Statistical modeling of causal effects in continuous time

This article studies the estimation of the causal effect of a time-varying treatment on time-to-an-event or on some other continuously distributed outcome. The paper applies to the situation where treatment is repeatedly adapted to time-dependent patient characteristics. The treatment effect cannot be estimated by simply conditioning on these time-dependent patient characteristics, as they may themselves be indications of the treatment effect. This time-dependent confounding is common in observational studies. Robins [(1992) Biometrika 79 321--334, (1998b) Encyclopedia of Biostatistics 6 4372--4389] has proposed the so-called structural nested models to estimate treatment effects in the presence of time-dependent confounding. In this article we provide a conceptual framework and formalization for structural nested models in continuous time. We show that the resulting estimators are consistent and asymptotically normal. Moreover, as conjectured in Robins [(1998b) Encyclopedia of Biostatistics 6 4372--4389], a test for whether treatment affects the outcome of interest can be performed without specifying a model for treatment effect. We illustrate the ideas in this article with an example.Comment: Published in at http://dx.doi.org/10.1214/009053607000000820 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Causal Induction from Continuous Event Streams: Evidence for Delay-Induced Attribution Shifts

Contemporary theories of Human Causal Induction assume that causal knowledge is inferred from observable contingencies. While this assumption is well supported by empirical results, it fails to consider an important problem-solving aspect of causal induction in real time: In the absence of well structured learning trials, it is not clear whether the effect of interest occurred because of the cause under investigation, or on its own accord. Attributing the effect to either the cause of interest or alternative background causes is an important precursor to induction. We present a new paradigm based on the presentation of continuous event streams, and use it to test the Attribution-Shift Hypothesis (Shanks & Dickinson, 1987), according to which temporal delays sever the attributional link between cause and effect. Delays generally impaired attribution to the candidate, and increased attribution to the constant background of alternative causes. In line with earlier research (Buehner & May, 2002, 2003, 2004) prior knowledge and experience mediated this effect. Pre-exposure to a causally ineffective background context was found to facilitate the discovery of delayed causal relationships by reducing the tendency for attributional shifts to occur. However, longer exposure to a delayed causal relationship did not improve discovery. This complex pattern of results is problematic for associative learning theories, but supports the Attribution-Shift Hypothesi

von Neumann-Morgenstern and Savage Theorems for Causal Decision Making

Causal thinking and decision making under uncertainty are fundamental aspects of intelligent reasoning. Decision making under uncertainty has been well studied when information is considered at the associative (probabilistic) level. The classical Theorems of von Neumann-Morgenstern and Savage provide a formal criterion for rational choice using purely associative information. Causal inference often yields uncertainty about the exact causal structure, so we consider what kinds of decisions are possible in those conditions. In this work, we consider decision problems in which available actions and consequences are causally connected. After recalling a previous causal decision making result, which relies on a known causal model, we consider the case in which the causal mechanism that controls some environment is unknown to a rational decision maker. In this setting we state and prove a causal version of Savage's Theorem, which we then use to develop a notion of causal games with its respective causal Nash equilibrium. These results highlight the importance of causal models in decision making and the variety of potential applications.Comment: Submitted to Journal of Causal Inferenc