Intervention types in causatr

causatr separates model fitting (causat()) from causal contrasts (contrast()). The intervention — the hypothetical change in treatment — is specified at contrast time, not fit time. This design lets you fit once and contrast under many different interventions without re-estimating nuisance models.

This vignette tours every intervention constructor, shows which estimators support it, and demonstrates the calling pattern on real and simulated data.

Intervention constructors at a glance

Constructor What it does G-comp IPW AIPW Matching
static(v) Set treatment to v for everyone All types Binary, categorical All types Binary
shift(d) Add d to observed treatment Continuous Continuous, count (integer d) Continuous —
scale_by(c) Multiply observed treatment by c Continuous Continuous, count (integer-preserving) Continuous —
threshold(lo, hi) Clamp treatment to [lo, hi] Continuous — — —
dynamic(rule) Apply a user-defined deterministic rule All types Binary, categorical All types —
ipsi(d) Multiply odds of treatment by d — Binary — —
stochastic(f) Draw treatment from user-supplied distribution All types — — —
grace_period(w) Delay treatment initiation by w periods (natural-history MTP) Longitudinal, discrete — — —
carry_forward() Carry the baseline treatment forward (LOCF; natural-history MTP) Longitudinal, discrete — — —
NULL Natural course (observed values) All types All types All types —

grace_period() and carry_forward() are natural-history modified treatment policies (G-LMTPs): the intervened treatment at time \(t\) depends on the counterfactual natural-value history of treatment, so they cannot be written as dynamic() rules (which see only the observed lag). They are estimated by an augmented-data sequential regression and require a longitudinal g-computation fit with a discrete treatment — see the longitudinal vignette for runnable examples.

Data: NHEFS

All examples use the NHEFS dataset (Hernán & Robins, 2025):

  • Binary treatment (\(A\)): qsmk — quit smoking (0/1). Used for static(), dynamic(), and ipsi() examples.
  • Continuous treatment (\(A\)): smokeintensity — cigarettes smoked per day. Used for shift(), scale_by(), and threshold() examples.
  • Outcome (\(Y\)): wt82_71 — weight change in kg.
  • Confounders (\(L\)): sex, age, race, education, smoking-related variables, exercise, activity, and baseline weight — common causes of both \(A\) and \(Y\).
Code 
library(causatr)
library(tinyplot)

data("nhefs")

nhefs_complete <- nhefs[!is.na(nhefs$wt82_71) & !is.na(nhefs$education), ]

static() — set treatment to a fixed value

The simplest and most common intervention. static(1) means “everyone is treated”; static(0) means “no one is treated”. For categorical treatments, pass the level name as a string (e.g. static("B")).

G-computation

Code 
fit_gc <- causat(
  nhefs_complete,
  outcome = "wt82_71",
  treatment = "qsmk",
  confounders = ~ sex + age + I(age^2) + race + factor(education) +
    smokeintensity + I(smokeintensity^2) + smokeyrs + I(smokeyrs^2) +
    factor(exercise) + factor(active) + wt71 + I(wt71^2),
  model_fn = stats::glm
)

contrast(
  fit_gc,
  interventions = list(quit = static(1), continue = static(0)),
  reference = "continue",
  type = "difference"
)

Estimator: gcomp  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1566

Intervention means
intervention estimate se ci_lower ci_upper
quit 5.21 0.421 4.384 6.035
continue 1.747 0.217 1.321 2.173
Contrasts
comparison estimate se ci_lower ci_upper
quit vs continue 3.462 0.468 2.546 4.379

IPW

Code 
fit_ipw <- causat(
  nhefs_complete,
  outcome = "wt82_71",
  treatment = "qsmk",
  confounders = ~ sex + age + I(age^2) + race + factor(education) +
    smokeintensity + I(smokeintensity^2) + smokeyrs + I(smokeyrs^2) +
    factor(exercise) + factor(active) + wt71 + I(wt71^2),
  estimator = "ipw",
  model_fn = stats::glm,
  propensity_model_fn = stats::glm
)

contrast(
  fit_ipw,
  interventions = list(quit = static(1), continue = static(0)),
  reference = "continue",
  type = "difference"
)

Estimator: ipw  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1566

Intervention means
intervention estimate se ci_lower ci_upper
quit 5.288 0.447 4.412 6.163
continue 1.788 0.217 1.363 2.214
Contrasts
comparison estimate se ci_lower ci_upper
quit vs continue 3.499 0.49 2.538 4.46

AIPW (doubly robust)

Code 
fit_aipw <- causat(
  nhefs_complete,
  outcome = "wt82_71",
  treatment = "qsmk",
  confounders = ~ sex + age + I(age^2) + race + factor(education) +
    smokeintensity + I(smokeintensity^2) + smokeyrs + I(smokeyrs^2) +
    factor(exercise) + factor(active) + wt71 + I(wt71^2),
  estimator = "aipw",
  model_fn = stats::glm,
  propensity_model_fn = stats::glm
)

contrast(
  fit_aipw,
  interventions = list(quit = static(1), continue = static(0)),
  reference = "continue",
  type = "difference"
)

Estimator: aipw  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1566

Intervention means
intervention estimate se ci_lower ci_upper
quit 5.254 0.44 4.391 6.116
continue 1.777 0.218 1.349 2.205
Contrasts
comparison estimate se ci_lower ci_upper
quit vs continue 3.477 0.483 2.531 4.423

Matching

Code 
fit_match <- causat(
  nhefs_complete,
  outcome = "wt82_71",
  treatment = "qsmk",
  confounders = ~ sex + age + I(age^2) + race + factor(education) +
    smokeintensity + I(smokeintensity^2) + smokeyrs + I(smokeyrs^2) +
    factor(exercise) + factor(active) + wt71 + I(wt71^2),
  estimator = "matching",
  estimand = "ATT"
)

contrast(
  fit_match,
  interventions = list(quit = static(1), continue = static(0)),
  reference = "continue",
  type = "difference"
)

Estimator: matching  ·  Estimand: ATT  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 403

Intervention means
intervention estimate se ci_lower ci_upper
quit 4.525 0.435 3.672 5.378
continue 1.184 0.383 0.433 1.935
Contrasts
comparison estimate se ci_lower ci_upper
quit vs continue 3.341 0.559 2.246 4.436

All four methods should give broadly similar estimates (methodological triangulation). Discrepancies signal model misspecification in one or more approaches.

shift() — add a constant to observed treatment

A modified treatment policy (MTP) that shifts each individual’s observed treatment by a fixed amount. For continuous treatments, this answers “what would happen if everyone’s exposure increased (or decreased) by delta units?”

G-computation

Code 
fit_gc_cont <- causat(
  nhefs_complete,
  outcome = "wt82_71",
  treatment = "smokeintensity",
  confounders = ~ sex + age + I(age^2) + race + factor(education) +
    smokeyrs + I(smokeyrs^2) + factor(exercise) + factor(active) +
    wt71 + I(wt71^2),
  model_fn = stats::glm
)

res_shift_gc <- contrast(
  fit_gc_cont,
  interventions = list(reduce10 = shift(-10), observed = NULL),
  reference = "observed",
  type = "difference"
)
res_shift_gc

Estimator: gcomp  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1566

Intervention means
intervention estimate se ci_lower ci_upper
reduce10 2.684 0.256 2.183 3.186
observed 2.638 0.199 2.248 3.028
Contrasts
comparison estimate se ci_lower ci_upper
reduce10 vs observed 0.046 0.181 -0.308 0.4

IPW

Under IPW, shift(delta) uses a density-ratio weight: the ratio of the treatment density evaluated at the inverse-shifted value to the density at the observed value. The pushforward sign matters — shift(delta) evaluates at A - delta, not A + delta — because the weight uses the inverse map.

Code 
fit_ipw_cont <- causat(
  nhefs_complete,
  outcome = "wt82_71",
  treatment = "smokeintensity",
  confounders = ~ sex + age + I(age^2) + race + factor(education) +
    smokeyrs + I(smokeyrs^2) + factor(exercise) + factor(active) +
    wt71 + I(wt71^2),
  estimator = "ipw",
  model_fn = stats::glm,
  propensity_model_fn = stats::glm
)

res_shift_ipw <- contrast(
  fit_ipw_cont,
  interventions = list(reduce10 = shift(-10), observed = NULL),
  reference = "observed",
  type = "difference"
)
res_shift_ipw

Estimator: ipw  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1566

Intervention means
intervention estimate se ci_lower ci_upper
reduce10 2.69 0.248 2.205 3.175
observed 2.638 0.199 2.248 3.028
Contrasts
comparison estimate se ci_lower ci_upper
reduce10 vs observed 0.051 0.163 -0.268 0.371

Comparing shifts across methods

Code 
est <- data.frame(
  method = c("G-comp", "IPW"),
  estimate = c(
    res_shift_gc$contrasts$estimate[1],
    res_shift_ipw$contrasts$estimate[1]
  ),
  ci_lower = c(
    res_shift_gc$contrasts$ci_lower[1],
    res_shift_ipw$contrasts$ci_lower[1]
  ),
  ci_upper = c(
    res_shift_gc$contrasts$ci_upper[1],
    res_shift_ipw$contrasts$ci_upper[1]
  )
)

tinyplot(
  estimate ~ method,
  data = est,
  type = "pointrange",
  ymin = est$ci_lower,
  ymax = est$ci_upper,
  xlab = "Method",
  ylab = "Difference in weight change (kg)",
  main = "shift(-10): reduce smoking by 10 cigs/day"
)
abline(h = 0, lty = 2, col = "grey40")

Point estimates and confidence intervals for a shift(-10) intervention under g-computation and IPW.

Note

threshold() is not supported under IPW because the pushforward of a continuous density under a boundary clamp is a mixed measure (point masses at the bounds plus continuous density in the interior). Use estimator = "gcomp" for threshold interventions.

Count treatment (Poisson / negative binomial)

For integer-valued count treatments, pass propensity_family = "poisson" or "negbin" to use a count density model instead of the default Gaussian.

DGM. A Poisson-distributed count treatment (e.g. number of clinic visits) confounded by \(L\), with a linear outcome model.

\[ \begin{aligned} L &\sim N(0,1) \\ A &\sim \text{Poisson}\!\bigl(\exp(0.5\,L)\bigr) \\ Y &= 2 + 1.5\,A + L + \varepsilon, \quad \varepsilon \sim N(0,1) \end{aligned} \]

True contrast: \(\mathbb{E}[Y(A+1)] - \mathbb{E}[Y(A)] = 1.5\).

Code 
set.seed(6)
n <- 3000
L <- rnorm(n)
A <- rpois(n, exp(0.5 * L))
Y <- 2 + 1.5 * A + L + rnorm(n)
count_df <- data.frame(Y = Y, A = A, L = L)

fit_pois <- causat(
  count_df,
  outcome = "Y",
  treatment = "A",
  confounders = ~ L,
  estimator = "ipw",
  propensity_family = "poisson",
  model_fn = stats::glm,
  propensity_model_fn = stats::glm
)

res_pois <- contrast(
  fit_pois,
  interventions = list(plus1 = shift(1), observed = NULL),
  reference = "observed",
  type = "difference"
)
res_pois

Estimator: ipw  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 3000

Intervention means
intervention estimate se ci_lower ci_upper
plus1 5.267 0.069 5.133 5.402
observed 3.692 0.049 3.595 3.788
Contrasts
comparison estimate se ci_lower ci_upper
plus1 vs observed 1.576 0.05 1.478 1.674

The shift delta must be integer — shift(0.5) on a count treatment aborts because dpois() returns 0 at non-integer arguments.

scale_by() — multiply observed treatment by a factor

A proportional MTP. scale_by(0.5) halves each individual’s exposure; scale_by(2) doubles it.

G-computation

Code 
res_scale_gc <- contrast(
  fit_gc_cont,
  interventions = list(halved = scale_by(0.5), observed = NULL),
  reference = "observed",
  type = "difference"
)
res_scale_gc

Estimator: gcomp  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1566

Intervention means
intervention estimate se ci_lower ci_upper
halved 2.686 0.259 2.178 3.193
observed 2.638 0.199 2.248 3.028
Contrasts
comparison estimate se ci_lower ci_upper
halved vs observed 0.047 0.185 -0.316 0.411

IPW

Under IPW, scale_by(c) evaluates the density at A / c and includes the Jacobian |1/c| in the density-ratio weight.

Code 
res_scale_ipw <- contrast(
  fit_ipw_cont,
  interventions = list(halved = scale_by(0.5), observed = NULL),
  reference = "observed",
  type = "difference"
)
res_scale_ipw

Estimator: ipw  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1566

Intervention means
intervention estimate se ci_lower ci_upper
halved 2.45 0.291 1.88 3.021
observed 2.638 0.199 2.248 3.028
Contrasts
comparison estimate se ci_lower ci_upper
halved vs observed -0.188 0.223 -0.625 0.249

threshold() — clamp treatment within bounds (g-comp only)

Caps treatment at a ceiling and/or floor. threshold(0, 20) means “nobody smokes more than 20 cigarettes per day; those below 0 are set to 0”.

Code 
res_thresh <- contrast(
  fit_gc_cont,
  interventions = list(cap20 = threshold(0, 20), observed = NULL),
  reference = "observed",
  type = "difference"
)
res_thresh

Estimator: gcomp  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1566

Intervention means
intervention estimate se ci_lower ci_upper
cap20 2.659 0.208 2.252 3.066
observed 2.638 0.199 2.248 3.028
Contrasts
comparison estimate se ci_lower ci_upper
cap20 vs observed 0.021 0.08 -0.137 0.178

This intervention is only available under g-computation. Under IPW, the density-ratio weight is not well-defined at the boundary clamp points (point-mass discontinuity in the pushforward density). causatr rejects threshold() under estimator = "ipw" with an informative error pointing at g-comp.

dynamic() — deterministic treatment rule

A dynamic intervention assigns treatment based on individual characteristics. The rule function receives two arguments — the full data and the observed treatment vector — and returns a vector of counterfactual treatment values.

G-computation (binary treatment)

Assign quitting only to heavy smokers (> 20 cigarettes/day at baseline):

Code 
res_dyn_gc <- contrast(
  fit_gc,
  interventions = list(
    rule = dynamic(\(data, trt) ifelse(data$smokeintensity > 20, 1, 0)),
    all_quit = static(1)
  ),
  reference = "all_quit",
  type = "difference"
)
res_dyn_gc

Estimator: gcomp  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1566

Intervention means
intervention estimate se ci_lower ci_upper
rule 2.725 0.204 2.325 3.124
all_quit 5.21 0.421 4.384 6.035
Contrasts
comparison estimate se ci_lower ci_upper
rule vs all_quit -2.485 0.337 -3.146 -1.824

IPW (binary treatment)

Under IPW, dynamic() on a binary treatment uses Horwitz–Thompson indicator weights: w_i = I(A_i = rule_i) / f(A_i | L_i). This is well-defined because the treatment takes only two values and each individual’s counterfactual is deterministic.

Code 
res_dyn_ipw <- contrast(
  fit_ipw,
  interventions = list(
    rule = dynamic(\(data, trt) ifelse(data$smokeintensity > 20, 1, 0)),
    all_quit = static(1)
  ),
  reference = "all_quit",
  type = "difference"
)
res_dyn_ipw

Estimator: ipw  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1566

Intervention means
intervention estimate se ci_lower ci_upper
rule 2.803 0.355 2.107 3.499
all_quit 5.288 0.447 4.412 6.163
Contrasts
comparison estimate se ci_lower ci_upper
rule vs all_quit -2.485 0.385 -3.239 -1.73

G-computation (continuous treatment)

Dynamic rules on continuous treatments work under g-comp (predict-then-average on the outcome model). Here, heavy smokers are reduced to 20 while others keep their observed level:

Code 
res_dyn_cont <- contrast(
  fit_gc_cont,
  interventions = list(
    capped = dynamic(\(data, trt) pmin(trt, 20)),
    observed = NULL
  ),
  reference = "observed",
  type = "difference"
)
res_dyn_cont

Estimator: gcomp  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1566

Intervention means
intervention estimate se ci_lower ci_upper
capped 2.659 0.208 2.252 3.066
observed 2.638 0.199 2.248 3.028
Contrasts
comparison estimate se ci_lower ci_upper
capped vs observed 0.021 0.08 -0.137 0.178
Note

dynamic() on continuous treatment is not supported under IPW. A deterministic rule on a continuous treatment is a Dirac per individual, which has no Lebesgue density — the density ratio is not defined. Rewrite the rule as a smooth shift() or scale_by(), or use estimator = "gcomp".

ipsi() — incremental propensity score intervention (IPW only)

Kennedy (2019)’s incremental propensity score intervention multiplies each individual’s odds of treatment by delta. It is a stochastic MTP that never materialises a specific counterfactual treatment value — instead, it shifts the entire propensity score distribution.

The closed-form weight is: \[w_i = \frac{\delta \cdot A_i + (1 - A_i)}{\delta \cdot p_i + (1 - p_i)}\]

where \(p_i = P(A = 1 \mid L_i)\) is the fitted propensity.

IPSI is binary-treatment, IPW-only — g-comp and matching cannot evaluate it because there is no counterfactual treatment column to predict at.

Doubling the odds of quitting

Code 
res_ipsi_2 <- contrast(
  fit_ipw,
  interventions = list(double_odds = ipsi(2), natural = NULL),
  reference = "natural",
  type = "difference"
)
res_ipsi_2

Estimator: ipw  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1566

Intervention means
intervention estimate se ci_lower ci_upper
double_odds 3.125 0.218 2.697 3.552
natural 2.638 0.199 2.248 3.028
Contrasts
comparison estimate se ci_lower ci_upper
double_odds vs natural 0.486 0.066 0.357 0.615

Halving the odds of quitting

Code 
res_ipsi_half <- contrast(
  fit_ipw,
  interventions = list(half_odds = ipsi(0.5), natural = NULL),
  reference = "natural",
  type = "difference"
)
res_ipsi_half

Estimator: ipw  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1566

Intervention means
intervention estimate se ci_lower ci_upper
half_odds 2.284 0.197 1.898 2.669
natural 2.638 0.199 2.248 3.028
Contrasts
comparison estimate se ci_lower ci_upper
half_odds vs natural -0.355 0.051 -0.455 -0.255

IPSI dose-response

Varying delta traces out a dose-response curve on the odds scale:

Code 
deltas <- c(0.25, 0.5, 1, 2, 4)
ipsi_results <- lapply(deltas, function(d) {
  res <- contrast(
    fit_ipw,
    interventions = list(shifted = ipsi(d), natural = NULL),
    reference = "natural",
    type = "difference"
  )
  data.frame(
    delta = d,
    estimate = res$contrasts$estimate[1],
    ci_lower = res$contrasts$ci_lower[1],
    ci_upper = res$contrasts$ci_upper[1]
  )
})
ipsi_df <- do.call(rbind, ipsi_results)

tinyplot(
  estimate ~ delta,
  data = ipsi_df,
  type = "pointrange",
  ymin = ipsi_df$ci_lower,
  ymax = ipsi_df$ci_upper,
  xlab = expression(delta ~ "(odds multiplier)"),
  ylab = "E[Y(IPSI)] - E[Y(natural)] (kg)",
  main = "IPSI dose-response: effect on weight change"
)
abline(h = 0, lty = 2, col = "grey40")

Dose-response curve showing the estimated effect of incrementally shifting the odds of quitting smoking.

At delta = 1 the intervention is the natural course, so the contrast is zero. Larger delta makes quitting more likely and the effect on weight gain grows.

stochastic() — user-defined randomised intervention (g-comp only)

A stochastic intervention draws each individual’s counterfactual treatment from a user-supplied distribution that may depend on covariates. Unlike dynamic(), which assigns a single deterministic value, stochastic() integrates over the randomness by Monte Carlo: the g-formula is evaluated n_mc times, each with an independent draw from the sampler, and the predictions are averaged.

The sampler function has the same signature as a dynamic() rule — function(data, treatment) — but should return an independent random draw each time it is called.

Binary treatment: covariate-dependent randomisation

Assign quitting with probability that depends on smoking intensity:

Code 
set.seed(42)
res_stoch <- contrast(
  fit_gc,
  interventions = list(
    random_quit = stochastic(
      \(data, trt) rbinom(nrow(data), 1,
                          plogis(-1 + 0.05 * data$smokeintensity)),
      n_mc = 200L
    ),
    all_quit = static(1)
  ),
  reference = "all_quit",
  type = "difference"
)
res_stoch

Estimator: gcomp  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1566

Intervention means
intervention estimate se ci_lower ci_upper
random_quit 3.489 0.242 3.014 3.963
all_quit 5.21 0.421 4.384 6.035
Contrasts
comparison estimate se ci_lower ci_upper
random_quit vs all_quit -1.721 0.232 -2.176 -1.266

The estimate is a population average over both individuals and the stochastic policy.

Continuous treatment: random shift

Add a random perturbation (rather than a fixed shift) to each individual’s smoking intensity:

Code 
set.seed(42)
res_stoch_cont <- contrast(
  fit_gc_cont,
  interventions = list(
    noisy_reduce = stochastic(
      \(data, trt) trt + rnorm(length(trt), mean = -5, sd = 2),
      n_mc = 200L
    ),
    observed = NULL
  ),
  reference = "observed",
  type = "difference"
)
res_stoch_cont

Estimator: gcomp  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1566

Intervention means
intervention estimate se ci_lower ci_upper
noisy_reduce 2.661 0.211 2.248 3.074
observed 2.638 0.199 2.248 3.028
Contrasts
comparison estimate se ci_lower ci_upper
noisy_reduce vs observed 0.023 0.09 -0.154 0.2
Tip

Choosing n_mc: 100–500 is typical. The sandwich SE accounts for the MC draws used at estimation time, so there is no need to inflate n_mc just for inference. If point estimates visibly change when you re-run with a different seed, increase n_mc.

Note

stochastic() is only supported under estimator = "gcomp" (point and longitudinal). IPW and matching cannot evaluate it because the density ratio of a user-defined stochastic policy is generally intractable.

NULL — the natural course

NULL means “do not intervene; use the observed treatment values”. It is the natural reference for MTPs:

Code 
res_multi <- contrast(
  fit_gc_cont,
  interventions = list(
    reduce10 = shift(-10),
    halved   = scale_by(0.5),
    cap20    = threshold(0, 20),
    observed = NULL
  ),
  reference = "observed",
  type = "difference"
)
res_multi

Estimator: gcomp  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1566

Intervention means
intervention estimate se ci_lower ci_upper
reduce10 2.684 0.256 2.183 3.186
halved 2.686 0.259 2.178 3.193
cap20 2.659 0.208 2.252 3.066
observed 2.638 0.199 2.248 3.028
Contrasts
comparison estimate se ci_lower ci_upper
reduce10 vs observed 0.046 0.181 -0.308 0.4
halved vs observed 0.047 0.185 -0.316 0.411
cap20 vs observed 0.021 0.08 -0.137 0.178

Combining interventions in one contrast

Both g-comp and IPW support multiple interventions in a single contrast() call. All pairwise differences against the reference are computed, and the variance-covariance matrix covers all interventions jointly.

G-computation

Code 
est <- res_multi$contrasts
tinyplot(
  estimate ~ comparison,
  data = est,
  type = "pointrange",
  ymin = est$ci_lower,
  ymax = est$ci_upper,
  xlab = "Comparison",
  ylab = "Difference in weight change (kg)",
  main = "Multiple interventions (g-comp)"
)
abline(h = 0, lty = 2, col = "grey40")

Point estimates and confidence intervals for multiple continuous-treatment interventions under g-computation.

IPW

Code 
res_multi_ipw <- contrast(
  fit_ipw_cont,
  interventions = list(
    reduce10 = shift(-10),
    halved   = scale_by(0.5),
    observed = NULL
  ),
  reference = "observed",
  type = "difference"
)
res_multi_ipw

Estimator: ipw  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1566

Intervention means
intervention estimate se ci_lower ci_upper
reduce10 2.69 0.248 2.205 3.175
halved 2.45 0.291 1.88 3.021
observed 2.638 0.199 2.248 3.028
Contrasts
comparison estimate se ci_lower ci_upper
reduce10 vs observed 0.051 0.163 -0.268 0.371
halved vs observed -0.188 0.223 -0.625 0.249

Intervention support by estimator

The table below summarises which combinations are supported and which are rejected with an informative error. The restrictions reflect genuine architectural limits of the density-ratio framework, not implementation gaps.

Intervention G-comp (point) G-comp (longitudinal) IPW AIPW Matching
static() All treatment types All treatment types Binary, categorical All types Binary only
shift() Continuous Continuous Continuous, count (integer delta) Continuous —
scale_by() Continuous Continuous Continuous, count (integer-preserving) Continuous —
threshold() Continuous Continuous — (mixed pushforward) — —
dynamic() All treatment types All treatment types Binary, categorical All types —
ipsi() — — Binary only — —
stochastic() All treatment types All treatment types — (intractable density ratio) — —
NULL All All All All —

Why some combinations are rejected:

  • threshold() under IPW: The pushforward of a continuous density under a boundary clamp is a mixed measure — point masses at lo/hi plus continuous density in the interior. The density ratio is not well-defined.
  • dynamic() on continuous treatment under IPW: A deterministic rule on a continuous treatment is a Dirac per individual with no Lebesgue density.
  • static(v) on continuous treatment under IPW: Nobody is observed exactly at v, so the HT indicator I(A = v) is zero almost surely.
  • ipsi() under g-comp/matching: IPSI shifts the propensity, not the treatment value. There is no counterfactual treatment column to predict at.
  • stochastic() under IPW/matching: The density ratio of an arbitrary user-defined stochastic policy is generally intractable. Only g-computation (Monte Carlo integration) supports it.
  • static() / dynamic() / threshold() / ipsi() on count treatments: Count treatments (enabled via propensity_family = "poisson" or "negbin") use dpois() / dnbinom() for the density ratio. static() is degenerate (HT indicator is zero almost surely on a count distribution). dynamic() has the same Dirac problem as on continuous. threshold() has the same mixed- measure problem. ipsi() is Bernoulli-specific. Only shift() (integer delta) and scale_by() (where A / factor is integer for every observation) are well-defined.

References

Hernán MA, Robins JM (2025). Causal Inference: What If. Chapman & Hall/CRC.

Kennedy EH (2019). Nonparametric causal effects based on incremental propensity score interventions. Journal of the American Statistical Association 114:645–656.

Díaz I, van der Laan MJ (2012). Population intervention causal effects based on stochastic interventions. Biometrics 68:541–549.

Díaz I, Williams N, Hoffman KL, Schenck EJ (2023). Non-parametric causal effects based on longitudinal modified treatment policies. Journal of the American Statistical Association 118:846–857.