DAPSm

Distance Adjusted Propensity Score Matching R Package

Installing DAPSm

Installing and using DAPSm in Rstudio is straightforward. You will first need the devtools R package.

Install and load devtools

Simply write install.packages('devtools') in the console to install it, and load it using library(devtools).

Install and load DAPSm

library(devtools)

devtools::install_github("gpapadog/DAPSm")

DAPSm example

toyData2

toyData2 is a simulated data set where the locations of the observations are 200 power plant locations. The data set includes a binary treatment indicator Z, a continuous outcome Y, a spatial confounder U and other confounders X₁, X₂, X₃, X₄. The data set can be loaded using data('toyData2').

Analyzing a data set

There are three main ways to analyze a data set for which we have set of observed confounders, location information (such as longitude, latitude), a binary treatment, and propensity score estimates of the treatment on the observed covariates.

These ways include

• DAPSm with fixed weight
• DAPSm with fast search of the optimal weight
• DAPSm with extensive search of the optimal weight (recommended)

For each one of the three ways to choose the paramter $w$, we have a greedy algorithm, and an optimal algorithm available, which can be specified using the argument matching_algorithm equal to 'greedy' or 'optimal' accordingly. When the matching algorithm is set equal to optimal, the additional argument remove.unmatchables can be set equal to TRUE to allow the drop of treated units that do not have an appropriate match.

DAPSm with fixed weight, and greedy algorithm

If the investigator has a prior belief of the relative importance of propensity score similarity and distance in the matching, DAPSm could be fit with fixed w expressing these beliefs.

For example, in the toyData2 data set, one could fit DAPSm with w = 0.7 by performing

data('toyData2')
toyData2$prop.scores <- glm(Z ~ X1 + X2 + X3 + X4, family = binomial,
                            data = toyData2)$fitted.values

daps <- DAPSest(toyData2, out.col = 2, trt.col = 1, caliper = 0.3,
                weight = 0.7, coords.columns = c(4, 5),
                pairsRet = TRUE, cov.cols = 6:9, cutoff = 0.1,
                coord_dist = TRUE, caliper_type = 'DAPS',
                matching_algorithm = 'greedy')

DAPSm with fixed weight, and optimal algorithm

Optimal algorithm can often fail to return matches.

daps <- DAPSest(toyData2, out.col = 2, trt.col = 1, caliper = 0.5,
                weight = 0.7, coords.columns = c(4, 5),
                pairsRet = TRUE, cov.cols = 6:9, cutoff = 0.15,
                coord_dist = TRUE, caliper_type = 'DAPS',
                matching_algorithm = 'optimal',
                remove.unmatchables = TRUE)

DAPSm with fast search of the optimal weight (greedy algorithm)

The optimal weight is defined as the minimum w for which the absolute standardized difference of means (ASDM) of all covariates is less than a cutoff.

This includes a fast search of the optimal weight. The algorithm assumes a decreasing trend in ASDM for increasing w. It starts at 0.5 and checks balance of the covariates. If balance is acheived w is decreased to 0.25. If balance is not acheived, w is increased to 0.75. The algorithm continues this way, and w is moved by 1/2_{n + 1} at each step n.

The fast algorithm should only be used for large data sets for which an extensive search of the optimal w is not feasible.

Fit this algorithm by performing

daps <- DAPSest(toyData2, out.col = 2, trt.col = 1, caliper = 0.3,
                weight = 'optimal', coords.columns = c(4, 5),
                pairsRet = TRUE, cov.cols = 6:9, cutoff = 0.15,
                w_tol = 0.001, coord_dist = TRUE, caliper_type = 'DAPS',
                matching_algorithm = 'greedy')

DAPSm with extensive search for the optimal weight - Recommended

Instead, we can fit the algorithm for varying values of w and assess balance of covariates at every step. This can be performed by

bal <- CalcDAPSWeightBalance(toyData2, weights = seq(0, 1, length.out = 40),
                             cov.cols = 6:9, trt.col = 1,
                             coords.columns = c(4, 5), caliper = 0.3,
                             matching_algorithm = 'greedy')

Balance of the covariates can be assessed by checking the ASDM as a function of w using

PlotWeightBalance(bal$balance, weights = seq(0, 1, length.out = 40), cutoff = 0.15)

The function that can be used to choose the optimal weight and fit the model and return estimates is

DAPS <- DAPSchoiceModel(toyData2, trt.col = 1, balance = bal$balance,
                        cutoff = 0.15, pairs = bal$pairs,
                        weights = seq(0, 1, length.out = 40))

The weight chosen is equal to approximately 0.231.

Plot of matched pairs.

We can plot the matched pairs for different weights. The function CalcDAPSWeightBalance() already returned information of the matched pairs for 40 different values of w. We will plot the set of matched pairs for the optimal w chosen above, as well as a larger w.

MatchedDataMap(x = bal$full_pairs[[10]], trt_coords = c(3, 4),
               con_coords = c(7, 8))

Comparing the plots of matched pairs for the two choices of w we see that for larger w the matched pairs are further away from each other. This is expected since matching weigth given to distance is decreased for increasing w.

DAPSm with extensive search for the optimal weight with optimal matching

bal <- CalcDAPSWeightBalance(toyData2, weights = seq(0, 1, length.out = 40),
                             cov.cols = 6:9, trt.col = 1,
                             coords.columns = c(4, 5), caliper = 1,
                             matching_algorithm = 'optimal',
                             remove.unmatchables = TRUE)
                             
DAPS <- DAPSchoiceModel(toyData2, trt.col = 1, balance = bal$balance,
                        cutoff = 0.2, pairs = bal$pairs,
                        weights = seq(0, 1, length.out = 40))