Propensity score method: a non-parametric technique to reduce model dependence

Abstract

Propensity score analysis (PSA) is a powerful technique that it balances pretreatment covariates, making the causal effect inference from observational data as reliable as possible. The use of PSA in medical literature has increased exponentially in recent years, and the trend continue to rise. The article introduces rationales behind PSA, followed by illustrating how to perform PSA in R with MatchIt package. There are a variety of methods available for PS matching such as nearest neighbors, full matching, exact matching and genetic matching. The task can be easily done by simply assigning a string value to the method argument in the matchit() function. The generic summary() and plot() functions can be applied to an object of class matchit to check covariate balance after matching. Furthermore, there is a useful package PSAgraphics that contains several graphical functions to check covariate balance between treatment groups across strata. If covariate balance is not achieved, one can modify model specifications or use other techniques such as random forest and recursive partitioning to better represent the underlying structure between pretreatment covariates and treatment assignment. The process can be repeated until the desirable covariate balance is achieved.

Keywords: Propensity score; logistic regression; observational study.

Zhongheng Zhang, MMed.

Figure 1

Jittered plot showing matched and unmatched observations, as well as their distribution on propensity score values. It appears that many observations with high propensity scores in the treated group and many with low propensity scores in the control group are excluded.

Figure 2

Histograms showing the density of propensity score distribution in the treated and control groups before and after matching.

Figure 3

Quantile-quantile (QQ) plot compares the probability distributions of the treated and control groups on a given covariate by plotting their quantiles against each other. The results show that although the points are not located on the y=x line exactly after matching, it is much improved as compared to law data.

Figure 4

Histogram of a permutation distribution and reference statistic to assess balance across strata. The balance statistic locates at the left end of the mass of permutation distribution, indicating a good balance.

Figure 5

Side-by-side boxplots, 5 strata, for covariate x.cont produced by box.pdf.

Figure 6

Side-by-side barplots comparing proportion of cases in each category for variable x.cat.

Figure 7

Propensity score analysis assessment plot of outcome variable y, 5 strata, constructed using circ.psa.