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---
title: "A Practical Introduction to Propensity Score Analysis using R"
author: "Ehsan Karim [http://ehsank.com/]"
date: "30 Sept 2020: SPPH, UBC"
output:
beamer_presentation:
keep_md: yes
highlight: tango
ioslides_presentation:
widescreen: yes
smaller: yes
keep_md: yes
highlight: tango
css: slides.css
slidy_presentation:
widescreen: yes
smaller: yes
keep_md: yes
highlight: tango
css: slides.css
classoption: "aspectratio=169"
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = FALSE)
options("kableExtra.html.bsTable" = TRUE)
require(knitr)
require(kableExtra)
require(tableone)
require(MatchIt)
require(Matching)
require(optmatch)
require(Publish)
require(SASxport)
require(DiagrammeR)
require(DiagrammeRsvg)
require(rsvg)
library(magrittr)
library(svglite)
library(png)
require(cobalt)
```
\newcommand{\indep}{\perp \!\!\! \perp}
## About this event
- [TI Methods Speaker Series page](https://www.ti.ubc.ca/2020/08/06/sep-30-ti-methods-speaker-series-a-practical-introduction-to-propensity-score-analysis-using-r/): Therapeutics Initiative
- Dr. Carole Lunny
- [SARGC page](https://ssc.ca/en/students-and-recent-graduates-committee-0): Students and Recent Graduates Committee (SARGC) coordinate activities for the Statistical Society of Canada (SSC)'s student and recent graduate members
- Md. Erfanul Hoque
- Janie Coulombe
## Assumptions of the webinar
- *Target audience*:
- Familiar with regression
- Familiar with R
- will explain some necessary package / functions / arguments
- have no/minimal idea about propensity score
- *Topics covered*
- Not covering any new research
- Not covering statistical theory
- implementation being the goal here
- Not attempting to reach any clinical conclusion
## Format of the webinar
- *Presentation format*
- Rather informal
- 1 hr vs. 2 hr
- Q/A at
- 45 min and
- at the end
- *Webinar Materials*
- All reproducible codes provided
- [ehsanx.github.io/SARGC-TIMethods/](https://ehsanx.github.io/SARGC-TIMethods/)
- Necessary references cited in respective slides
## Outline
- [1] Data and Regression
- (Diagnostics)
- [2] Exact matching
- (motivation)
- [3] Propensity score matching
- (4 steps)
- [4] Propensity score Reviews in different disease areas
- (brief)
## [1] Right Heart Catheterization (RHC) Dataset
The [dataset](http://biostat.mc.vanderbilt.edu/wiki/pub/Main/DataSets/rhc.html) that we will use today is from Connors et al. (1996).
```{r out.width = "40%", fig.show = "hold", cache=TRUE}
include_graphics("images/citeRHC.png")
include_graphics("images/rhcvars.png")
```
### Notations
- Outcome `Death` ($Y$)
- Death at any time up to 180 Days
- Treatment `swang1` ($A$: Swan-Ganz catheter)
- Whether or not a patient received a RHC
- [Covariate list](http://biostat.mc.vanderbilt.edu/wiki/pub/Main/DataSets/Crhc.html): $L$ (`age`, `sex`, `race` , $\ldots$)
- Analysis strategy: matching RHC patients with non-RHC patients
## [1] Right Heart Catheterization (RHC) Dataset
- `RHC` is helpful in guiding therapy decision
- Helps determine the pressures within the heart
- Popularly beleived that `RHC` is benefitial
- Conducting RCT is hard (ethical reasons)
- Benefit of `RHC` was not shown earlier (1996)
- SUPPORT data has 2 phases
- phase 1: prospective observational study
- phase 2: cluster RCT
- Data in this study is combined
```{r out.width = "20%", cache=TRUE}
include_graphics("images/RHC.png")
```
## [1] Load data
```{r load, cache=TRUE, echo = TRUE}
# Load the cleaned up data.
# Reproducible codes:
# https://ehsanx.github.io/SARGC-TIMethods/
analytic.data <- readRDS("data/RHC.Rds")
# Data size and number of variables
dim(analytic.data)
# variable names
names(analytic.data)
```
## [1] Inspecting data: Crude
```{r tab0, cache=TRUE, echo = TRUE}
require(tableone)
# 2 x 2 table
tab0 <- CreateTableOne(vars = "RHC",
data = analytic.data,
strata = "Death")
print(tab0, showAllLevels = TRUE)
```
## [1] Inspecting data: Some baseline variables
```{r tab1, cache=TRUE, echo = TRUE}
baselinevars <- c("age","sex", "race")
# Table 1
tab1 <- CreateTableOne(vars = baselinevars,
data = analytic.data,
strata = "Death", includeNA = TRUE,
test = TRUE, smd = FALSE)
print(tab1, showAllLevels = FALSE, smd = FALSE)
```
## [1] Crude regression
```{r reg1, cache=TRUE, echo = TRUE}
# adjust the exposure variable (primary interest)
fit0 <- glm(I(Death=="Yes")~RHC,
family=binomial, data = analytic.data)
require(Publish)
publish(fit0)
```
## [1] Adjusted regression
```{r reg2, cache=TRUE, echo = TRUE}
# adjust the exposure variable + demographics
fit1 <- glm(I(Death=="Yes")~RHC + age + sex + race,
family=binomial, data = analytic.data)
publish(fit1)
```
## [1] Why adjust?
### Continuous outcome ($Y$)
- treated group $A=1$ (`RHC`)
- control group $A=0$ (`no RHC`)
Treatment effect = $E[Y|A=1]$ vs. $E[Y|A=0]$
- Would only work if 2 groups are comparable / exchangeable / ignorable treatment assignment
- Randomization with enough sample size is one
### Binary outcome ($Y$)
Treatment effect = $prob[Y = 1|A=1]$ vs. $prob[Y=1|A=0]$
## [1] Why adjust?
In absence of randomization,
$E[Y|A=1] - E[Y|A=0]$
includes
- Treatment effect
- Systematic differences in 2 groups (‘confounding’)
- Doctors may prescribe tx more to frail and older age patients.
- In here, $L$ = age is a confounder.
## [1] Why adjust?
In absence of randomization, if age is a known issue
### Causal effect for young
- $E[Y|A=1, L =$ `younger age`$]$ - $E[Y|A=0, L =$ `younger age`$]$
### Causal effect for old
- $E[Y|A=1, L =$ `older age`$]$ - $E[Y|A=0, L =$ `older age`$]$
Conditional exchangeability; only works if $L$ is measured
## [1] Why adjust?
```{r graph1ttt, echo=FALSE, cache=TRUE, eval = TRUE}
g2 <- grViz("
digraph causal {
# Nodes
node [shape = box]
# node [shape = circle]
A [label = 'RHC']
Y [label = 'Death']
L1 [label = 'Sex']
L2 [label = 'Race']
L3 [label = 'Age']
L4 [label = 'Heart rate']
# Edges
edge [color = black,
arrowhead = vee]
rankdir = LR
A -> Y
{L1 L2 L3 L4} -> {A Y}
# Graph
graph [overlap = true, fontsize = 10]
}")
g2 %>% export_svg %>% charToRaw %>% rsvg %>% png::writePNG("images/dag1.png")
```
```{r graph1xttt, echo=FALSE, out.width = '50%'}
knitr::include_graphics("images/dag1.png")
```
This was not a completely randomized data; some observational data was combined.
## [1] Adjusted regression (v2)
```{r reg3, cache=TRUE, echo = TRUE}
# adjust the exposure variable + adjustment variables
baselinevars <- c("age","sex", "race","Disease.category",
"DNR.status", "APACHE.III.score",
"Pr.2mo.survival","No.of.comorbidity",
"DASI.2wk.prior","Temperature",
"Heart.rate", "Blood.pressure",
"Respiratory.rate", "WBC.count",
"PaO2.by.FIO2","PaCO2","pH",
"Creatinine","Albumin","GComa.Score")
out.formula <- as.formula(paste("I(Death=='Yes')", "~ RHC +",
paste(baselinevars,
collapse = "+")))
out.formula
```
## [1] Adjusted regression (v2)
```{r reg3b, cache=TRUE, echo = TRUE}
fit2 <- glm(out.formula,
family=binomial, data = analytic.data)
publish(fit2)
```
## [1] Adjusted regression (v2)
```{r reg3bc1, out.width = "50%", cache=TRUE, echo = TRUE}
plot(fit2, which =1)
```
- curvilinear trends?
- logistic regression IS curvilinear by nature
## [1] Adjusted regression (v2)
```{r reg3bc3, out.width = "50%", cache=TRUE, echo = TRUE}
plot(fit2, which =3)
```
- red line is approximately horizontal?
- points have approximately equal spread around the red line?
- more about detecting heteroscedasticity?
## [1] Adjusted regression (v2)
```{r reg3bc3jr, out.width = "50%", cache=TRUE, echo = TRUE}
plot(fit2, which =4)
```
- Cook's D estimates the influence of data points
## [2] Alternate to Regression
How sure are you about the model-specification?
- Interaction?
- Polynomial?
- Potential solution?
- Exact Matching
## [2] Exact Matching: 2 variables
```{r combin, cache=TRUE, echo = TRUE}
var.comb <- do.call('paste0',
analytic.data[, c('race', 'sex')])
length(table(var.comb))
table(var.comb)
table(analytic.data$RHC,var.comb)
```
## [2] Exact Matching: 2 variables
```{r match0, cache=TRUE, echo = TRUE}
require(MatchIt)
# exact match by sex and race
m.out = matchit (RHC=="RHC" ~ sex + race,
data = analytic.data,
method = "exact")
m.out
```
## [2] Exact Matching: 3 variables
```{r combin2, cache=TRUE, echo = TRUE}
var.comb <- do.call('paste0',
analytic.data[, c('race', 'sex', 'age')])
length(table(var.comb))
table(analytic.data$RHC,var.comb=="otherMale[80, Inf)")
table(analytic.data$RHC,var.comb=="otherFemale[80, Inf)")
```
## [2] Exact Matching: 3 variables
```{r match1, cache=TRUE, echo = TRUE}
# exact match by age, sex and race
m.out = matchit (RHC=="RHC" ~ age + sex + race,
data = analytic.data,
method = "exact")
m.out
```
## [2] Exact Matching: 3 variables
```{r match1a, cache=TRUE, echo = TRUE}
matched.data <- match.data(m.out)
dim(matched.data)
nrow(analytic.data)-nrow(matched.data) # subjects deleted
# Not taking into account of matched sets
fit1m <- glm(I(Death=="Yes")~RHC,
family=binomial, data = matched.data)
publish(fit1m)
```
## [2] Exact Matching: many categorical variables
```{r match2, cache=TRUE, echo = TRUE}
m.out = matchit (RHC=="RHC" ~ age + sex + race +
Disease.category + DNR.status,
data = analytic.data,
method = "exact")
m.out
```
## [2] Exact Matching: many categorical variables
```{r match2a, cache=TRUE, echo = TRUE}
matched.data <- match.data(m.out)
dim(matched.data)
fit2m <- glm(I(Death=="Yes")~RHC,
family=binomial, data = matched.data)
publish(fit2m)
```
## [2] Exact Matching: including a continuous variable
```{r match3, cache=TRUE, echo = TRUE}
m.out = matchit (RHC=="RHC" ~ age + sex + race +
Disease.category + DNR.status+
Heart.rate, # continuous
data = analytic.data,
method = "exact")
m.out
```
## [2] Exact Matching: including more continuous variables
```{r match4, cache=TRUE, echo = TRUE}
m.out = matchit (RHC=="RHC" ~ age + sex + race +
Disease.category + DNR.status+
Heart.rate + Blood.pressure +
Temperature,
data = analytic.data,
method = "exact")
m.out
```
## [2] Exact Matching: including more continuous variables
```{r match4a, cache=TRUE, echo = TRUE}
matched.data <- match.data(m.out)
dim(matched.data)
nrow(analytic.data)-nrow(matched.data) # subjects deleted
fit3m <- glm(I(Death=="Yes")~RHC,
family=binomial, data = matched.data)
publish(fit3m)
```
## [3] Propensity Score
### Defining Propensity score (PS)
- Conditional Probability of getting treatment, given the observed covariates
- Prob(treatment: `A` = 1 | baseline or pre-treatment covariates: `L`)
- Prob(`RHC` = treated/RHC group | `age`, `sex`, `race`, etc.)
- f(L) = Prob(A=1|L)
```{r ps, cache=TRUE, echo = TRUE}
baselinevars
```
## [3] Propensity Score
```{r out.width = "50%", cache=TRUE}
include_graphics("images/citePS.png")
```
### Theoretical result
**Rosenbaum, Rubin (1983)** showed:
- For potential outcomes $(Y^0, Y^1)$, if you have sufficient observed covariate list $L$ to reduce confounding (`strong ignoribility'): $A$ being treatment assignment here:
- i.e., if $(Y^0, Y^1) \indep A | L$ (Note that is this NOT $Y \indep A | L$)
- then
- $(Y^0, Y^1) \indep A | PS$ and
- $A \indep L | PS$
## [3] Propensity Score
### Assumptions
- no unmeasured confounding
- positivity ($ 0 < PS < 1 $)
- well-defined treatment
- sufficient overlap
- model-specification
## [3] Propensity Score
```{r out.width = "50%", fig.show = "hold", cache=TRUE}
include_graphics("images/psvar.png")
include_graphics("images/psdesign.png")
```
- Observed covariates are used to fix design
- Which covariates should be selected:
- known to be a confounder (causes of `Death` and `RHC`)
- known to be a cause of the outcome (risk factors of `Death`)
- avoid known instruments or noise variables: **SE suffers**
- mediating factors should be avoided (total effect = goal)
- Stepwise (p-value or criterion based) not recommended
- depending on sample size, different values can get selected
- may select variables highly associated with $A$
- Don't look at the outcome (`Death`) in your data to select covariates
## [3] Propensity Score
Many ways to use propensity scores (PS) in the analysis
- **PS matching** [our focus today: intuitive!]
- PS weighting
- PS stratification
- PS used as a covariate
## [3] Propensity Score Matching
```{r out.width = "50%", cache=TRUE}
include_graphics("images/citeaustin.png")
```
### Propensity score matching has 4 steps
- Stage 1: exposure modelling: $PS = Prob(A=1|L)$
- Stage 2: Match by $PS$
- Stage 2: Assess balance and overlap ($PS$ and $L$)
- Stage 4: outcome modelling: $Prob(Y=1|A=1)$
## [3] Propensity Score Matching
```{r out.width = "50%", cache=TRUE}
include_graphics("images/citeaustin0.png")
```
- Assessment of Balance in the whole data
- balance = similarity of the covariate distributions
- $d$ or $SMD > 0.1$ can be considered as imbalance
```{r out.width = "20%", cache=TRUE}
include_graphics("images/d1.png")
```
```{r out.width = "40%", cache=TRUE}
include_graphics("images/d2.png")
```
```{r ps1g, cache=TRUE, echo = TRUE}
tab1e <- CreateTableOne(vars = baselinevars,
data = analytic.data, strata = "RHC",
includeNA = TRUE,
test = FALSE, smd = TRUE)
```
## [3] Propensity Score Matching
```{r ps1gres, cache=TRUE, echo = TRUE}
print(tab1e, smd = TRUE)
```
## [3] Propensity Score Matching
### Step 1: PS estimation
Specify the propensity score model to estimate propensity scores, and fit the model
```{r ps1, cache=TRUE, echo = TRUE}
ps.formula <- as.formula(paste("I(RHC == 'RHC')", "~",
paste(baselinevars, collapse = "+")))
ps.formula
```
- Coef of PS model fit is not of concern
- Model can be rich: to the extent that prediction is better
- But look for multi-collinearity issues
- SE too high?
## [3] Propensity score Matching
While PS has balancing property, PS is unknown and needs to be estimated:
```{r ps1vd, cache=TRUE, echo = TRUE}
# fit logistic regression to estimate propensity scores
PS.fit <- glm(ps.formula,family="binomial",
data=analytic.data)
# extract estimated propensity scores from the fit
analytic.data$PS <- predict(PS.fit,
newdata = analytic.data, type="response")
```
- Other machine learning alternatives are possible to use instead of logistic regression.
- tree based methods have better ability to detect non-linearity / non-additivity (model-specification aspect)
- shrinkage methods - lasso / elastic net may better deal with multi-collinearity
- ensemble learners / super learners were successfully used
- shallow/deep learning!
## [3] Propensity score Matching
- Don't loose sight that better *balance* is the ultimate goal for propensity score
- Prediction of $A$ is just a means to that end (as true PS is unknown).
- May attract variables highly associated with $A$
```{r out.width = "50%", fig.show = "hold", cache=TRUE}
include_graphics("images/citesuper0.png")
include_graphics("images/citesuper.png")
include_graphics("images/psalt.png")
include_graphics("images/psml.png")
```
## [3] Propensity score Matching
### Step 1
```{r ps2, cache=TRUE, echo = TRUE}
# summarize propensity scores
summary(analytic.data$PS)
# summarize propensity scores by exposure group
tapply(analytic.data$PS, analytic.data$RHC, summary)
```
## [3] Propensity Score Matching
### Step 2: PS matching
```{r ps5, cache=TRUE, echo = TRUE}
logitPS <- -log(1/analytic.data$PS - 1)
# logit of the propensity score
.2*sd(logitPS) # suggested in the literature
0.1*sd(logitPS) # we are using this
# choosing too strict PS has unintended consequences
```
```{r out.width = "50%", fig.show = "hold", cache=TRUE}
include_graphics("images/citecapiler.png")
include_graphics("images/pscal.png")
```
## [3] Propensity Score Matching
### Step 2
Match using estimates propensity scores
- nearest-neighbor (NN) matching
- without replacement
- with caliper = .1*SD of logit of propensity score
- with 1:1 ratio (pair-matching)
```{r out.width = "30%", cache=TRUE}
# Image from Wiki
include_graphics("images/nn.png")
```
## [3] Propensity Score Matching
### Step 2
Match using estimates propensity scores
```{r ps6, cache=TRUE, echo = TRUE}
set.seed(123)
match.obj <- matchit(ps.formula, data = analytic.data,
distance = analytic.data$PS,
method = "nearest", replace=FALSE,
caliper = .1*sd(logitPS), ratio = 1)
# see matchit function options here
# https://www.rdocumentation.org/packages/MatchIt/versions/1.0-1/topics/matchit
analytic.data$PS <- match.obj$distance
summary(match.obj$distance)
```
## [3] Propensity Score Matching
### Step 2
```{r ps7b, cache=TRUE, echo = TRUE}
match.obj
```
## [3] Propensity Score Matching
### Step 2
Step 1 and 2 can be done together by specifying `distance`
```{r ps7, cache=TRUE, echo = TRUE}
match.obj <- matchit(ps.formula, data = analytic.data,
distance = 'logit',
method = "nearest",
replace=FALSE,
caliper = .1*sd(logitPS),
ratio = 1)
analytic.data$PS <- match.obj$distance
summary(match.obj$distance)
```
## [3] Propensity Score Matching
### Step 2: Taking a closer look at the matches
```{r ps3dfg, cache=TRUE, echo = TRUE}
# Ref: https://lists.gking.harvard.edu/pipermail/matchit/2013-October/000559.html
matches <- as.data.frame(match.obj$match.matrix)
colnames(matches)<-c("matched_unit")
matches$matched_unit<-as.numeric(
as.character(matches$matched_unit))
matches$treated_unit<-as.numeric(rownames(matches))
matches.only<-matches[!is.na(matches$matched_unit),]
head(matches.only)
```
## [3] Propensity Score Matching
### Step 2: Taking a closer look at the matches (1st pair)
```{r ps3cvf, cache=TRUE, echo = TRUE}
analytic.data[analytic.data$ID %in%
as.numeric(matches.only[1,]),]
```
## [3] Propensity Score Matching
### Step 2: Taking a closer look at the matches (2nd pair)
```{r ps3cvf2, cache=TRUE, echo = TRUE}
analytic.data[analytic.data$ID %in%
as.numeric(matches.only[2,]),]
```
## [3] Propensity score Matching
### Step 3: Assessing balance and overlap
**Balance is more important than prediction**!
- Criteria to assess success of step 2: PS estimation
- better balance
- better overlap [no extrapolation!]
- PS = 0 or PS = 1 needs close inspection
```{r ps3, out.width = "30%", cache=TRUE, echo = TRUE}
boxplot(PS ~ RHC=='RHC', data = analytic.data,
lwd = 2, ylab = 'PS')
stripchart(PS ~ RHC=='RHC', vertical = TRUE,
data = analytic.data, method = "jitter",
add = TRUE, pch = 20, col = 'blue')
```
## [3] Propensity Score Matching
### Step 3
Vizualization
```{r ps8, out.width = "50%", cache=TRUE, echo = TRUE}
plot(match.obj, type = "jitter")
```
## [3] Propensity Score Matching
### Step 3
Vizualization for assessing overlap issues
```{r ps9, out.width = "50%", cache=TRUE, echo = TRUE}
plot(match.obj, type = "hist")
```
## [3] Propensity Score Matching
### Step 3
Assessment of Balance: Better than regression diagnostics!
```{r ps10, cache=TRUE, echo = TRUE}
matched.data <- match.data(match.obj)
tab1m <- CreateTableOne(vars = baselinevars,
data = matched.data, strata = "RHC",
includeNA = TRUE,
test = TRUE, smd = TRUE)
```
Compare the similarity of baseline characteristics between treated and untreated subjects in a the propensity score-matched sample.
- In this case, we will compare SMD < 0.1 or not.
- In some literature, other generous values (0.25) are proposed.
```{r out.width = "50%", fig.show = "hold", cache=TRUE}
include_graphics("images/citeaustin0.png")
include_graphics("images/smdcut.png")
```
## [3] Propensity Score Matching
### Step 3
```{r ps10a, cache=TRUE, echo = TRUE}
print(tab1m, showAllLevels = FALSE, smd = TRUE, test = FALSE)
```
## [3] Propensity Score Matching
### Step 3
Possible to get p-values to check balance: but strongly discouraged
- P-value based balance assessment can be influenced by sample size
```{r out.width = "50%", fig.show = "hold", cache=TRUE}
include_graphics("images/citeaustin.png")
```
```{r ps10ax, cache=TRUE, echo = TRUE}
print(tab1m, showAllLevels = FALSE, smd = FALSE, test = TRUE)
```
## [3] Propensity Score Matching
### Step 3
Assessment of balance in the matched data
```{r ps11, cache=TRUE, echo = TRUE}
smd.res <- ExtractSmd(tab1m)
t(round(smd.res,2))
```
## [3] Propensity Score Matching
### Step 3: Variance ratio
- Variance ratios $\sim$ 1 means:
- equal variances in groups
- group balance
- could vary from 1/2 to 2
- other cut-points are suggested as well (0.8 to 1.2)
```{r out.width = "50%", fig.show = "hold", cache=TRUE}
include_graphics("images/psbal.png")
include_graphics("images/vr.png")
```
## [3] Propensity Score Matching
### Step 3: Variance ratio
```{r vr, cache=TRUE, echo = TRUE}
require(cobalt)
baltab.res <- bal.tab(x = match.obj, data = analytic.data,
treat = analytic.data$RHC,
disp.v.ratio = TRUE)
baltab.res$Balance$V.Ratio.Adj
```
## [3] Propensity Score Matching
### Step 4: Outcome modelling
- Some flexibility in choosing outcome model
- considered independent of exposure modelling
- some propose double robust approach
- adjusting imbalanced covariates only?
Estimate the effect of treatment on outcomes using propensity score-matched sample
```{r ps12, cache=TRUE, echo = TRUE}
fit3 <- glm(I(Death=="Yes")~RHC,
family=binomial, data = matched.data)
publish(fit3)
```
## [3] Propensity Score Matching
### Step 4: Outcome modelling
```{r ps12b, cache=TRUE, echo = TRUE}
out.formula
fit3b <- glm(out.formula,
family=binomial, data = matched.data)
publish(fit3b)
```
## [3] Propensity Score Matching
### Step 4: Other cosiderations for outcome model
The above analysis do not take matched pair into consideration while regressing. Literature proposes different strategies:
- do not control for pairs / clusters
- use `glm` as is
- control for pairs / clusters
- use `cluster` option or GEE or conditional logistic
- Bootstrap for matched pairfor WOR
- may not be appropriate for WR
```{r out.width = "50%", cache=TRUE}
include_graphics("images/boot.png")
```
## [3] Propensity Score Matching
### Step 4
- The example compared `RHC` (a treated group; target) vs `No RHC` (untreated).
- Thc corresponding treatment effect estimate is known as
- Average Treatment Effects on the Treated (ATT)
- Other estimates from PS analysis are possible that compared the whole population
- what if everyone treated vs. what if nobody was treated (ATE)
## [3] Propensity Score Matching
### Other matching algorithms
- Optimal
- genetic matching
- CEM
- variable ratio NN
## [3] Propensity Score Matching
- MatchIt
- Matching
Other useful packages
- cobalt
- twang
Outdated package
- nonrandom
## [4] Discipline-specific PS Systematic Reviews
- Propensity score matching most popular
- Cardiovascular / Infective endocarditis / Intensive care
- Critical care / anesthesiology / Sepsis / Psychology
- Cancer / Multiple sclerosis
- Not meta-analysis; but reviews of usage of PS methods in different disciplines
```{r out.width = "30%", fig.show = "hold", cache=TRUE}
include_graphics("images/r1.png")
include_graphics("images/r2.png")
include_graphics("images/r3.png")
include_graphics("images/r4.png")
include_graphics("images/r5.png")
include_graphics("images/r6.png")
include_graphics("images/r7.png")
include_graphics("images/r8.png")
include_graphics("images/r9.png")
```
## [4] Discipline-specific PS Systematic Reviews
### Reporting Guideline
- Be specific about population of interest
- ATT vs. ATE
- exclusion criteria
- Be specific about exposure
- no multiple version of treatment
- no interference
- comparator
- Report clearly about missing data
- how handled
- Why PS matching (or other approach) was selected?
- Software
## [4] Discipline-specific PS Systematic Reviews
### Reporting Guideline
- How variables selected
- Any important variables not measured
- proxy
- Model selection
- interaction or polynomials
- logistic vs. machine learning
- Overlap vs. balance
- numeric and visual
```{r out.width = "30%", cache=TRUE}
include_graphics("images/books.png")
```
## [4] Discipline-specific PS Systematic Reviews
### Reporting Guideline
- Reduction % of the matched data: main objection against this method!
- Residual imbalance
- refit PS model
- Subgroup analysis
- Refit within each group for matching
- Sensitivity analysis
- unmeasured confounder / hdPS
- any positivity issue? Deleting extremes has consequences!
- ad-hoc methods: truncation / trimming: bias-variance trade-off