文档介绍：孟德尔随机化 以及在流行病学中的应用
一、流行病学病因研究中的理论问题
病因问题是一切医疗实践活动 诊断、治疗及预防 的重要理论基础,因此它在医学研究领域中始终占有重要地位，
流行病学从群体的角度出发对病因问题提出了许多独到的见ndomization analysis of two large cohorts
尿酸,高尿酸血症
缺血性性脏病
年龄,性别,吸烟,教育…………..
SLC2A9
SLC2A9与暴露关系
SLC2A9与尿酸有很强的线性相关
SLC2A9与混杂的关系
SLC2A9与暴露及结局的关系
队列CGPC和CCHS
尿酸/高尿酸血症与缺血性心脏病关系 观察性研究
调整混杂：age, sex, smoking, education, and income
结论：尿酸与缺血性心脏病没有因果关系
五、软件实现
r package instrumental variables google AER
例子 数据
A data frame containing 48 observations on 7 variables for 2 periods.
state Factor indicating state.
year Factor indicating year.
cpi Consumer price index.
population State population.
packs Number of packs per capita.
income State personal income total, nominal .
tax Average state, federal and average local excise taxes for fiscal year.
price Average price during fiscal year, including sales tax.
taxs Average excise taxes for fiscal year, including sales tax.
数据
CigarettesSW$rprice <- with CigarettesSW, price/cpi
CigarettesSW$rincome <- with CigarettesSW, income/population/cpi
CigarettesSW$tdiff <- with CigarettesSW, taxs - tax /cpi
c1985 <- subset CigarettesSW, year == "1985"
c1995 <- subset CigarettesSW, year == "1995"
程序
## data
data "CigarettesSW"
CigarettesSW$rprice <- with CigarettesSW, price/cpi
CigarettesSW$rincome <- with CigarettesSW, income/population/cpi
CigarettesSW$tdiff <- with CigarettesSW, taxs - tax /cpi
## model
fm <- ivreg log packs ~ log rprice + log rincome | log rincome + tdiff + I tax/cpi ,
data = CigarettesSW, subset = year == "1995"
summary fm
模型所要研究的变量叫内生变量,能够对内生变量产生影响,但其本身是在模型之外,由其他变量决定的变量 通常视为既定 叫做外生变量，例如在价格决定的模型中,价格、需求量、供给量都是内生变量,而决定需求的变量如收入、偏好,有或是决定供给的成本等等都是外生变量
Details
Regressors and instruments for ivreg are most easily specified in a formula with two parts on the right-hand side, ., y ~ x1 + x2 | z1 + z2 + z3, where x1 and x2 are the regressors and z1, z2, and z3 are the instruments. Note that exogenous regressors have to be included as instruments for themselves