Propensity-score matching is a popular analytic method to estimate the effects of treatments when using observational data. Matching on the propensity score typically requires a pool of potential controls that is larger than the number of treated or exposed subjects. The most common approach to matching on the propensity score is matching without replacement, in which each control subject is matched to at most one treated subject. Failure to find a matched control for each treated subject can lead to "bias due to incomplete matching." To avoid this bias, it is important to identify a matched control subject for each treated subject. An alternative to matching without replacement is matching with replacement, in which control subjects are allowed to be matched to multiple treated subjects. A limitation to the use of matching with replacement is that variance estimation must account for both the matched nature of the sample and for some control subjects being included in multiple matched sets. While a variance estimator has been proposed for when outcomes are continuous, no such estimator has been proposed for use with time-to-event outcomes, which are common in medical and epidemiological research. We propose a variance estimator for the hazard ratio when matching with replacement. We conducted a series of Monte Carlo simulations to examine the performance of this estimator. We illustrate the utility of matching with replacement to estimate the effect of smoking cessation counseling on survival in smokers discharged from hospital with a heart attack.
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