A patient receives treatment despite having a propensity score of 0.05 (very unlikely to be treated given their covariates). What is their approximate IPW weight, and what does it represent?
AWeight ≈ 0.05; they receive a small weight because they were unlikely to be treated
BWeight ≈ 20; they receive a large weight because they are unusual among the treated and represent many similar patients who were not treated
CWeight ≈ 1; all treated patients receive the same weight regardless of propensity score
DWeight ≈ 0.95; the weight is based on the probability of not being treated
The IPW weight for a treated patient is 1/propensity_score = 1/0.05 = 20. This large weight reflects that this patient is a rare treated individual among a pool of people who mostly went untreated. In the reweighted pseudo-population, they 'stand in for' many similar patients. This is the core mechanism: unusual treated patients receive high weights to make the treated group resemble the overall population, removing confounding by measured covariates.
Question 2 Multiple Choice
A regression model estimates the effect of a drug conditional on specific covariate values (age, sex, comorbidities). An IPW analysis estimates the marginal effect. Why might a clinician prefer the marginal estimate for a policy decision?
ABecause marginal effects are always larger and more convincing to policymakers
BBecause conditional effects assume covariates are measured without error, which is rarely true
CBecause the marginal effect answers 'what if everyone in the population received this drug?' — the relevant question for population-level policy
DBecause regression cannot adjust for confounding, while IPW can
The marginal effect averages over the entire population distribution of covariates — it answers 'what would happen at the population level if we treated everyone versus no one?' A conditional effect from regression holds covariates fixed and asks 'what is the effect for someone with exactly these covariate values?' For policy decisions (e.g., whether to approve a drug for a population), the marginal effect is the appropriate target. Both regression and IPW adjust for confounding; the difference is the *type* of effect estimated.
Question 3 True / False
IPW with correctly estimated propensity scores removes confounding by both measured and unmeasured variables.
TTrue
FFalse
Answer: False
IPW only adjusts for *measured* confounders — those included in the propensity score model. If important confounders are unmeasured and therefore absent from the model, the propensity score is misspecified, the weights do not achieve the intended balance, and bias persists regardless of how well the weighting balances observed covariates. This is the fundamental limitation shared with all propensity score methods and observational causal inference generally.
Question 4 True / False
Stabilized IPW weights reduce variance compared to raw weights without introducing bias into the treatment effect estimate.
TTrue
FFalse
Answer: True
Stabilized weights are formed by multiplying the raw weight (1/P[T=t|X]) by the marginal probability of receiving that treatment P[T=t]. This bounds the weights from above and reduces their variance without introducing systematic bias, because the stabilizing factor is the same for everyone in a given treatment group and cancels out in the weighted estimator. The trade-off is that stabilized weights don't fully eliminate confounding if the marginal model is misspecified, but in practice they are strongly preferred over raw weights whenever weight instability is a concern.
Question 5 Short Answer
Why do extreme propensity scores (near 0 or 1) create problems for IPW, and what is the intuition behind stabilized weights as a solution?
Think about your answer, then reveal below.
Model answer: When a propensity score is near 0 or 1, treatment was nearly deterministic — everyone in that region either always got treatment or never did. The inverse weight (1/p or 1/(1-p)) becomes very large, so a handful of observations can dominate the entire analysis, inflating variance and making the estimate sensitive to those few data points. Stabilized weights multiply the raw weight by the marginal probability of treatment P(T=t), which caps the maximum possible weight at the ratio of marginal to conditional treatment probabilities. This reduces the range of weights while preserving their confounder-balancing property.
The deeper issue is positivity: IPW requires that every individual has a non-zero probability of receiving each treatment level (the positivity assumption). Near violations of positivity — propensity scores near 0 or 1 — don't break the method theoretically but create practical instability. Stabilized weights are a principled fix: they bound the weights while remaining unbiased under correct model specification, and diagnostics (plotting weight distribution, examining max weight, checking effective sample size) help identify when instability is severe enough to invalidate the analysis.