Matching
What question does this help answer?
The same causal question that regression adjustment addresses, approached by design rather than by model. The appeal is that the balance achieved can be inspected and reported without reference to the outcome.
Design before outcome
The strongest feature of matching is procedural: the whole matching process happens without looking at outcomes, so it cannot be tuned toward a preferred result. That separation is worth preserving deliberately, and it is lost the moment the matching specification is revised after seeing what it produced.
How matches are chosen
- Exact matching on a few categorical variables: clean, and quickly infeasible as the variables multiply.
- Coarsened exact matching: exact matching on coarsened versions of the variables, a practical compromise.
- Propensity score matching: match on the estimated probability of exposure, which condenses many covariates into one number.
- Nearest neighbour with a caliper: refuse matches beyond a maximum distance, accepting that some subjects go unmatched.
- Ratios above one to one increase precision when controls are plentiful, with diminishing returns after about four.
What matching within a caliper looks like
Judge it by balance, not by the model
Report standardised mean differences for every covariate before and after matching, and examine overlap: a region where no comparison subjects exist is a region where no comparison can be made, and matching that discards those subjects has changed the population the estimate applies to. Say which population that is.
Analyse the matching you did
Matched case-control data need a conditional analysis, which for a binary exposure is conditional logistic regression on the matched sets. Matched cohort data need standard errors that account for the matched structure. And a matched case-control study has no closed-form sizing in Mallard's catalog: the discordant-set method is the right approach, named in prose rather than approximated with an unmatched formula.
What to watch out for
Matching only balances what was MEASURED, so it addresses no more confounding than adjustment does and should never be described as approximating randomization. Its real advantages are that balance can be checked before outcomes are looked at and that the analysis is transparent. Matching on a variable also removes it as a possible effect modifier, and matched sets must be respected in the analysis: a matched design analysed as if it were unmatched discards the pairing and, for case-control data, biases the estimate.
Clinical example
Question: Does a surgical approach reduce complications, in registry data? Analysis: Propensity score matching with a caliper, balance reported as standardised mean differences before and after, overlap examined, and the analysis accounting for the matched structure.
- Matching methods for causal inference: A review and a look forward (opens in a new tab) · Stat Sci · doi 10.1214/09-STS313
- A review of the application of propensity score methods yielded increasing use, advantages in specific settings, but not substantially different estimates compared with conventional multivariable methods (opens in a new tab) · J Clin Epidemiol · doi 10.1016/j.jclinepi.2005.07.004