An Implementation of Automated Individual Matching for Observational Studies

Summary

Objectives: Individual matching is frequently used in observational studies. Its main purpose lies in efficiency of study conduct and parameter estimation. Ideally, an individually matched index subject differs from the reference subject(s) only by the factor(s) of interest. Matching is used to select comparable subgroups on which further data analysis can then concentrate. Finding optimal subsets is then a closed problem, which may include a lot of guesswork. It is a task that begs an algorithmic solution that can be obtained automatically.

Methods: The problem can be formalized as a minimization of a global loss function that summarizes the deviation from perfect agreement over different variables. Through the representation by a network formed by a bipartite graph of index and reference subjects, one can obtain a solution by finding a minimum cost flow in a certain network. We have implemented a Web-based application using the efficient CS2 algorithm.

Results: Variations of the individual matching procedures that have been implemented comprise 1:N matching and matching with a variable number of controls. The user can upload own data, view the proposed result in a list and finally download the matching plan. Representation of quality of individual matches as background colors allows rapid checks for overall matching accuracy.

Conclusions: The computer-assisted variation reduces the human interaction to the tuning of a few parameters, rather than individual decisions on forming separate matches. This not only saves a lot of work but also simplifies communicating the matching process. The program addresses a general class of matching problems. The use of this tool for special cases of matching, as caliper matching or exact category matching, is highlighted.

Keywords

Matching - observational studies - case-control studies - caliper matching - categorial matching

• References

• 1 Rosenbaum PR. Optimal Matching for Observational Studies. J Amer Statist Assoc 1989; 84 (408) 1024-32.
• 2 Goldberg AV. An Efficient Implementation of a Scaling Minimum-Cost Flow Algorithm. Journal of Algorithms 1997; 22: 1-29.
• 3 Rothman KJ, Greenland S. Modern Epidemiology. 1998
• 4 D’Agostino Jr RB. Tutorial in Biostatistics: Propensity score methods for bias reduction in the comparison of a treatment to a non-randomized control group. Statist Med 1998; 17: 2265-81.
• 5 Stürmer T, Brenner H. Degree of Matching and Gain in Power and Efficiency in Case-Control Studies. Epidemiology 2001; 12: 101-8.
• 6 Rubin DB. Matching methods that are equal percent bias reducing: some examples. Biometrics 1976; 32: 109-20.