IP weighting (IPTW and IPCW)

Adjust for confounding or for censoring/missing outcomes with inverse-probability weights

Published

July 2, 2026

Warning

Under development.

IP weighting (inverse probability weighting) is one technique with two applications. You model the probability of whatever skews the comparison and weight each person by its inverse. This creates a pseudo-population in which the skew is gone:

IPTW (treatment weighting) against confounding: weight by the probability of being exposed.
IPCW (censoring weighting) against selection bias from censoring, dropout or missing outcomes: weight by the probability of being observed.

Both are handled in the analysis rather than by design.

Note

The code examples use generic path and variable names. Adapt them to your project. The packages (WeightIt, cobalt, sandwich, lmtest) must be installed in your R environment on DST.

Part 1: IPTW - weighting against confounding

Where matching (Phase 10) balances the groups by selecting people, IPTW weights them: each person gets a weight based on their probability of being exposed (the propensity score), so exposed and unexposed become comparable on the measured confounders.

Note

Propensity score, three ways. The propensity score (each person’s probability of being exposed given the confounders) can be used by weighting (IPTW, this page), by matching exposed to unexposed on the score, or by stratifying / adjusting on it. They are alternative routes to the same end, balancing measured confounders, and all share the same positivity diagnostic: poor overlap shows up as extreme weights or as people who cannot be matched. See Hernán & Robins, What If, ch. 15.

Note

Three assumptions for IPTW to work (the general identifiability conditions for any causal estimate, introduced in Phase 1):

Exchangeability: you have measured and included the main confounders (no substantial unmeasured confounding).
Positivity (overlap): within each combination of confounders, both exposed and unexposed must be possible. Very large weights are a warning sign of poor overlap.
Consistency: the exposure must be a well-defined intervention, so a “what if everyone were / were not exposed” world makes sense.

Step 1: estimate the weights

library(WeightIt)                          # weightit(): computes the weights
library(cobalt)                            # bal.tab(), love.plot(): check balance

df <- readRDS("path/to/analysis.rds")      # analysis-ready dataset, one row per person

W <- weightit(
  exposure ~ age + sex + calendar_year + ses,  # treatment ~ confounders (NOT the outcome)
  data     = df,
  method   = "glm",                        # propensity score via logistic regression
  estimand = "ATE"                         # target: average effect in the whole population
)

The left side of ~ is the exposure (treatment), the right side the confounders - never the outcome.
method = "glm" computes the propensity score with logistic regression.
estimand = "ATE" weights so both groups come to resemble the whole population.

Step 2: check balance

The weights are only good if they actually balance the confounders. Check that before looking at the outcome.

bal.tab(W)                                 # standardised differences (SMD) before and after weighting
love.plot(W)                               # same as a figure; rule of thumb: |SMD| < 0.1 after weighting

bal.tab() / love.plot() show how far each confounder is from being balanced (SMD = standardised difference between the groups) - before and after weighting. The goal is for all of them to sit close to 0 after weighting. If some are still skewed, or a few weights are very large, reconsider the model (more/other confounders) or consider stabilising/trimming the weights.

Step 3: weighted outcome model

Once balance is acceptable, fit the outcome model with the weights. Weighting requires robust standard errors (same idea as in Regression).

library(sandwich)                          # vcovHC(): robust variance
library(lmtest)                            # coeftest()

df$w <- W$weights                          # add the weights as a column

model <- glm(outcome ~ exposure,           # weighted model: just the treatment (confounders are "weighted away")
             data = df, weights = w, family = binomial)

coeftest(model, vcov = vcovHC(model))      # coefficients with robust standard errors

Tip

Expected warning. With non-integer weights, glm(..., family = binomial) prints the warning “non-integer #successes in a binomial glm”. It is harmless here and can be ignored: the estimates are correct, and the robust standard errors are exactly what fixes the uncertainty. (Don’t switch to family = quasibinomial to remove it - that changes the model’s variance assumption.) The robust standard errors treat the weights as fixed; to be fully rigorous you can bootstrap the whole procedure.

Note

See also: standardization (the g-formula). IPTW has a twin for confounding control: standardization (also called g-computation or the parametric g-formula). Instead of weighting, you fit an outcome model and average its predictions over the confounder distribution. It often gives more stable estimates and lets you report marginal risk differences and ratios, not just an odds ratio. The two answer the same causal question and make a good cross-check on each other. See Hernán & Robins, What If, ch. 13 (and §13.4, “IP weighting or standardization?”).

Part 2: IPCW - weighting against censoring and missing outcomes

The same machinery can fix a different skew: selection bias from censoring, dropout or missing outcomes. Think of censoring as a “second treatment”: instead of asking “what is the effect of the exposure?” (which requires complete data) you ask “what would the effect be if nobody had been censored?”. This converts selection bias into a confounding problem for censoring, and confounding can be weighted away.

Each observed person is weighted by 1/Pr(observed), so they stand in for the similar people who dropped out. This rebuilds the full population.

Example (from Hernán & Robins, What If, chapter 8): a randomised trial of wasabi and death. Dropout is highest among precisely the exposed and the sick, so censoring becomes uneven:

Completers only	N	Deaths	Risk
Exposed	9	4	44%
Control	22	11	50%

The completer analysis gives RR = 0.89 - wasabi looks protective. But that is an illusion created by the uneven dropout: the exposed who stayed are systematically healthier. Weighted back to the full population, the risk is 57% in both groups, RR = 1.00 - no effect.

library(sandwich)                          # vcovHC(): robust variance
library(lmtest)                            # coeftest()

df$observed <- as.integer(!is.na(df$outcome))   # 1 = outcome observed, 0 = censored/missing

# model WHO is observed, from predictors of both dropout AND outcome
cens <- glm(observed ~ exposure + age + sex + ses,
            data = df, family = binomial)

df$p_obs  <- predict(cens, type = "response") # Pr(observed | predictors)
df$w_cens <- 1 / df$p_obs                      # censoring weight = 1 / Pr(observed)

# fit the outcome model on the observed ONLY, weighted (robust SE as for IPTW)
fit <- glm(outcome ~ exposure,
           data = subset(df, observed == 1),
           weights = w_cens, family = binomial)

coeftest(fit, vcov = vcovHC(fit))           # same harmless non-integer warning as above

Important

The three assumptions apply here too (Hernán & Robins, ch. 8):

Exchangeability: the one that fails most often. The predictors in the weight model must contain everything that predicts both dropout AND outcome. We rarely know the true reasons people drop out, and there is no test for whether we caught them all - only substantive judgement.
Positivity: everyone must be able to stay observed: Pr(observed) > 0 in every group. If a group is certain to drop out, there is no one left to weight up from.
Consistency: a “no censoring” world must be coherent. Fine for loss to follow-up. Not fine for competing events (for example death from another cause), where you cannot remove one cause without touching the others.

For missing outcomes, IPCW is an alternative to multiple imputation, see Missing data.

Note

Remember: anything leaving DST must go through output control - no small cells, only aggregated results. See Phase 14 - Export and repatriation.