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We consider causal inference for observational studies with data spread over two files. One file includes the treatment, outcome, and some covariates measured on a set of individuals, and the other file includes additional causally-relevant covariates measured on a partially overlapping set of individuals. By linking records in the two databases, the analyst can control for more covariates, thereby reducing the risk of bias compared to using only one file alone. When analysts do not have access to a unique identifier that enables perfect, error-free linkages, they typically rely on probabilistic record linkage to construct a single linked data set, and estimate causal effects using these linked data. This typical practice does not propagate uncertainty from imperfect linkages to the causal inferences. Further, it does not take advantage of relationships among the variables to improve the linkage quality. We address these shortcomings by fusing regression-assisted, Bayesian probabilistic record linkage with causal inference. The Markov chain Monte Carlo sampler generates multiple plausible linked data files as byproducts that analysts can use for multiple imputation inferences. Here, we show results for two causal estimators based on propensity score overlap weights. Using simulations and data from the Italy Survey on Household Income and Wealth, we show that our approach can improve the accuracy of estimated treatment effects.
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Interactive rank testing by betting
In order to test if a treatment is perceptibly different from a placebo in a randomized experiment with covariates, classical nonparametric tests based on ranks of observations/residuals have been employed (eg: by Rosenbaum), with finite-sample valid inference enabled via permutations. This paper proposes a different principle on which to base inference: if — with access to all covariates and outcomes, but without access to any treatment assignments — one can form a ranking of the subjects that is sufficiently nonrandom (eg: mostly treated followed by mostly control), then we can confidently conclude that there must be a treatment effect. Based on a more nuanced, quantifiable, version of this principle, we design an interactive test called i-bet: the analyst forms a single permutation of the subjects one element at a time, and at each step the analyst bets toy money on whether that subject was actually treated or not, and learns the truth immediately after. The wealth process forms a real-valued measure of evidence against the global causal null, and we may reject the null at level if the wealth ever crosses 1= . Apart from providing a fresh “game-theoretic” principle on which to base the causal conclusion, the i-bet has other statistical and computational benefits, for example (A) allowing a human to adaptively design the test statistic based on increasing amounts of data being revealed (along with any working causal models and prior knowledge), and (B) not requiring permutation resampling, instead noting that under the null, the wealth forms a nonnegative martingale, and the type-1 error control of the aforementioned decision rule follows from a tight inequality by Ville. Further, if the null is not rejected, new subjects can later be added and the test can be simply continued, without any corrections (unlike with permutation p-values). Numerical experiments demonstrate good power under various heterogeneous treatment effects. We first describe i-bet test for two-sample comparisons with unpaired data, and then adapt it to paired data, multi-sample comparison, and sequential settings; these may be viewed as interactive martingale variants of the Wilcoxon, Kruskal-Wallis, and Friedman tests.
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- Award ID(s):
- 1945266
- PAR ID:
- 10334958
- Editor(s):
- Scholkopf, Bernhard; Uhler, Caroline; Zhang, Kun
- Publisher / Repository:
- OpenReview
- Date Published:
- Journal Name:
- First Conference on Causal Learning and Reasoning, PMLR
- Volume:
- 140
- Page Range / eLocation ID:
- 1-35
- Format(s):
- Medium: X
- Location:
- Causal Learning and Reasoning
- Sponsoring Org:
- National Science Foundation
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