Yuzuru Otonashi's sister Hatsune had cancer and there were indications that it was getting worse. When Christmas came, the doctors refused to let her out but keeping his word Yuzuru snuck in and took her out.
When we seem them together outside and when Yuzuru talks to her, she seems very weak and Yuzuru monologue's saying he continued to have a one-sided conversation. The next scene we see is Yuzuru is being asked if he is ok following Hatsune's death.
I am wondering, while Hatsune was probably bound to be killed by her cancer later on, was Yuzuru taking Hatsune out that night what caused her cancer to kill her ?