Previous efforts in vision community are mostly made on learning good representations from visual patterns. Beyond this, this paper emphasizes the high-level ability of causal reasoning. We thus present a case study of solving the challenging task of Overall Survival (OS) time in primary liver cancers. Critically, the prediction of OS time at the early stage remains challenging, due to the unobvious image patterns of reflecting the OS. To this end, we propose a causal inference system by leveraging the intraoperative attributes and the correlation among them, as an intermediate supervision to bridge the gap between the images and the final OS. Particularly, we build a causal graph, and train the images to estimate the intraoperative attributes for final OS prediction. We present a novel Causally-aware Intraoperative Imputation Model (CAWIM) that can sequentially predict each attribute using its parent nodes in the estimated causal graph. To determine the causal directions, we propose a splitting-voting mechanism, which votes for the direction for each pair of adjacent nodes among multiple predictions obtained via causal discovery from heterogeneity. The practicability and effectiveness of our method are demonstrated by the promising result on liver cancer dataset of 361 patients with long-term observations.