Fast and optimal algorithm for case-control matching using registry data: application on the antibiotics use of...

In case-control studies most algorithms allow the controls to be sampled several times, which is not always optimal. If many controls are available and adjustment for several covariates is necessary, matching without replacement might increase statistical efficiency. Comparing similar units when having observational data is of utter importance, since confounding and selection bias is present. The aim was twofold, firstly to create a method that accommodates the option that a control is not resampled, and second, to display several scenarios that identify changes of Odds Ratios (ORs) while increasing the balance of the matched sample.

The algorithm was derived in an iterative way starting from the pre-processing steps to derive the data until its application in a study to investigate the risk of antibiotics on colorectal cancer in the INTEGO registry (Flanders, Belgium). Different scenarios were developed to investigate the fluctuation of ORs using the combination of exact and varying variables with or without replacement of controls. To achieve balance in the population, we introduced the Comorbidity Index (CI) variable, which is the sum of chronic diseases as a means to have comparable units for drawing valid associations.

This algorithm is fast and optimal. We simulated data and demonstrated that the run-time of matching even with millions of patients is minimal. Optimal, since the closest controls is always captured (using the appropriate ordering and by creating some auxiliary variables), and in the scenario that a case has only one control, we assure that this control will be matched to this case, thus maximizing the cases to be used in the analysis. In total, 72 different scenarios were displayed indicating the fluctuation of ORs, and revealing patterns, especially a drop when balancing the population.

We created an optimal and computationally efficient algorithm to derive a matched case-control sample with and without replacement of controls. The code and the functions are publicly available as an open source in an R package. Finally, we emphasize the importance of displaying several scenarios and assess the difference of ORs while using an index to balance population in observational data.