倾向性评分匹配完整实例（R实现）

倾向性评分匹配（propensity score matching, PSM）主要是在随机对照试验(Randomized controlled trials,RCT)中用于衡量treat组和control组样本的其他各项特征（如年龄、体重、身高、人种等）的整体均衡性的度量。比如说研究一种药物对疾病的影响，在临床实验中，treat组和control组除了使用药物（安慰剂）不同外，其他的临床特征（如年龄、体重等）都应该基本是相似的，这样treat和control组才有可比性，进而才能验证药物的有效性。

如下图所示，该治疗方法实际上是无效的，但是由于分组中年龄的不平衡导致得出错误的结论。

    对于衡量同一特征的组间差异或者距离，我们通常使用标准均值误差（Standardized mean difference，SMD，PMC3144483）。
对于连续性特征变量公式如下：

对于离散型特征变量，公式如下：

下面我们使用tableone包来统计每个变量的标准均值误差SMD,数据来源是右心导管插入(right heart catheterization, RHC)数据，treat组是"RHC"，control是"No RHC"（变量 swang1）

library(tableone)
## PS matching
library(Matching)
## Weighted analysis
library(survey)
library(reshape2)
library(ggplot2)
## Right heart cath dataset
rhc <- read.csv("http://biostat.mc.vanderbilt.edu/wiki/pub/Main/DataSets/rhc.csv")
# 待统计的协变量：
vars <- c("age","sex","race","edu","income","ninsclas","cat1","das2d3pc","dnr1",
          "ca","surv2md1","aps1","scoma1","wtkilo1","temp1","meanbp1","resp1",
          "hrt1","pafi1","paco21","ph1","wblc1","hema1","sod1","pot1","crea1",
          "bili1","alb1","resp","card","neuro","gastr","renal","meta","hema",
          "seps","trauma","ortho","cardiohx","chfhx","dementhx","psychhx",
          "chrpulhx","renalhx","liverhx","gibledhx","malighx","immunhx",
          "transhx","amihx")
## Construct a table
tabUnmatched <- CreateTableOne(vars = vars, strata = "swang1", data = rhc, test = FALSE)
## Show table with SMD
print(tabUnmatched, smd = TRUE)

下图是统计结果，第一列是协变量，第二列是按照有无RHC（treat、contol组）各变量的统计值（mean和SD），最后一列是SMD，可以看出treat和control组的age和sex差异都较小（<10%），income较高（>10%）。

接下来计算通过logit回归计算每个样本的倾向性分数（Propensity Score, PS），也就是被分配为RHC的概率.

## Fit model
psModel <- glm(formula = swang1 ~ age + sex + race + edu + income + ninsclas +
                 cat1 + das2d3pc + dnr1 + ca + surv2md1 + aps1 + scoma1 +
                 wtkilo1 + temp1 + meanbp1 + resp1 + hrt1 + pafi1 +
                 paco21 + ph1 + wblc1 + hema1 + sod1 + pot1 + crea1 +
                 bili1 + alb1 + resp + card + neuro + gastr + renal +
                 meta + hema + seps + trauma + ortho + cardiohx + chfhx +
                 dementhx + psychhx + chrpulhx + renalhx + liverhx + gibledhx +
                 malighx + immunhx + transhx + amihx,
                 family  = binomial(link = "logit"),
                 data    = rhc)

## Predicted probability of being assigned to RHC
rhc$pRhc <- predict(psModel, type = "response")
## Predicted probability of being assigned to no RHC
rhc$pNoRhc <- 1 - rhc$pRhc
## Predicted probability of being assigned to the treatment actually assigned (either RHC or no RHC)
rhc$pAssign <- NA
rhc$pAssign[rhc$swang1 == 1]    <- rhc$pRhc[rhc$swang1   == 1]
rhc$pAssign[rhc$swang1 == 0] <- rhc$pNoRhc[rhc$swang1 == 0]
## Smaller of pRhc vs pNoRhc for matching weight
rhc$pMin <- pmin(rhc$pRhc, rhc$pNoRhc)

然后使用Matching包进行匹配一致性样本(1:1匹配)。

listMatch <- Match(Tr       = (rhc$swang1 == 1),      # Need to be in 0,1
                   ## logit of PS,i.e., log(PS/(1-PS)) as matching scale
                   X        = log(rhc$pRhc / rhc$pNoRhc),
                   ## 1:1 matching
                   M        = 1,
                   ## caliper = 0.2 * SD(logit(PS))
                   caliper  = 0.2,
                   replace  = FALSE,
                   ties     = TRUE,
                   version  = "fast")
# determining if balance exists in any unmatched dataset and in matched datasets
mb <- MatchBalance(psModel$formula, data=rhc, match.out=listMatch, nboots=50)

将匹配的样本提取出来：

rhcMatched <- rhc[unlist(listMatch[c("index.treated","index.control")]), ]

再看下现在匹配后的SMD，现在所有变量的SMD都小于10%了。

## Construct a table
tabMatched <- CreateTableOne(vars = vars, strata = "swang1", data = rhcMatched, test = FALSE)
## Show table with SMD
print(tabMatched, smd = TRUE)

然后给样本进行加权，使得各组中的倾向性评分基本一致，进而消除混杂因素，作为标准平衡数据参考。一般有两种加权方法：逆概率处理加权法（the inverse probability of treatment weighting，IPTW）和标准化死亡比加权法（the standardized mortality ratio weighting，SMRW）,本次我们是有IPTW的进阶版（PMID:26238958）:

## Matching weight
rhc$mw <- rhc$pMin / rhc$pAssign
# IPTW:
rhc$mw1=ifelse(rhc$swang1==1,1/(rhc$pRhc),1/(1-rhc$pRhc))

## Weighted data
rhcSvy <- svydesign(ids = ~ 1, data = rhc, weights = ~ mw)
## Construct a table (This is a bit slow.)
tabWeighted <- svyCreateTableOne(vars = vars, strata = "swang1", data = rhcSvy, test = FALSE)
## Show table with SMD
print(tabWeighted, smd = TRUE)

加权后变量组间差异（很小）：

进行作图比较 Unmatched、Mathced和Weighted结果：

library(data.table)
## Construct a data frame containing variable name and SMD from all methods
dataPlot <- data.table(variable  = rownames(ExtractSmd(tabUnmatched)),
                       Unmatched = ExtractSmd(tabUnmatched),
                       Matched   = ExtractSmd(tabMatched),
                       Weighted  = ExtractSmd(tabWeighted))
colnames(dataPlot) <- c("variable","Unmatched","Matched","Weighted")
## Create long-format data for ggplot2
dataPlotMelt <- melt(data          = dataPlot,
                     id.vars       = c("variable"),
                     variable.name = "Method",
                     value.name    = "SMD")

## Order variable names by magnitude of SMD
varNames <- as.character(dataPlot$variable)[order(dataPlot$Unmatched)]

## Order factor levels in the same order
dataPlotMelt$variable <- factor(dataPlotMelt$variable,
                                levels = varNames)

## Plot using ggplot2
ggplot(data = dataPlotMelt, mapping = aes(x = variable, y = SMD,
                                          group = Method, color = Method)) +
  geom_line() +
  geom_point() +
  geom_hline(yintercept = 0.1, color = "black", size = 0.1) +
  coord_flip() +
  theme_bw() + theme(legend.key = element_blank())

可以看出加权后的"标准数据"和我们PSM后的结果基本是一致的。最后还看看右心导管插不插对于生存是否有影响，使用ShowRegTable函数计算风险比（hazard ratio,HR）[95% CI)]和pvalue。

## Unmatched model (unadjsuted)
glmUnmatched <- glm(formula = (death == "Yes") ~ swang1,
                    family  = binomial(link = "logit"),
                    data    = rhc)
## Matched model
glmMatched <- glm(formula = (death == "Yes") ~ swang1,
                  family  = binomial(link = "logit"),
                  data    = rhcMatched)
## Weighted model
glmWeighted <- svyglm(formula = (death == "Yes") ~ swang1,
                      family  = binomial(link = "logit"),
                      design    = rhcSvy)

## Show results together
resTogether <- list(Unmatched = ShowRegTable(glmUnmatched, printToggle = FALSE),
                    Matched   = ShowRegTable(glmMatched, printToggle = FALSE),
                    Weighted  = ShowRegTable(glmWeighted, printToggle = FALSE))
print(resTogether, quote = FALSE)

。

参考：
https://cran.r-project.org/web/packages/tableone/vignettes/smd.html
https://www.mediecogroup.com/method_topic_article_detail/131/

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