Symmetric Pair Matching Design for Causal Inference • SPMD

Author: Robin Denz

Description

SPMD is a small R Package implementing the Symmetric Pair Matching Design (SPMD). Briefly, SPMD is a self-controlled method that allows estimation of the causal effect of a possible re-current binary exposure on a possible re-current event. It is similar in spirit to the famous self-controlled case series (SCCS) design in the sense that it is bi-directional, using both time before and after exposures as controls (irrespective of events). However, unlike the SCCS method, it not only automatically adjusts for time-invariant confounders, but also automatically adjusts for all time-effects, without requiring any assumptions on the functional form of these time effects.

It does so by creating pairs of individuals, in which each individual acts as a control for the other individual at their respective exposure time. It can be shown that under mild assumptions of multiplicative effects and no interactions, both individual-level effects and time effects cancel out perfectly. For more details, please consult the associated paper (Denz et al. 2026).

Installation

This package is not finished. It is still under active development, so breaking changes may occur at any time without warning. The developmental version may be installed from github using the remotes R-Package:

library(remotes)

remotes::install_github("RobinDenz1/SPMD")

Bug Reports and Feature Requests

If you encounter any bugs or have any specific feature requests, please file an Issue.

Examples

Suppose we have data that looks like this:

library(data.table)
library(SPMD)

set.seed(1234)
data <- sim_example_data(n=500)
head(data)
#> Key: <.id, start>
#>      .id start  stop          X      A      Y
#>    <int> <num> <num>      <num> <lgcl> <lgcl>
#> 1:     1     0   249 -1.2070657  FALSE  FALSE
#> 2:     1   249   289 -1.2070657   TRUE  FALSE
#> 3:     1   289  1000 -1.2070657  FALSE  FALSE
#> 4:     2     0   221  0.2774292  FALSE  FALSE
#> 5:     2   221   261  0.2774292   TRUE  FALSE
#> 6:     2   261   623  0.2774292  FALSE   TRUE

This is a simple simulated dataset. Here, A is the time-dependent exposure and Y is the outcome. The probability for both exposure and outcome are time-dependent, thus making time itself a sort of confounder. In addition, X is a time-fixed confounder. Suppose though, that X was unmeasured. If we want to estimate the causal effect of A on Y adjusting for both, we could use:

spmd <- sym_pair_matching(Surv(start, stop, Y) ~ A, data=data,
                          id=".id", risk_period=40, pairs="all",
                          estimator="moments", bootstrap=TRUE)
summary(spmd)
#> Symmetric Pair Matching using an estimating equation based estimator
#>   Formula: Surv(start, stop, Y) ~ A 
#>   Risk period: 40 
#> 
#>   No. individuals in data = 500 
#>   No. exposed individuals = 339 
#>   No. unique exposure times = 339 
#>   No. exposed individuals with event(s) = 339 
#>   49247 symmetric pairs were created
#>   96.57% of the included observation time was used
#> 
#> Final estimate: 2.457 
#> 95% CI: [1.596; 3.718]
#> P-Value: 0.001 
#> 
#> Estimated using: exp(0.5 * log(489/81))
#> Bootstrap CI based on 1000 bootstrap replications

The true effect is 2.5 (see ?sim_example_data), so the estimate is actually very close.

Citation

If you use this package, please cite the associated article:

Denz, Robin, Filippo Saatkamp, Katharina Meiszl and Nina Timmesfeld (2026). “The Symmetric Pair Matching Design: A Self-Controlled Method with Automatic Adjustment for Time Effects”. arXiv Preprint. doi: 10.48550/arXiv.2608.25979.

License

The contents of this repository are distributed under the GNU General Public License. You can find the full text of this License in this github repository. Alternatively, see http://www.gnu.org/licenses/.