潜在结果

Potential outcomes

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定义

潜在结果：给定一个单元，和一系列动作，我们把一个“动作-单元”确定为一个潜在结果。“潜在(potential)”这个词表达的意思是我们并不总是能在现实中观察到这个结果(outcome)，但原则上它们可能发生。

样例介绍

Suppose that Joe is participating in an FDA test for a new hypertension drug. If we were omniscient, we would know the outcomes for Joe under both treatment (the new drug) and control (either no treatment or the current standard treatment). The causal effect, or treatment effect, is the difference between these two potential outcomes.

【终译】假设乔正在参与 FDA 对一种新的高血压药物的测试。如果我们是无所不知的，我们就会知道乔在治疗组和控制组下的结果。我们想要探究的因果效应，或者说治疗效果，就是指这两种潜在结果之间的差异。

subject	Yt(u)	Yc (u)	Yt (u)-Yc (u）
Joe	130	135	−5

Yt(u) is Joe's blood pressure if he takes the new pill. In general, this notation expresses the potential outcome which results from a treatment, t, on a unit, u. Similarly,  Yc(u) is the effect of a different treatment, c or control, on a unit, u. In this case,  Yt(u) - Yc(u) is Joe's blood pressure if he doesn't take the pill.  is the causal effect of taking the new drug.

【终译】 Yt(u) 表示如果乔服用了这种新药物之后对应的血压。一般来说，这个符号表示一个单位 u 上的治疗结果 t 的潜在结果。类似地，Yc (u)是一个单位 u 上的不同治疗效果 c 的潜在结果或控制组的结果。Yc (u)若表示控制组，则在这种情况下，Yt (u)-Yc (u)就是表示乔不吃这种新药物时的血压，也就是服用这种新药物的因果效应。

From this table we only know the causal effect on Joe. Everyone else in the study might have an increase in blood pressure if they take the pill. However, regardless of what the causal effect is for the other subjects, the causal effect for Joe is lower blood pressure, relative to what his blood pressure would have been if he had not taken the pill.

【终译】从这个表格中我们只知道对乔的因果效应。研究中的其他人如果服用新药，血压可能会升高。然而，不管其他受试者的因果效应如何，我们可以得出结论，对于乔来说，相比于他没有服用新药的情况，服用该药，他的血压会降低。

Consider a larger sample of patients:

【终译】考虑更为大量的病患样本

subject	Yt(u)	Yc (u)	Yt (u)-Yc (u）
Joe	130	135	−5
Mary	140	150	−10
Sally	135	125	10
Bob	135	150	−15

The causal effect is different for every subject, but the drug works for Joe, Mary and Bob because the causal effect is negative. Their blood pressure is lower with the drug than it would have been if each did not take the drug. For Sally, on the other hand, the drug causes an increase in blood pressure.

【终译】每个实验对象的因果效应是不同的，从该表中，可知效应为负值，说明药物仅对乔，玛丽和鲍勃起作用。他们服用这种药物后的血压比没有服用这种药物时的血压要低。另一方面，对于 Sally 来说，这种药物会导致血压升高。

In order for a potential outcome to make sense, it must be possible, at least a priori. For example, if there is no way for Joe, under any circumstance, to obtain the new drug, then  is impossible for him. It can never happen. And if  can never be observed, even in theory, then the causal effect of treatment on Joe's blood pressure is not defined.

【终译】为了让一个潜在的结果有意义，它必须是可能的，至少是先验的。例如，如果乔在任何情况下都没有办法获得新药，那么他就不可能获得效应。这永远不可能发生在乔身上。如果不能观察到效应，即使在理论上，那么治疗对乔的血压的因果效应也不能确定。