Balanced Risk Set Matching

A new form of matching–optimal balanced risk set matching–is applied in an observational study of a treatment, cystoscopy and hydrodistention, given in response to the symptoms of the chronic, nonlethal disease interstitial cystitis. When a patient receives the treatment at time t, that patient is matched to another patient with a similar history of symptoms up to time t who has not received the treatment up to time t; this is risk set matching. By using a penalty function in integer programming in a new way, we force the marginal distributions of symptoms to be balanced in the matched treated and control groups. Among all balanced matchings, we pick the one that is optimal in the sense of minimizing the multivariate pretreatment covariate distance within matched pairs. Under a simple model for the treatment assignment mechanism, we study the sensitivity of the findings to hidden biases. In particular, we show that a simple, conventional sensitivity analysis is appropriate with risk set matching when the time to treatment follows a proportional hazards model with a time-dependent unobserved covariate.