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Background  Propensity score methods have become a popular tool for reducing selection bias in making causal inference from observational studies in medical research. Propensity score matching, a key component of propensity score methods, normally matches units based on the distance between point estimates of the propensity scores. The problem with this technique is that it is difficult to establish a sensible criterion to evaluate the closeness of matched units without knowing estimation errors of the propensity scores.    Methods  The present study introduces  interval matching  using bootstrap confidence intervals for accommodating estimation errors of propensity scores. In interval matching, if the confidence interval of a unit in the treatment group overlaps with that of one or more units in the comparison group, they are considered as matched units.    Results  The procedure of interval matching is illustrated in an empirical example using a real-life dataset from the Nursing Home Compare, a national survey conducted by the Centers for Medicare and Medicaid Services. The empirical example provided promising evidence that interval matching reduced more selection bias than did commonly used matching methods including the rival method, caliper matching. Interval matching’s approach methodologically sounds more meaningful than its competing matching methods because interval matching develop a more “scientific” criterion for matching units using confidence intervals.    Conclusions  Interval matching is a promisingly better alternative tool for reducing selection bias in making causal inference from observational studies, especially useful in secondary data analysis on national databases such as the Centers for Medicare and Medicaid Services data.    Electronic supplementary material  The online version of this article (doi:10.1186/s12874-015-0049-3) contains supplementary material, which is available to authorized users.

Propensity score interval matching: using bootstrap confidence intervals for accommodating estimation errors of propensity scores