Related papers: Probabilities of Causation with Nonbinary Treatmen…
Probabilities of Causation (PoC) play a fundamental role in decision-making in law, health care and public policy. Nevertheless, their point identification is challenging, requiring strong assumptions, in the absence of which only bounds…
Given empirical evidence for the dependence of an outcome variable on an exposure variable, we can typically only provide bounds for the "probability of causation" in the case of an individual who has developed the outcome after being…
Probabilities of Causation play a fundamental role in decision making in law, health care and public policy. Nevertheless, their point identification is challenging, requiring strong assumptions such as monotonicity. In the absence of such…
This paper extends my research applying statistical decision theory to treatment choice with sample data, using maximum regret to evaluate the performance of treatment rules. The specific new contribution is to study as-if optimization…
To answer questions of "causes of effects", the probability of necessity is introduced for assessing whether or not an observed outcome was caused by an earlier treatment. However, the statistical inference for probability of necessity is…
We study causal inference under case-control and case-population sampling. Specifically, we focus on the binary-outcome and binary-treatment case, where the parameters of interest are causal relative and attributable risks defined via the…
Causal inference in completely randomized treatment-control studies with binary outcomes is discussed from Fisherian, Neymanian and Bayesian perspectives, using the potential outcomes framework. A randomization-based justification of…
Mediation analysis for probabilities of causation (PoC) provides a fundamental framework for evaluating the necessity and sufficiency of treatment in provoking an event through different causal pathways. One of the primary objectives of…
We study the complexity of satisfiability problems in probabilistic and causal reasoning. Given random variables $X_1, X_2,\ldots$ over finite domains, the basic terms are probabilities of propositional formulas over atomic events $X_i =…
Outcome-dependent sampling designs are common in many different scientific fields including epidemiology, ecology, and economics. As with all observational studies, such designs often suffer from unmeasured confounding, which generally…
Suppose X and Y are binary exposure and outcome variables, and we have full knowledge of the distribution of Y, given application of X. From this we know the average causal effect of X on Y. We are now interested in assessing, for a case…
Probability of necessity and sufficiency (PNS) measures the likelihood of a feature set being both necessary and sufficient for predicting an outcome. It has proven effective in guiding representation learning for unimodal data, enhancing…
Propensity scores are commonly used to estimate treatment effects from observational data. We argue that the probabilistic output of a learned propensity score model should be calibrated -- i.e., a predictive treatment probability of 90%…
We present a basis for studying questions of cause and effect in statistics which subsumes and reconciles the models proposed by Pearl, Robins, Rubin and others, and which, as far as mathematical notions and notation are concerned, is…
Causal models are crucial for understanding complex systems and identifying causal relationships among variables. Even though causal models are extremely popular, conditional probability calculation of formulas involving interventions pose…
Many legal cases require decisions about causality, responsibility or blame, and these may be based on statistical data. However, causal inferences from such data are beset by subtle conceptual and practical difficulties, and in general it…
Some units from a population receive the same treatment that is different from treatments available for other reservoir populations. The minimal sufficient statistic $s$ for the pre-treatment $x$-covariates's distributions in the…
Individual treatment effects are not point-identified from data. The Probability of Necessity and Sufficiency (PNS) circumvents this limitation by characterizing individual-level causality through intersection bounds derived from combined…
An individual has been subjected to some exposure and has developed some outcome. Using data on similar individuals, we wish to evaluate, for this case, the probability that the outcome was in fact caused by the exposure. Even with the best…
We develop a Bayesian nonparametric (BNP) approach to evaluate the causal effect of treatment in a randomized trial where a nonterminal event may be censored by a terminal event, but not vice versa (i.e., semi-competing risks). Based on the…