Transportability and generalizability

Causal effects estimated by causat() are, by default, effects in the study sample — the rows of data. In applied work the scientific question is often about a different population: a clinic, country, or cohort that differs in covariate distribution from the study. Moving the estimand from study to target is the job of transportability (or generalizability) weights.

This vignette shows how to transport causal estimates to a target population using the target = argument.

Setup

Code 
library(causatr)

Simulated data

We simulate a mixed dataset with study rows (\(S = 1\), full data) and target rows (\(S = 0\), covariates only):

Code 
set.seed(42)
n <- 3000
L <- rnorm(n)
S <- rbinom(n, 1, plogis(-0.5 + 1.0 * L))
A <- ifelse(S == 1L, rbinom(n, 1, plogis(0.2 + 0.3 * L)), NA_integer_)
Y <- ifelse(S == 1L, 2 + 3 * A + 1.5 * L + 1.0 * A * L + rnorm(n), NA_real_)

df <- data.frame(Y = Y, A = A, L = L, S = S)
head(df)
#>          Y  A          L S
#> 1 8.600228  1  1.3709584 1
#> 2       NA NA -0.5646982 0
#> 3       NA NA  0.3631284 0
#> 4 7.208478  1  0.6328626 1
#> 5       NA NA  0.4042683 0
#> 6       NA NA -0.1061245 0
table(df$S)
#> 
#>    0    1 
#> 1843 1157

The true ATE in any population is \(3 + 1 \cdot E[L]\) (a constant main effect of 3 plus an interaction \(A \times L\)). Because the sampling model shifts the \(L\)-distribution, the study (\(E[L \mid S=1] \approx 0.5\)) and target (\(E[L \mid S=0] \approx -0.35\)) populations have different ATEs: roughly 3.5 vs 2.65.

The covariate shift is visible in the density of \(L\) by selection status. The study (\(S = 1\)) overrepresents high values of \(L\), while the target (\(S = 0\)) is shifted left:

Code 
dens_df <- data.frame(
  L = df$L,
  Population = ifelse(df$S == 1L, "Study (S = 1)", "Target (S = 0)")
)

tinyplot::tinyplot(
  ~ L | Population,
  data = dens_df,
  type = "density",
  lwd = 2,
  xlab = "Confounder L",
  ylab = "Density",
  main = "Covariate shift between study and target",
  palette = "dark2"
)
Density plot of confounder L stratified by selection status S. The study population (S = 1) is shifted right compared to the target population (S = 0), illustrating the covariate shift that motivates transportability.
Figure 1

This shift is exactly what the sampling model \(P(S = 1 \mid L)\) captures. Without transport weights, causal estimates reflect the study’s skewed \(L\)-distribution rather than the target’s.

The target = argument

Pass the name of the binary selection indicator (\(S\)) to target =:

Code 
fit_gc <- causat(
  df,
  outcome = "Y",
  treatment = "A",
  confounders_outcome = ~ L + A:L,
  confounders_treatment = ~ L,
  confounders_sampling = ~ L,
  target = "S"
)
#> Warning: `model_fn` not specified; defaulting to `stats::glm`.
#> ℹ Set `model_fn` explicitly (e.g. `model_fn = stats::glm` or `model_fn = mgcv::gam`).
fit_gc
#> <causatr_fit>
#>  Estimator:  G-computation
#>  Type:       point
#>  Outcome:    Y (gaussian)
#>  Treatment:  A
#>  Estimand:   ATE
#>  Conf (outcome):   ~L + A:L 
#>  Conf (treatment): ~L 
#>  Conf (sampling):  ~L 
#>  N:          3000

The outcome model includes the A:L interaction to capture the heterogeneous treatment effect. Without it, g-comp would estimate a constant ATE (\(\approx 3\)) regardless of target population.

This tells causatr to:

  1. Fit the outcome model on study rows (\(S = 1\)) only.
  2. Fit a sampling model \(P(S = 1 \mid L)\) on all rows.
  3. At contrast time, standardise predictions over target-population covariates (not study covariates).

Use confounders_sampling to specify a different covariate set for the sampling model than for the outcome or treatment models.

Contrasting

Code 
res_gc <- contrast(
  fit_gc,
  interventions = list(a1 = static(1), a0 = static(0)),
  reference = "a0"
)
res_gc

Estimator: gcomp  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1843

Intervention means
intervention estimate se ci_lower ci_upper
a1 4.169 0.078 4.015 4.323
a0 1.578 0.063 1.455 1.701
Contrasts
comparison estimate se ci_lower ci_upper
a1 vs a0 2.591 0.082 2.43 2.752

Compare with the study-only estimate (no target =):

Code 
fit_study <- causat(
  df[df$S == 1, ],
  outcome = "Y",
  treatment = "A",
  confounders = ~ L + A:L
)
#> Warning: `model_fn` not specified; defaulting to `stats::glm`.
#> ℹ Set `model_fn` explicitly (e.g. `model_fn = stats::glm` or `model_fn = mgcv::gam`).

res_study <- contrast(
  fit_study,
  interventions = list(a1 = static(1), a0 = static(0)),
  reference = "a0"
)
res_study

Estimator: gcomp  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1157

Intervention means
intervention estimate se ci_lower ci_upper
a1 6.357 0.078 6.205 6.51
a0 2.842 0.06 2.725 2.959
Contrasts
comparison estimate se ci_lower ci_upper
a1 vs a0 3.516 0.067 3.385 3.647

The two estimates differ because the target population has a different distribution of \(L\) than the study sample:

Code 
study_transport_df <- data.frame(
  Target = c("Study only", "Transport (S = 0)"),
  Estimate = c(res_study$contrasts$estimate[1],
               res_gc$contrasts$estimate[1]),
  CI_lower = c(res_study$contrasts$ci_lower[1],
               res_gc$contrasts$ci_lower[1]),
  CI_upper = c(res_study$contrasts$ci_upper[1],
               res_gc$contrasts$ci_upper[1])
)

tinyplot::tinyplot(
  Estimate ~ Target,
  data = study_transport_df,
  type = "pointrange",
  ymin = study_transport_df$CI_lower,
  ymax = study_transport_df$CI_upper,
  pch = 19,
  ylab = "ATE estimate (95% CI)",
  main = "Study-population vs target-population ATE"
)
Pointrange plot comparing the study-only ATE (~3.5) with the transported ATE (~2.6). The study estimate is higher because the study population has higher L values, and the A*L interaction makes treatment more effective at high L.
Figure 2

Transportability vs generalizability

The target_subset argument controls which rows define the target:

  • target_subset = "target" (default): the target population is \(S = 0\) only. This is transportability — the study is external to the target.
  • target_subset = "all": the target population is \(S = 0 \cup S = 1\) (the full combined sample). This is generalizability — the study is a biased subsample of the target.
Code 
fit_gen <- causat(
  df,
  outcome = "Y",
  treatment = "A",
  confounders_outcome = ~ L + A:L,
  confounders_treatment = ~ L,
  confounders_sampling = ~ L,
  target = "S",
  target_subset = "all"
)
#> Warning: `model_fn` not specified; defaulting to `stats::glm`.
#> ℹ Set `model_fn` explicitly (e.g. `model_fn = stats::glm` or `model_fn = mgcv::gam`).

res_gen <- contrast(
  fit_gen,
  interventions = list(a1 = static(1), a0 = static(0)),
  reference = "a0"
)
res_gen

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

Intervention means
intervention estimate se ci_lower ci_upper
a1 5.013 0.067 4.882 5.144
a0 2.065 0.053 1.961 2.17
Contrasts
comparison estimate se ci_lower ci_upper
a1 vs a0 2.948 0.069 2.812 3.083

Three estimators

All three point-treatment estimators support target =:

IPW transport

Under IPW, the treatment density-ratio weights are multiplied by sampling weights \(w^S_i = [1 - \hat P(S = 1 \mid L_i)] / \hat P(S = 1 \mid L_i)\):

Code 
fit_ipw <- causat(
  df,
  outcome = "Y",
  treatment = "A",
  confounders = ~ L,
  estimator = "ipw",
  target = "S"
)
#> Warning: `model_fn` not specified; defaulting to `stats::glm`.
#> ℹ Set `model_fn` explicitly (e.g. `model_fn = stats::glm` or `model_fn = mgcv::gam`).
#> Warning: `propensity_model_fn` not specified; defaulting to `stats::glm`.
#> ℹ Set `propensity_model_fn` explicitly if you need a different fitter (e.g. `mgcv::gam`).

res_ipw <- contrast(
  fit_ipw,
  interventions = list(a1 = static(1), a0 = static(0)),
  reference = "a0"
)
res_ipw

Estimator: ipw  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1843

Intervention means
intervention estimate se ci_lower ci_upper
a1 3.989 0.252 3.496 4.482
a0 1.611 0.122 1.373 1.85
Contrasts
comparison estimate se ci_lower ci_upper
a1 vs a0 2.377 0.274 1.84 2.914

AIPW transport (doubly robust)

AIPW combines the outcome model and treatment weights with sampling weights, providing consistency if either the outcome model or the treatment model is correctly specified:

Code 
fit_aipw <- causat(
  df,
  outcome = "Y",
  treatment = "A",
  confounders_outcome = ~ L + A:L,
  confounders_treatment = ~ L,
  confounders_sampling = ~ L,
  estimator = "aipw",
  target = "S"
)
#> Warning: `model_fn` not specified; defaulting to `stats::glm`.
#> ℹ Set `model_fn` explicitly (e.g. `model_fn = stats::glm` or `model_fn = mgcv::gam`).
#> Warning: `propensity_model_fn` not specified; defaulting to `stats::glm`.
#> ℹ Set `propensity_model_fn` explicitly if you need a different fitter (e.g. `mgcv::gam`).

res_aipw <- contrast(
  fit_aipw,
  interventions = list(a1 = static(1), a0 = static(0)),
  reference = "a0"
)
res_aipw

Estimator: aipw  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1843

Intervention means
intervention estimate se ci_lower ci_upper
a1 4.127 0.115 3.902 4.352
a0 1.554 0.069 1.418 1.689
Contrasts
comparison estimate se ci_lower ci_upper
a1 vs a0 2.573 0.108 2.362 2.784

Comparison

Code 
methods_df <- data.frame(
  Method = c("G-comp", "IPW", "AIPW"),
  Estimate = c(
    res_gc$contrasts$estimate[1],
    res_ipw$contrasts$estimate[1],
    res_aipw$contrasts$estimate[1]
  ),
  CI_lower = c(
    res_gc$contrasts$ci_lower[1],
    res_ipw$contrasts$ci_lower[1],
    res_aipw$contrasts$ci_lower[1]
  ),
  CI_upper = c(
    res_gc$contrasts$ci_upper[1],
    res_ipw$contrasts$ci_upper[1],
    res_aipw$contrasts$ci_upper[1]
  )
)

tinyplot::tinyplot(
  Estimate ~ Method,
  data = methods_df,
  type = "pointrange",
  ymin = methods_df$CI_lower,
  ymax = methods_df$CI_upper,
  ylab = "Target-population ATE",
  main = "Transport estimates: three methods"
)

Forest plot comparing gcomp, IPW, and AIPW transport estimates.

Censored outcomes (IPCW × transport)

When outcomes are subject to right-censoring, censoring = adds inverse-probability-of-censoring weights (IPCW). These compose seamlessly with transportability weights — the three weight components (treatment, censoring, sampling) multiply pointwise:

Code 
set.seed(99)
n2 <- 4000
L2 <- rnorm(n2)
S2 <- rbinom(n2, 1, plogis(-0.5 + 1.0 * L2))
A2 <- ifelse(S2 == 1L, rbinom(n2, 1, plogis(0.2 + 0.3 * L2)), NA_integer_)
C2 <- ifelse(S2 == 1L, rbinom(n2, 1, plogis(-1.5 + 0.5 * A2 + 0.3 * L2)), 0L)
#> Warning in rbinom(n2, 1, plogis(-1.5 + 0.5 * A2 + 0.3 * L2)): NAs produced
Y2_full <- ifelse(S2 == 1L, 2 + 3 * A2 + 1.5 * L2 + rnorm(n2), NA_real_)
Y2 <- ifelse(C2 == 1L, NA_real_, Y2_full)

df2 <- data.frame(Y = Y2, A = A2, L = L2, S = S2, C = C2)

All three estimators support IPCW + transport:

Code 
fit_ipcw_gc <- causat(
  df2,
  outcome = "Y",
  treatment = "A",
  confounders = ~ L,
  target = "S",
  censoring = "C"
)
#> Warning: `model_fn` not specified; defaulting to `stats::glm`.
#> ℹ Set `model_fn` explicitly (e.g. `model_fn = stats::glm` or `model_fn = mgcv::gam`).

res_ipcw_gc <- contrast(
  fit_ipcw_gc,
  interventions = list(a1 = static(1), a0 = static(0)),
  reference = "a0"
)
res_ipcw_gc

Estimator: gcomp  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 2384

Intervention means
intervention estimate se ci_lower ci_upper
a1 4.583 0.057 4.472 4.694
a0 1.529 0.055 1.421 1.636
Contrasts
comparison estimate se ci_lower ci_upper
a1 vs a0 3.055 0.061 2.936 3.174

The sandwich variance accounts for all three nuisance models (outcome, censoring, sampling) via the influence-function correction chain.

Modified treatment policies (MTP) + transport

For static interventions, target-row predictions use \(\hat{m}(a, L_i)\) directly. But MTP interventions — shift(), scale_by(), threshold(), dynamic() — transform the observed treatment via \(d(A, L)\), and target rows (S = 0) have \(A = \text{NA}\). causatr solves this via MC marginalization: it integrates \(E_{A \mid L, S=1}[\hat{m}(d(A,L), L)]\) over the study treatment distribution. For binary treatment this is exact enumeration; for continuous treatment it draws Monte Carlo samples from a fitted treatment model.

Code 
set.seed(201)
n3 <- 6000
L3 <- rnorm(n3)
S3 <- rbinom(n3, 1, plogis(-0.5 + L3))
A3 <- ifelse(S3 == 1L, rnorm(n3, 0.5 + 0.3 * L3, 1), NA_real_)
Y3 <- ifelse(
  S3 == 1L,
  2 + 3 * A3 + 1.5 * L3 + A3 * L3 + rnorm(n3),
  NA_real_
)
df3 <- data.frame(Y = Y3, A = A3, L = L3, S = S3)

fit_mtp <- causat(df3, "Y", "A", ~ L + A:L, target = "S")
#> Warning: `model_fn` not specified; defaulting to `stats::glm`.
#> ℹ Set `model_fn` explicitly (e.g. `model_fn = stats::glm` or `model_fn = mgcv::gam`).

res_mtp <- contrast(
  fit_mtp,
  interventions = list(shifted = shift(1), natural = NULL),
  reference = "natural",
  type = "difference",
  ci_method = "bootstrap",
  n_boot = 200
)
res_mtp

Estimator: gcomp  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: bootstrap  ·  N: 3633

Intervention means
intervention estimate se ci_lower ci_upper
shifted 5.34 0.098 5.148 5.532
natural 2.693 0.089 2.518 2.868
Contrasts
comparison estimate se ci_lower ci_upper
shifted vs natural 2.647 0.034 2.581 2.713

The analytical truth for this DGP is \(3 \delta + \delta \cdot E[L \mid S = 0]\); the bootstrap CI should bracket it.

Important: sandwich variance is not available for gcomp or AIPW with MTP + transport, because the MC marginalization introduces treatment-model dependence not captured by the current IF chain. Use ci_method = "bootstrap" instead. IPW + MTP + transport supports sandwich (no MC marginalization needed).

Longitudinal transport

Transportability composes with longitudinal IPW (id =, time =). The sampling model is fit on first-period rows, and the resulting sampling-odds weight is broadcast to all person-period rows for each individual. The sampling weight multiplies into the per-period treatment density-ratio weight inside the longitudinal Hájek MSM.

Code 
set.seed(314)
n_long <- 1500
L0 <- rnorm(n_long)
S <- rbinom(n_long, 1, plogis(-0.3 + 0.8 * L0))

A0 <- ifelse(S == 1L, rbinom(n_long, 1, plogis(0.3 * L0)), NA_integer_)
L1 <- ifelse(S == 1L, 0.5 * L0 + 0.4 * A0 + rnorm(n_long, sd = 0.5), NA_real_)
A1 <- ifelse(S == 1L, rbinom(n_long, 1, plogis(0.3 * L1)), NA_integer_)
#> Warning in rbinom(n_long, 1, plogis(0.3 * L1)): NAs produced
Y <- ifelse(
  S == 1L,
  2 * A0 + 2 * A1 + L0 + 0.5 * L1 + rnorm(n_long),
  NA_real_
)

# Build person-period data
wide <- data.frame(id = seq_len(n_long), L0 = L0, S = S,
                   A0 = A0, L_1 = L0, A1 = A1, L_2 = L1, Y = Y)
long <- to_person_period(
  wide,
  id = "id",
  time_varying = list(L = c("L_1", "L_2"), A = c("A0", "A1")),
  time_invariant = c("L0", "S", "Y")
)
Code 
fit_long <- causat(
  long,
  outcome = "Y",
  treatment = "A",
  confounders = ~ L0,
  confounders_tv = ~ L,
  id = "id",
  time = "time",
  estimator = "ipw",
  target = "S"
)

res_long <- contrast(
  fit_long,
  interventions = list(always = static(1), never = static(0)),
  reference = "never"
)
res_long

Estimator: ipw  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1500

Intervention means
intervention estimate se ci_lower ci_upper
always 3.975 0.12 3.739 4.211
never -0.737 0.148 -1.027 -0.448
Contrasts
comparison estimate se ci_lower ci_upper
always vs never 4.712 0.184 4.352 5.073

ICE g-computation also supports longitudinal transport — the outcome model is fit on study rows, and counterfactual predictions are averaged over the target population’s baseline covariates.

Multivariate treatment × transport

Joint-treatment IPW (treatment = c("A1", "A2")) composes with transport. The per-component density-ratio weights from the sequential MTP factorisation multiply with the sampling-odds weight:

Code 
set.seed(808)
n_mv <- 2000
L_mv <- rnorm(n_mv)
S_mv <- rbinom(n_mv, 1, plogis(-0.5 + 0.8 * L_mv))

A1_mv <- ifelse(
  S_mv == 1L, rbinom(n_mv, 1, plogis(0.2 + 0.3 * L_mv)), NA_integer_
)
A2_mv <- ifelse(
  S_mv == 1L,
  rbinom(n_mv, 1, plogis(0.1 + 0.2 * L_mv + 0.3 * A1_mv)),
  NA_integer_
)
#> Warning in rbinom(n_mv, 1, plogis(0.1 + 0.2 * L_mv + 0.3 * A1_mv)): NAs
#> produced
Y_mv <- ifelse(
  S_mv == 1L,
  1 + 2 * A1_mv + 1.5 * A2_mv + L_mv + 0.5 * A1_mv * L_mv + rnorm(n_mv),
  NA_real_
)

df_mv <- data.frame(Y = Y_mv, A1 = A1_mv, A2 = A2_mv, L = L_mv, S = S_mv)
Code 
fit_mv <- causat(
  df_mv,
  outcome = "Y",
  treatment = c("A1", "A2"),
  confounders = ~ L,
  estimator = "ipw",
  target = "S"
)
#> Warning: `model_fn` not specified; defaulting to `stats::glm`.
#> ℹ Set `model_fn` explicitly (e.g. `model_fn = stats::glm` or `model_fn = mgcv::gam`).
#> Warning: `propensity_model_fn` not specified; defaulting to `stats::glm`.
#> ℹ Set `propensity_model_fn` explicitly if you need a different fitter (e.g. `mgcv::gam`).

res_mv <- contrast(
  fit_mv,
  interventions = list(
    both = list(A1 = static(1), A2 = static(1)),
    neither = list(A1 = static(0), A2 = static(0))
  ),
  reference = "neither"
)
res_mv

Estimator: ipw  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1169

Intervention means
intervention estimate se ci_lower ci_upper
both 4.193 0.176 3.848 4.538
neither 0.736 0.112 0.517 0.954
Contrasts
comparison estimate se ci_lower ci_upper
both vs neither 3.458 0.196 3.073 3.842

Sandwich and bootstrap variance both work for multivariate IPW transport. Stabilized weights (stabilize = "marginal") also compose with transport.

Separate confounder specifications

Use confounders_sampling to control which covariates enter the sampling model \(P(S = 1 \mid L)\) independently of the outcome or treatment model covariates:

Code 
fit_sep <- causat(
  df,
  outcome = "Y",
  treatment = "A",
  confounders_outcome = ~ L + A:L + I(L^2),
  confounders_treatment = ~ L,
  confounders_sampling = ~ L,
  estimator = "aipw",
  target = "S"
)
#> Warning: `model_fn` not specified; defaulting to `stats::glm`.
#> ℹ Set `model_fn` explicitly (e.g. `model_fn = stats::glm` or `model_fn = mgcv::gam`).
#> Warning: `propensity_model_fn` not specified; defaulting to `stats::glm`.
#> ℹ Set `propensity_model_fn` explicitly if you need a different fitter (e.g. `mgcv::gam`).

res_sep <- contrast(
  fit_sep,
  interventions = list(a1 = static(1), a0 = static(0)),
  reference = "a0"
)
res_sep

Estimator: aipw  ·  Estimand: ATE  ·  Contrast: difference  ·  CI method: sandwich  ·  N: 1843

Intervention means
intervention estimate se ci_lower ci_upper
a1 4.131 0.112 3.911 4.351
a0 1.552 0.069 1.417 1.686
Contrasts
comparison estimate se ci_lower ci_upper
a1 vs a0 2.579 0.104 2.375 2.783

This is especially useful when the outcome model benefits from flexible specifications (splines, polynomials) while the sampling model needs only the core set of baseline confounders.

Diagnostics

diagnose() includes a sampling model panel for transport fits, reporting the sampling-score distribution, sampling-weight summary, and extreme-weight flags:

Code 
diag <- diagnose(fit_ipw)
#> Note: `s.d.denom` not specified; assuming "pooled".
diag
#> <causatr_diag>
#>  Estimator:ipw
#>  Treatment: binary
#>  Estimand:  ATE
#> 
#> Positivity:
#>       statistic     value
#>          <char>     <num>
#>             min 0.3283844
#>             q25 0.5232723
#>          median 0.5772245
#>             q75 0.6320640
#>             max 0.8095657
#>   n_below_lower 0.0000000
#>   n_above_upper 0.0000000
#>    n_violations 0.0000000
#>  pct_violations 0.0000000
#> 
#> Covariate balance:
#> Balance Measures
#>      Type Diff.Un     M.Threshold.Un V.Ratio.Un
#> L Contin.  0.3319 Not Balanced, >0.1     1.1408
#> 
#> Balance tally for mean differences
#>                    count
#> Balanced, <0.1         0
#> Not Balanced, >0.1     1
#> 
#> Variable with the greatest mean difference
#>  Variable Diff.Un     M.Threshold.Un
#>         L  0.3319 Not Balanced, >0.1
#> 
#> Sample sizes
#>     Control Treated
#> All     492     665
#> 
#> Weight distribution:
#>    group     n     mean        sd      min      max       ess
#>   <char> <int>    <num>     <num>    <num>    <num>     <num>
#>  treated   665 1.742163 0.2607069 1.235230 2.994992  650.4557
#>  control   492 2.346339 0.4437681 1.488947 5.075262  475.0418
#>  overall  1157 1.999081 0.4604115 1.235230 5.075262 1098.7680
#> 
#> Sampling model:
#>        statistic     value
#>           <char>     <num>
#>          n_study 1157.0000
#>         n_target 1843.0000
#>        pct_study   38.5700
#>    target_subset        NA
#>      p_study_min    0.0159
#>      p_study_q05    0.0875
#>   p_study_median    0.3619
#>      p_study_q95    0.7599
#>      p_study_max    0.9619
#>  p_study_mean_s1    0.4980
#>  p_study_mean_s0    0.3152
#>          sw_mean    1.5937
#>            sw_sd    1.9389
#>           sw_min    0.0396
#>           sw_max   18.6510
#>           sw_ess  466.7700
#>     sw_n_extreme    0.0000

Key diagnostics to check:

  • Sampling positivity: \(P(S = 1 \mid L)\) should not be too close to 0 or 1. The p_study_min and p_study_max quantiles flag overlap violations.
  • Extreme weights: large sampling weights indicate regions of \(L\) where the study underrepresents the target, leading to instability.
  • ESS: the effective sample size after sampling reweighting. Low ESS signals that a few observations drive the estimate.

Identification assumptions

Transport estimates require four assumptions (Dahabreh et al. 2020):

  1. Conditional exchangeability in the study: \(Y^a \perp A \mid L, S = 1\).
  2. Treatment positivity in the study: \(0 < P(A = a \mid L, S = 1) < 1\).
  3. Exchangeability over populations (transportability): \(E[Y^a \mid L, S = 1] = E[Y^a \mid L, S = 0]\) — the conditional potential-outcome mean is the same across populations given \(L\).
  4. Sampling positivity: \(P(S = 1 \mid L) > 0\) on the target support.

Assumptions 1–2 are the standard causal assumptions (checked via diagnose() balance and positivity panels). Assumption 3 is the transportability leap — it is not directly testable but requires domain knowledge. Assumption 4 is checked by the sampling diagnostics.

Matching is not supported

Matching + transportability is a hard rejection:

Code 
causat(
  df,
  outcome = "Y",
  treatment = "A",
  confounders = ~ L,
  estimator = "matching",
  target = "S"
)
#> Error in `causat()`:
#> ! `target` is not supported with `estimator = "matching"`.
#> ℹ Transportability does not compose cleanly with matching. Use `estimator = "gcomp"` or `"ipw"` instead.

This is by design: MatchIt’s match-weight pathway does not compose cleanly with external sampling weights.

Summary of covered combinations

Estimator Treatment Transport Sandwich IPCW Status
gcomp binary Yes Yes Yes Yes
gcomp continuous (MTP) Yes (MC) No (bootstrap) --- Yes
gcomp multivariate Yes Yes --- Yes
gcomp longitudinal (ICE) Yes Yes --- Yes
IPW binary Yes Yes Yes Yes
IPW continuous (MTP) Yes Yes --- Yes
IPW multivariate Yes Yes --- Yes
IPW longitudinal Yes Yes Yes Yes
AIPW binary Yes Yes Yes Yes
AIPW continuous (MTP) Yes (MC) No (bootstrap) --- Yes
AIPW multivariate Yes Yes --- Yes
matching any No --- --- Rejected

See FEATURE_COVERAGE_MATRIX.md for the full test-level coverage breakdown.

References

  • Dahabreh IJ, Robertson SE, Steingrimsson JA, Stuart EA, Hernán MA (2020). Extending inferences from a randomized trial to a new target population. Stat Med 39:1999–2014.
  • Cole SR, Stuart EA (2010). Generalizing evidence from randomized clinical trials to target populations. Am J Epidemiol 172:107–115.
  • Hernán MA, VanderWeele TJ (2017). Causal inference under multiple versions of treatment. J Causal Inf 5(2):20160014.