In this talk, I will talk on two concepts: causal effects (Effect of Cause) and posterior causal effects (Cause of Effect).

For causal effects, we study covariate adjusted average treatment effect estimate problem. We specify a working model for the potential outcome and the covariates. We show that even when the working model is misspecified, the   difference estimator for the average treatment effect is consistent and asymptotically normal. We propose a well designed generalized estimation equation method, with which the estimated average treatment effect is always   more efficient than the simple difference in mean estimator, under mild conditions. Extensive simulation studies verify our theoretical results.

For posterior causal effects, I will first introduce a few historical work on this concept. For the case with a single causal variable, Dawid et al. (2014) defined the probability of causation and Pearl (2000) defined the probability of necessity to assess the causes of effects. For a case with multiple causes which may affect each other, we define the posterior total and direct causal effects based on the evidences observed for post-treatment variables, which could be viewed as measurements of causes of effects. The posterior causal effects involve the probabilities of counterfactual variables. Thus, like probability of causation, probability of necessity and the direct causal effects, the identifiability of the posterior total and direct causal effects requires more assumptions than the identifiability of the traditional causal effects conditional on pre-treatment variables.We present assumptions required for the identifiability of the posterior causal effects and provide identification equations. Further, when the causal relationships among multiple causes and an endpoint may be depicted by causal networks, we can simplify both the required assumptions and the identification equations of the posterior total and direct causal effects. Finally, using numerical examples, we compare the posterior total and direct causal effects with other measures for evaluating the causes of effects and the population attributable risks.