什么是协变量

I've found a good passage talking about covariate:Covariate:

In design of experiments, a covariate is an independent variable not manipulatedby the experimenter but still affecting the response. See Variables (in designof experiments) for an explanatory example.

协变量:在实验的设计中,协变量是⼀个独⽴变量(解释变量),不为实验者所操纵,但仍影响响应。

Variables (in design of experiments):

Many statistical methods rest on a statistical model which states a relationship

Y = f(X1,..,XN)

between a dependent variable (Y) and independent variable(s) X1,...,XN. In designed experiments, the dependent variable is often named \"response\independent variables manipulated by the experimenter \"factors\response) \"covariates\". The values which a factor can take on are named \"levels\" of this factor. Tested combinations of levels of all factors are called\"treatments\".

许多统计⽅法基于⼀个统计模型

Y = f(X1,..,XN)

描述依存变量（被解释变量）Y 和独⽴变量（解释变量） X1,...,XN 之间的关系。在设计的实验中，依存变量（被解释变量）经常被称为“反应”，被实验者所操纵的独⽴变量（解释变量）被称为“影响因素”，

不被实验者所操纵（但仍然影响“反应”）的独⽴变量（解释变量）被称为“协变量”，⼀个影响因素所取的值称为该因素的“⽔平”。⽤于检验的所有影响因素的⽔平的不同组合被称为“⽅案”。

Consider an example of a clinical trial of drugs. The question addressed by the trial is how combinations of two drugs affect the survival rate. Twodrugs have been tested: \"Drug 1\" and \"Drug 2\". Drug 1 has been administered in three ways - \"None\

administered in a single way, but in 4 different doses \"Nonewo drugs have been tested. The following model is used to interpret outcomes of the trial:

Y = Tij + B X + E ; i=1,...,3; j=1,...,4;

where Y is the survival rate, indices i and j correspond to the methods of administration of the drug 1 and drug 2 respectively, X is age, and E is randomvariation in survival rate. Coefficients Tij, which characterize the effect of the two drugs on the survival rate, are of primary interest.

考虑⼀个药品临床试验的例⼦，试验提出的问题是，两种药品的不同组合如何影响救活率。试验的两种药品分别是 “药品1”、“药品2”。药品1的使⽤⽅式有3种：“不⽤”、“⼝服”、“注射”；药品2的使⽤⽅式只有1种，但有4种不同的剂量：“不⽤”、“低剂量”、“中剂量”、“⾼剂量”。2种药品在试验中的⽅案有12种（3*4）可能的组合。试验的结果⽤模型表⽰为：

Y = Tij + B X + E ; i=1,...,3; j=1,...,4;

The response here is the survival rate. We have two factors - \"drug 1\" and \"drug 2\". The first factor has three levels (\"none\second factor - four levels (\"none\levels are related to methods of administration). We have here 12 treatments being tested - all the possible combinations of the three levels of factor 1and the four levels of factor 4 (specified above).

系数Tij 是相应治疗⽅式的成效。举个例⼦，T23 是药物1⼝服和药物2中等剂量治疗⽅案的治疗效果。年龄在这⾥作为协变量⽽存在，它虽然不被实验者所控制，但确实会对存活率产⽣影响。

Coefficients Tij are \"effects\" of the corresponding treatments. For example, T23 is the effect of the treatment by drug 1 orally plus drug 2 in moderatedose. Age here is a covariate - it is not manipulated by the experimenter but still may have effect on the survival rate.