Question

as is often the case with children，amy was better by the time the doctor arrived什么意思

Answer 1

翻译：小孩子通常就这样，医生一到艾米就好多了。

as is often the case with sb./sth.
情况常常如此；这是常有的事；通常就是这样
例如：
As is often the case with persuasion, what you do first matters.
就想通常有说服力的案例一样，你首先做什么关系重大。
by the time...到……时候
By the time you graduate, wewill be in Australia for one year.
到你毕业的时候，我们在澳洲居住就会有一年了。

Answer 2

　　as is often the case with children，amy was better by the time the doctor arrived

　　有孩子的情况常常如此,艾米被医生到达的时间更好