exposure to instruction in a training program. Review of Economics and Statistics, 94(1), 153–171.

Citation

citation("CausalSpline")

License

GPL (>= 3)

Maintainer: Subir Hait haitsubi@msu.edu
Michigan State University

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.