Calculate propensity score weights

Compute inverse probability weights for causal inference under different estimands. Each function targets a different population:

wt_ate(): Average Treatment Effect – the full population.
wt_att(): Average Treatment Effect on the Treated – the treated (focal) group.
wt_atu(): Average Treatment Effect on the Untreated – the untreated (reference) group. wt_atc() is an alias.
wt_atm(): Average Treatment Effect for the Evenly Matchable – units with the most overlap.
wt_ato(): Average Treatment Effect for the Overlap Population – weights proportional to overlap.
wt_entropy(): Entropy-weighted Average Treatment Effect – the entropy-tilted population.
wt_cens(): Inverse probability of censoring weights – uses the same formula as wt_ate() but labels the estimand "uncensored". Use these to adjust for censoring in survival analysis, not for treatment weighting. Remaining uncensored is a two-level event, so wt_cens() supports binary and continuous exposures only.

.propensity accepts a numeric vector of predicted probabilities, a data.frame or matrix of per-level probabilities, a fitted glm object, or a modified propensity score created by ps_trim(), ps_trunc(), ps_refit(), or ps_calibrate().

All functions return a psw object – a numeric vector that tracks the estimand, stabilization status, and any trimming or truncation applied.

Usage

wt_ate(
  .propensity,
  .exposure,
  .sigma = NULL,
  exposure_type = c("auto", "binary", "categorical", "continuous"),
  .focal_level = NULL,
  .reference_level = NULL,
  stabilize = FALSE,
  stabilization_score = NULL,
  ...,
  .treated = NULL,
  .untreated = NULL
)

# S3 method for class 'data.frame'
wt_ate(
  .propensity,
  .exposure,
  .sigma = NULL,
  exposure_type = c("auto", "binary", "categorical", "continuous"),
  .focal_level = NULL,
  .reference_level = NULL,
  stabilize = FALSE,
  stabilization_score = NULL,
  ...,
  .propensity_col = NULL,
  .treated = NULL,
  .untreated = NULL
)

wt_att(
  .propensity,
  .exposure,
  exposure_type = c("auto", "binary", "categorical"),
  .focal_level = NULL,
  .reference_level = NULL,
  ...,
  .treated = NULL,
  .untreated = NULL
)

# S3 method for class 'data.frame'
wt_att(
  .propensity,
  .exposure,
  exposure_type = c("auto", "binary", "categorical"),
  .focal_level = NULL,
  .reference_level = NULL,
  ...,
  .propensity_col = NULL,
  .treated = NULL,
  .untreated = NULL
)

wt_atu(
  .propensity,
  .exposure,
  exposure_type = c("auto", "binary", "categorical"),
  .focal_level = NULL,
  .reference_level = NULL,
  ...,
  .treated = NULL,
  .untreated = NULL
)

# S3 method for class 'data.frame'
wt_atu(
  .propensity,
  .exposure,
  exposure_type = c("auto", "binary", "categorical"),
  .focal_level = NULL,
  .reference_level = NULL,
  ...,
  .propensity_col = NULL,
  .treated = NULL,
  .untreated = NULL
)

wt_atm(
  .propensity,
  .exposure,
  exposure_type = c("auto", "binary", "categorical"),
  .focal_level = NULL,
  .reference_level = NULL,
  ...,
  .treated = NULL,
  .untreated = NULL
)

# S3 method for class 'data.frame'
wt_atm(
  .propensity,
  .exposure,
  exposure_type = c("auto", "binary", "categorical"),
  .focal_level = NULL,
  .reference_level = NULL,
  ...,
  .propensity_col = NULL,
  .treated = NULL,
  .untreated = NULL
)

wt_ato(
  .propensity,
  .exposure,
  exposure_type = c("auto", "binary", "categorical"),
  .focal_level = NULL,
  .reference_level = NULL,
  ...,
  .treated = NULL,
  .untreated = NULL
)

# S3 method for class 'data.frame'
wt_ato(
  .propensity,
  .exposure,
  exposure_type = c("auto", "binary", "categorical"),
  .focal_level = NULL,
  .reference_level = NULL,
  ...,
  .propensity_col = NULL,
  .treated = NULL,
  .untreated = NULL
)

wt_entropy(
  .propensity,
  .exposure,
  exposure_type = c("auto", "binary", "categorical"),
  .focal_level = NULL,
  .reference_level = NULL,
  ...,
  .treated = NULL,
  .untreated = NULL
)

# S3 method for class 'data.frame'
wt_entropy(
  .propensity,
  .exposure,
  exposure_type = c("auto", "binary", "categorical"),
  .focal_level = NULL,
  .reference_level = NULL,
  ...,
  .propensity_col = NULL,
  .treated = NULL,
  .untreated = NULL
)

wt_atc(
  .propensity,
  .exposure,
  exposure_type = c("auto", "binary", "categorical"),
  .focal_level = NULL,
  .reference_level = NULL,
  ...,
  .treated = NULL,
  .untreated = NULL
)

wt_cens(
  .propensity,
  .exposure,
  .sigma = NULL,
  exposure_type = c("auto", "binary", "continuous"),
  .focal_level = NULL,
  .reference_level = NULL,
  stabilize = FALSE,
  stabilization_score = NULL,
  ...,
  .treated = NULL,
  .untreated = NULL
)

# S3 method for class 'data.frame'
wt_cens(
  .propensity,
  .exposure,
  .sigma = NULL,
  exposure_type = c("auto", "binary", "continuous"),
  .focal_level = NULL,
  .reference_level = NULL,
  stabilize = FALSE,
  stabilization_score = NULL,
  ...,
  .propensity_col = NULL,
  .treated = NULL,
  .untreated = NULL
)

Arguments

.propensity

Propensity scores in one of several forms:

A numeric vector of predicted probabilities (binary/continuous).
A data frame or matrix with one column per exposure level. Both shapes are read the same way, for categorical exposures and for binary ones alike, including the default choice of column described under .propensity_col. That argument is itself a formal of the data frame methods only, so selecting a column by name means passing a data frame.
A fitted glm object – fitted values are extracted automatically.
A modified propensity score created by ps_trim(), ps_trunc(), ps_refit(), or ps_calibrate().

For a binary exposure, .propensity is the probability of the focal level, so a numeric vector must be supplied on the scale of whichever level .focal_level or .reference_level resolves to. The glm methods derive it from the fitted values, which give the probability of the response's second level, and subtract them from one when the resolved focal level is the first level instead. A data frame or matrix reduces to a single column, read on the same scale; see .propensity_col for how that column is chosen. A matrix reduces by those same defaults, but .propensity_col belongs to the data frame methods alone, so a matrix whose column you want to name has to be converted with as.data.frame() first.

.exposure

The exposure (treatment) variable. For binary exposures, a numeric 0/1 vector, logical, or two-level factor. For categorical exposures, a factor or character vector. For continuous exposures, a numeric vector. Optional when .propensity is a glm object (extracted from the model). Missing values are not counted as a level of their own, and are carried through to the weights as missing.

.sigma

Observation-level standard deviations of the conditional density for continuous exposures, one per observation (e.g., influence(model)$sigma). Optional: with none supplied, including when .propensity is a glm object, the conditional density uses the pooled residual standard deviation of .exposure around .propensity. Weights built with an observation-level .sigma cannot be used with ipw(); see Continuous exposures in Details.

Must be numeric, holding either a single standard deviation or one per observation, and applies only to continuous exposures. .sigma sits in the third position, which is where a value meant for exposure_type arrives when it is supplied without a name, so anything else is refused with an error of class propensity_sigma_error.

exposure_type

Type of exposure: "auto" (default), "binary", "categorical", or "continuous". "auto" detects the type from .exposure. Not every weight function answers every type; see Exposure types in Details for which does which. Naming a type a function does not support, or supplying an exposure detection reads as one, is an error of class causalgenerics_unsupported_exposure_type.

.focal_level

The value of .exposure representing the focal (treated) group. Every binary coding honors it: 0/1 numeric, logical, two-level factor, and two-level character exposures are all coded with the named level as focal, and a level the exposure never takes is an error. With no level named, a binary exposure defaults to its higher level, which is 1 for a 0/1 exposure, TRUE for a logical one, and the second of the two levels a factor or character exposure takes. Levels a factor declares but never takes are not candidates. Naming any other level reverses the coding, so .propensity must then hold the probability of the named level. Required for wt_att() and wt_atu() with categorical exposures.

.reference_level

The value of .exposure representing the reference (control) group. For a binary exposure, naming it makes the exposure's other level focal, with the same consequence for .propensity, and a level the exposure never takes is an error. Automatically detected if not supplied.

stabilize

If TRUE, multiply weights by an estimate of the marginal treatment probability (binary) or density (continuous). Only supported by wt_ate() and wt_cens(). See Stabilization in Details.

stabilization_score

Optional stabilization multiplier to use instead of the default described under Stabilization: the marginal mean of .exposure, or its marginal normal density for a continuous exposure. Either a single value applied to every weight or a numeric vector holding one value per observation, which is multiplied into the weights observation by observation. Every value must be positive and finite, and any other length or value is refused with an error of class propensity_stabilization_score_error. A per-observation score is recorded on the result and is dropped, with a warning, by any operation that changes the length of the weight vector, since it cannot be re-indexed for the new length. Ignored when stabilize = FALSE.

...

These dots are for future extensions and must be empty.

.treated

Use .focal_level instead.

.untreated

Use .reference_level instead.

.propensity_col

Column to use when .propensity is a data frame with a binary exposure. Accepts a column name (quoted or unquoted) or numeric index. Whichever column is selected is read as the probability of the resolved focal level.

With no column named, the exposure's levels drive the choice. When the data frame has a column named for every level of .exposure, the column named for the resolved focal level is used, wherever it sits in the frame. Otherwise the second column is used, or the only column when the frame has just one. Falling back to position after .focal_level or .reference_level was supplied warns and reports the column used, since the named level could not be matched to a column; the fallback is silent when no level was named and when the frame has a single column.

Ignored for categorical exposures, where all columns are used.

Value

A psw vector (a double vector with class psw) carrying these attributes:

estimand: character, e.g. "ate", "att", "uncensored".
stabilized: logical, whether stabilization was applied.
stabilization_score: double, the user-supplied stabilization score (one value, or one per observation), or NULL if none was supplied.
trimmed: logical, whether the propensity scores were trimmed.
truncated: logical, whether the propensity scores were truncated.
calibrated: logical, whether the propensity scores were calibrated.

Details

Exposure types

All weight functions support binary exposures. wt_ate() and wt_cens() also support continuous exposures. All except wt_cens() support categorical exposures; naming a categorical exposure to wt_cens(), or handing it one detection reads as categorical, is an error of class causalgenerics_unsupported_exposure_type.

Binary: .exposure is a two-level vector (e.g., 0/1, logical, or a two-level factor). .propensity is a numeric vector of P(treatment | X), or a matrix or data frame holding it in one of its columns.
Categorical: .exposure is a factor or character vector with 3+ levels. .propensity must be a matrix or data frame with one column per level, where rows sum to 1.
Continuous: .exposure is a numeric vector. .propensity is a vector of conditional means (fitted values). Weights use a normal density ratio; stabilization is strongly recommended.
Auto (default): Detects the exposure type from .exposure.

Stabilization

Setting stabilize = TRUE multiplies the base weight by an estimate of P(A) (binary) or f_A(A) (continuous), reducing variance. When no stabilization_score is supplied, that estimate is the marginal mean of .exposure for a binary or categorical exposure, and for a continuous exposure the marginal normal density evaluated at the population mean and standard deviation of .exposure. Stabilization is supported for ATE and censoring weights (wt_ate() and wt_cens()) and is strongly recommended for continuous exposures.

The default numerator conditions on nothing, and stabilization_score replaces it with one of your own. The case that pays is a numerator conditioning on a variable the model the estimates are read from also reads, such as an effect modifier. Fit that numerator and evaluate it at the exposure each unit actually took, which is the shape the default already has:

num <- glm(A ~ V, data = dat, family = binomial())
p <- fitted(num)
wt_ate(ps_mod, stabilize = TRUE,
       stabilization_score = ifelse(dat$A == 1, p, 1 - p))

Passing fitted(num) on its own is P(A = 1 | V) for every unit, which is not the probability of the exposure an untreated unit took, so the untreated weights would carry the wrong numerator. Whether a numerator may condition on V at all is a question about the reported model rather than about the weights; see Effect modification in ipw().

Handling extreme weights

Extreme weights signal positivity violations, poor model fit, or limited overlap. You can address them by:

Choosing an overlap-focused estimand (wt_ato(), wt_atm(), wt_entropy()), which down-weight units in regions of poor overlap.
Trimming (ps_trim()) or truncating (ps_trunc()) propensity scores before computing weights.
Calibrating weights with ps_calibrate().
Stabilizing ATE weights (stabilize = TRUE).

See the halfmoon package for weight diagnostics and visualization.

Propensity scores at 0 and 1

Propensity scores must lie strictly inside (0, 1), since a score at either endpoint leaves the weight undefined. A score of exactly 0 or 1 is refused with an error of class propensity_range_error. For a categorical exposure that rule reads every cell of the matrix rather than only the column holding each unit's observed level, which is the same open interval the binary path enforces on the single score and its complement.

ipw() applies a narrower rule to the propensity scores it rebuilds from its own propensity score model. For a categorical exposure it refuses only a probability of exactly zero at the level a unit was actually assigned, since that alone leaves the unit's own weight undefined, and a column for a level the unit was not assigned may reach zero without the fit being refused. The difference is deliberate: the weight functions can refuse a matrix that holds nothing ipw() would have objected to. The weights still have to be built before ipw() can be reached, so the refusal here is the one to resolve.

nnet::multinom() reaches the endpoints readily. Under separation the softmax puts the probability at a unit's assigned level at exactly 1 in double precision, and the columns for the other levels can underflow to exactly 0. Trimming is no way around the refusal: ps_trim() and ps_trunc() validate a categorical matrix under the same open interval and refuse it before either reaches a threshold. Bound the fitted probabilities away from 0 and 1 yourself, renormalizing each row to sum to 1, or refit the propensity score model so that it does not separate.

Weight formulas

Binary exposures

For binary treatments ($A \in \{0, 1\}$), with propensity score $e(X) = P(A=1 \mid X)$:

ATE: $w = \frac{A}{e(X)} + \frac{1-A}{1-e(X)}$
ATT: $w = A + \frac{(1-A) \cdot e(X)}{1-e(X)}$
ATU: $w = \frac{A \cdot (1-e(X))}{e(X)} + (1-A)$
ATM: $w = \frac{\min(e(X), 1-e(X))}{A \cdot e(X) + (1-A) \cdot (1-e(X))}$
ATO: $w = A \cdot (1-e(X)) + (1-A) \cdot e(X)$
Entropy: $w = \frac{h(e(X))}{A \cdot e(X) + (1-A) \cdot (1-e(X))}$, where $h(e) = -[e \log(e) + (1-e) \log(1-e)]$

The entropy weight tilts the propensity score by $h(e)$, the entropy of the score itself, in the sense of Zhou, Matsouaka, and Thomas (2020). It is not entropy balancing, which solves for weights that satisfy exact covariate moment constraints rather than tilting a fitted propensity score.

Continuous exposures

Weights use the density ratio $w = f_A(A) / f_{A|X}(A \mid X)$, where $f_A$ is the marginal density and $f_{A|X}$ is the conditional density (both assumed normal). Only wt_ate() and wt_cens() support continuous exposures.

The marginal density is evaluated at the population mean and standard deviation of .exposure. The conditional density is centered on .propensity and spread by the propensity model's residual standard deviation. That spread is the pooled residual standard deviation $\sqrt{\mathrm{mean}((A - \hat{A})^2)}$ unless .sigma supplies an observation-level standard deviation for each unit, which the glm methods do not do on their own.

ipw() models the conditional density with a single pooled residual variance, estimated jointly with the rest of the parameter vector. Weights built with an observation-level .sigma therefore have no counterpart in that estimating equation, and ipw() rejects them in its weight consistency check. Build weights with the pooled default when the outcome model is headed for ipw().

Categorical exposures

For $K$-level treatments, weights take the tilting-function form $w_i = h(\mathbf{e}_i) / e_{i,Z_i}$, where $e_{i,Z_i}$ is the propensity for unit $i$'s observed level and $h(\cdot)$ depends on the estimand:

ATE: $h(\mathbf{e}) = 1$
ATT: $h(\mathbf{e}) = e_{\text{focal}}$
ATU: $h(\mathbf{e}) = 1 - e_{\text{focal}}$
ATM: $h(\mathbf{e}) = \min(e_1, \ldots, e_K)$
ATO: $h(\mathbf{e}) = \bigl(\sum_k 1/e_k\bigr)^{-1}$
Entropy: $h(\mathbf{e}) = -\sum_k e_k \log(e_k)$

References

Barrett, M., D'Agostino McGowan, L., & Gerke, T. Causal Inference in R. https://www.r-causal.org/

Rosenbaum, P. R., & Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70(1), 41–55.

Li, L., & Greene, T. (2013). A weighting analogue to pair matching in propensity score analysis. The International Journal of Biostatistics, 9(2), 215–234. (ATM weights)

Li, F., Morgan, K. L., & Zaslavsky, A. M. (2018). Balancing covariates via propensity score weighting. Journal of the American Statistical Association, 113(521), 390–400. (ATO weights)

Zhou, Y., Matsouaka, R. A., & Thomas, L. (2020). Propensity score weighting under limited overlap and model misspecification. Statistical Methods in Medical Research, 29(12), 3721–3756. (Entropy weights)

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).

Austin, P. C., & Stuart, E. A. (2015). Moving towards best practice when using inverse probability of treatment weighting (IPTW). Statistics in Medicine, 34(28), 3661–3679.

Examples

# -- Binary exposure, numeric propensity scores ----------------------
set.seed(123)
ps <- runif(100, 0.1, 0.9)
trt <- rbinom(100, 1, ps)

wt_ate(ps, trt)
#> ℹ Treating `.exposure` as binary
#> <psw{estimand = ate}[100]>
#>   [1] 1.492675 1.368655 1.745754 5.165661 1.173194 7.328950 2.094172 1.228599
#>   [9] 1.847923 1.870179 7.433103 1.861044 1.557495 2.262990 1.223002 1.219720
#>  [17] 1.422212 7.482363 1.568225 1.157940 1.232086 1.528485 1.632905 1.116800
#>  [25] 1.601115 3.001420 1.868276 1.738182 1.495501 1.278267 1.148871 5.612908
#>  [33] 2.878230 3.793252 1.135965 2.073670 3.410265 3.661309 2.820518 1.399190
#>  [41] 1.272653 1.759439 1.757406 1.653101 4.505402 1.267499 1.401399 1.896705
#>  [49] 1.455134 1.271840 1.158299 1.830697 1.352924 1.246136 1.822296 1.360961
#>  [57] 1.253173 1.423191 1.225436 1.665474 1.582048 1.213405 2.455942 1.469523
#>  [65] 1.330297 1.847790 1.336806 1.333490 1.359668 1.824369 1.421302 1.657339
#>  [73] 3.013373 1.111729 2.082235 1.381397 1.677439 1.694293 2.621656 1.232906
#>  [81] 3.391031 1.576182 2.303524 1.368819 1.222930 1.811313 1.126170 1.227836
#>  [89] 5.240410 4.165936 1.257160 1.606473 2.667996 1.598960 2.806635 1.333605
#>  [97] 1.377723 1.211939 1.899058 2.037508
wt_att(ps, trt)
#> ℹ Treating `.exposure` as binary
#> <psw{estimand = att}[100]>
#>   [1] 0.4926755 1.0000000 0.7457538 4.1656608 1.0000000 1.0000000 1.0941724
#>   [8] 1.0000000 1.0000000 0.8701789 6.4331026 0.8610445 1.0000000 1.2629898
#>  [15] 0.2230018 1.0000000 0.4222125 1.0000000 0.5682254 1.0000000 1.0000000
#>  [22] 1.0000000 1.0000000 1.0000000 1.0000000 2.0014200 1.0000000 1.0000000
#>  [29] 0.4955011 0.2782671 1.0000000 4.6129081 1.8782298 2.7932516 0.1359647
#>  [36] 1.0000000 2.4102647 1.0000000 1.0000000 0.3991897 0.2726533 0.7594392
#>  [43] 0.7574058 0.6531012 1.0000000 0.2674992 0.4013989 0.8967053 0.4551341
#>  [50] 1.0000000 0.1582988 0.8306973 1.0000000 0.2461361 1.0000000 0.3609610
#>  [57] 0.2531726 1.0000000 1.0000000 0.6654737 1.0000000 0.2134045 1.0000000
#>  [64] 0.4695226 1.0000000 0.8477904 1.0000000 1.0000000 1.0000000 0.8243692
#>  [71] 1.0000000 1.0000000 2.0133726 0.1117285 1.0000000 0.3813969 0.6774393
#>  [78] 1.0000000 1.0000000 0.2329063 1.0000000 1.0000000 1.0000000 1.0000000
#>  [85] 0.2229300 0.8113126 1.0000000 1.0000000 4.2404103 1.0000000 0.2571604
#>  [92] 1.0000000 1.0000000 1.0000000 1.0000000 0.3336052 1.0000000 0.2119390
#>  [99] 0.8990583 1.0375079
wt_atu(ps, trt)
#> ℹ Treating `.exposure` as binary
#> <psw{estimand = atu}[100]>
#>   [1] 1.0000000 0.3686554 1.0000000 1.0000000 0.1731942 6.3289497 1.0000000
#>   [8] 0.2285990 0.8479233 1.0000000 1.0000000 1.0000000 0.5574953 1.0000000
#>  [15] 1.0000000 0.2197205 1.0000000 6.4823626 1.0000000 0.1579396 0.2320863
#>  [22] 0.5284847 0.6329051 0.1167996 0.6011153 1.0000000 0.8682760 0.7381824
#>  [29] 1.0000000 1.0000000 0.1488715 1.0000000 1.0000000 1.0000000 1.0000000
#>  [36] 1.0736701 1.0000000 2.6613092 1.8205180 1.0000000 1.0000000 1.0000000
#>  [43] 1.0000000 1.0000000 3.5054016 1.0000000 1.0000000 1.0000000 1.0000000
#>  [50] 0.2718404 1.0000000 1.0000000 0.3529239 1.0000000 0.8222956 1.0000000
#>  [57] 1.0000000 0.4231912 0.2254357 1.0000000 0.5820478 1.0000000 1.4559422
#>  [64] 1.0000000 0.3302967 1.0000000 0.3368064 0.3334905 0.3596676 1.0000000
#>  [71] 0.4213022 0.6573389 1.0000000 1.0000000 1.0822347 1.0000000 1.0000000
#>  [78] 0.6942927 1.6216558 1.0000000 2.3910308 0.5761821 1.3035242 0.3688192
#>  [85] 1.0000000 1.0000000 0.1261698 0.2278362 1.0000000 3.1659355 1.0000000
#>  [92] 0.6064733 1.6679958 0.5989600 1.8066347 1.0000000 0.3777228 1.0000000
#>  [99] 1.0000000 1.0000000
wt_atm(ps, trt)
#> ℹ Treating `.exposure` as binary
#> <psw{estimand = atm}[100]>
#>   [1] 0.4926755 0.3686554 0.7457538 1.0000000 0.1731942 1.0000000 1.0000000
#>   [8] 0.2285990 0.8479233 0.8701789 1.0000000 0.8610445 0.5574953 1.0000000
#>  [15] 0.2230018 0.2197205 0.4222125 1.0000000 0.5682254 0.1579396 0.2320863
#>  [22] 0.5284847 0.6329051 0.1167996 0.6011153 1.0000000 0.8682760 0.7381824
#>  [29] 0.4955011 0.2782671 0.1488715 1.0000000 1.0000000 1.0000000 0.1359647
#>  [36] 1.0000000 1.0000000 1.0000000 1.0000000 0.3991897 0.2726533 0.7594392
#>  [43] 0.7574058 0.6531012 1.0000000 0.2674992 0.4013989 0.8967053 0.4551341
#>  [50] 0.2718404 0.1582988 0.8306973 0.3529239 0.2461361 0.8222956 0.3609610
#>  [57] 0.2531726 0.4231912 0.2254357 0.6654737 0.5820478 0.2134045 1.0000000
#>  [64] 0.4695226 0.3302967 0.8477904 0.3368064 0.3334905 0.3596676 0.8243692
#>  [71] 0.4213022 0.6573389 1.0000000 0.1117285 1.0000000 0.3813969 0.6774393
#>  [78] 0.6942927 1.0000000 0.2329063 1.0000000 0.5761821 1.0000000 0.3688192
#>  [85] 0.2229300 0.8113126 0.1261698 0.2278362 1.0000000 1.0000000 0.2571604
#>  [92] 0.6064733 1.0000000 0.5989600 1.0000000 0.3336052 0.3777228 0.2119390
#>  [99] 0.8990583 1.0000000
wt_ato(ps, trt)
#> ℹ Treating `.exposure` as binary
#> <psw{estimand = ato}[100]>
#>   [1] 0.3300620 0.2693559 0.4271815 0.8064139 0.1476262 0.8635548 0.5224844
#>   [8] 0.1860648 0.4588520 0.4652918 0.8654667 0.4626673 0.3579435 0.5581067
#>  [15] 0.1823397 0.1801400 0.2968702 0.8663524 0.3623366 0.1363971 0.1883685
#>  [22] 0.3457573 0.3875945 0.1045842 0.3754354 0.6668244 0.4647472 0.4246864
#>  [29] 0.3313278 0.2176909 0.1295806 0.8218392 0.6525642 0.7363739 0.1196909
#>  [36] 0.5177632 0.7067676 0.7268737 0.6454552 0.2853006 0.2142400 0.4316371
#>  [43] 0.4309795 0.3950764 0.7780442 0.2110449 0.2864273 0.4727700 0.3127781
#>  [50] 0.2137378 0.1366649 0.4537601 0.2608601 0.1975194 0.4512416 0.2652251
#>  [57] 0.2020253 0.2973537 0.1839637 0.3995702 0.3679078 0.1758725 0.5928243
#>  [64] 0.3195069 0.2482880 0.4588131 0.2519485 0.2500884 0.2645261 0.4518654
#>  [71] 0.2964199 0.3966231 0.6681459 0.1004998 0.5197467 0.2760951 0.4038532
#>  [78] 0.4097832 0.6185617 0.1889083 0.7051044 0.3655555 0.5658826 0.2694433
#>  [85] 0.1822917 0.4479142 0.1120344 0.1855591 0.8091752 0.7599579 0.2045566
#>  [92] 0.3775185 0.6251868 0.3745935 0.6437014 0.2501529 0.2741646 0.1748760
#>  [99] 0.4734232 0.5092044
wt_entropy(ps, trt)
#> ℹ Treating `.exposure` as binary
#> <psw{estimand = entropy}[100]>
#>   [1] 0.9466884 0.7974021 1.1914845 2.5383087 0.4910630 2.9202760 1.4494516
#>   [8] 0.5903003 1.2746181 1.2917997 2.9354392 1.2847853 1.0158386 1.5532690
#>  [15] 0.5808315 0.5752272 0.8649741 2.9425314 1.0267968 0.4612870 0.5961433
#>  [22] 0.9855373 1.0902253 0.3741728 1.0595945 1.9101181 1.2903427 1.1850225
#>  [29] 0.9498151 0.6697735 0.4429918 2.6301699 1.8588898 2.1880067 0.4161138
#>  [36] 1.4360497 2.0632803 2.1467853 1.8339424 0.8365617 0.6611694 1.2030532
#>  [43] 1.2013433 1.1091726 2.3850345 0.6531902 0.8393281 1.3118818 0.9040828
#>  [50] 0.6599161 0.4620024 1.2611029 0.7765170 0.6192602 1.2544407 0.7872501
#>  [57] 0.6305931 0.8661618 0.5849629 1.1205924 1.0407229 0.5643262 1.6597604
#>  [64] 0.9206519 0.7455600 1.2745145 0.7545814 0.7499980 0.7855318 1.2560894
#>  [71] 0.8638679 1.1130997 1.9149498 0.3626234 1.4416708 0.8139569 1.1315051
#>  [78] 1.1466626 1.7427820 0.5975110 2.0565825 1.0348389 1.5766261 0.7976169
#>  [85] 0.5807093 1.2456605 0.3950015 0.5890166 2.5542633 2.2959657 0.6369461
#>  [92] 1.0648287 1.7647932 1.0574806 1.8278454 0.7501570 0.8092153 0.5617751
#>  [99] 1.3136430 1.4119476

# Stabilized ATE weights (reduces variance)
wt_ate(ps, trt, stabilize = TRUE)
#> ℹ Treating `.exposure` as binary
#> <psw{estimand = ate; stabilized}[100]>
#>   [1] 0.7612645 0.6706411 0.8903344 2.6344870 0.5748651 3.5911853 1.0680279
#>   [8] 0.6020135 0.9054824 0.9537912 3.7908823 0.9491327 0.7631727 1.1541248
#>  [15] 0.6237309 0.5976630 0.7253284 3.6663577 0.7997950 0.5673904 0.6037223
#>  [22] 0.7489575 0.8001235 0.5472318 0.7845465 1.5307242 0.9154552 0.8517094
#>  [29] 0.7627055 0.6519162 0.5629470 2.8625831 1.4678972 1.9345583 0.5793420
#>  [36] 1.0160984 1.7392350 1.7940415 1.3820538 0.7135867 0.6490532 0.8973140
#>  [43] 0.8962770 0.8430816 2.2076468 0.6464246 0.7147134 0.9673197 0.7421184
#>  [50] 0.6232018 0.5907324 0.9336556 0.6629327 0.6355294 0.8929248 0.6940901
#>  [57] 0.6391180 0.6973637 0.6004635 0.8493916 0.7752034 0.6188363 1.2034117
#>  [64] 0.7494566 0.6518454 0.9423731 0.6550351 0.6534103 0.6662371 0.9304283
#>  [71] 0.6964381 0.8120960 1.5368200 0.5669815 1.0202950 0.7045124 0.8554940
#>  [78] 0.8302034 1.2846113 0.6287822 1.6616051 0.7723292 1.1287269 0.6707214
#>  [85] 0.6236943 0.9237694 0.5518232 0.6016397 2.6726093 2.0413084 0.6411518
#>  [92] 0.7871719 1.3073180 0.7834904 1.3752510 0.6801387 0.6750841 0.6180889
#>  [99] 0.9685198 1.0391291

# Inspect the result
w <- wt_ate(ps, trt)
#> ℹ Treating `.exposure` as binary
estimand(w)
#> [1] "ate"
summary(w)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   1.112   1.317   1.591   2.044   2.047   7.482 

# -- Overlap-focused estimands handle extreme PS better --------------
ps_extreme <- c(0.01, 0.02, 0.98, 0.99, rep(0.5, 4))
trt_extreme <- c(0, 0, 1, 1, 0, 1, 0, 1)

max(wt_ate(ps_extreme, trt_extreme))
#> ℹ Treating `.exposure` as binary
#> [1] 2
max(wt_ato(ps_extreme, trt_extreme))
#> ℹ Treating `.exposure` as binary
#> [1] 0.5

# -- From a fitted GLM -----------------------------------------------
x1 <- rnorm(100)
x2 <- rnorm(100)
trt2 <- rbinom(100, 1, plogis(0.5 * x1 + 0.3 * x2))
ps_model <- glm(trt2 ~ x1 + x2, family = binomial)

# Exposure is extracted from the model automatically
wt_ate(ps_model)
#> ℹ Using exposure variable "trt2" from GLM model
#> ℹ Treating `.exposure` as binary
#> <psw{estimand = ate}[100]>
#>   [1] 1.772299 2.816364 1.919886 2.059945 1.590514 2.019637 1.592626 3.675866
#>   [9] 1.731064 1.526937 2.194737 1.585679 1.604308 2.035997 1.836701 3.038426
#>  [17] 1.926720 2.527851 2.956648 1.456686 1.951071 2.308830 2.122857 1.859348
#>  [25] 1.333779 1.789153 2.089527 2.008161 1.809376 1.845397 1.236823 2.436497
#>  [33] 1.817852 2.352419 1.300776 1.637110 3.144659 2.924006 4.687625 1.406029
#>  [41] 2.396310 2.163061 2.510037 1.356974 1.430312 2.334509 3.102993 2.202745
#>  [49] 1.310198 1.607962 2.624988 2.535210 1.793952 1.647484 2.569296 2.061068
#>  [57] 3.046296 1.936586 1.517183 1.624578 2.826262 2.825176 1.554039 1.098856
#>  [65] 1.637046 1.507218 2.581387 1.554926 2.385541 1.698365 1.811373 1.670399
#>  [73] 1.760472 1.365580 1.911171 1.539045 2.208360 1.724933 1.617692 1.874702
#>  [81] 1.406166 3.813823 1.982021 2.553269 1.982884 1.957207 1.440986 1.560568
#>  [89] 1.603633 1.885138 1.584638 2.218637 1.630055 1.585865 1.872610 1.274698
#>  [97] 1.393716 1.394134 1.800220 1.778728

# -- Data frame input ------------------------------------------------
ps_df <- data.frame(
  control = c(0.9, 0.7, 0.3, 0.1),
  treated = c(0.1, 0.3, 0.7, 0.9)
)
exposure <- c(0, 0, 1, 1)
wt_ate(ps_df, exposure)
#> ℹ Treating `.exposure` as binary
#> <psw{estimand = ate}[4]>
#> [1] 1.111111 1.428571 1.428571 1.111111
wt_ate(ps_df, exposure, .propensity_col = "treated")
#> ℹ Treating `.exposure` as binary
#> <psw{estimand = ate}[4]>
#> [1] 1.111111 1.428571 1.428571 1.111111

# -- Censoring weights -----------------------------------------------
cens_ps <- runif(50, 0.6, 0.95)
cens_ind <- rbinom(50, 1, cens_ps)
wt_cens(cens_ps, cens_ind)
#> ℹ Treating `.exposure` as binary
#> <psw{estimand = uncensored}[50]>
#>  [1] 1.116412 1.447081 1.644465 1.108844 1.394494 1.217840 1.263824 3.727943
#>  [9] 1.503634 1.333104 1.218367 1.278290 1.203561 1.169213 1.298047 1.361360
#> [17] 1.660049 1.663092 1.054599 2.760604 3.945306 1.174730 1.162941 1.104729
#> [25] 1.230385 1.156509 1.115406 1.227788 1.139434 2.551015 1.340626 1.103498
#> [33] 1.209817 1.082758 2.943590 1.407391 1.134443 1.056929 1.402849 2.502609
#> [41] 1.055677 1.533923 1.620017 1.235981 3.477837 1.274250 1.138436 1.602240
#> [49] 1.185878 1.072937
estimand(wt_cens(cens_ps, cens_ind))  # "uncensored"
#> ℹ Treating `.exposure` as binary
#> [1] "uncensored"