A Semiparametric Model for Time-to-Event Data with Instrumental Variables

• Activity Number: 495
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Purushottan Laud*+ and Rodney Sparapani
• Companies: Medical College of Wisconsin and Medical College of Wisconsin
• Keywords: instrumental variables ; time-to-event data ; Bayesian inference ; semi-parametric model ; comparative effectiveness research ; non-ignorable selection

Abstract

In observational studies aimed at comparing medical treatments, patients are not randomized to treatment but their treatment choice is observed. Estimation of differences in treatment effects must therefore account for this treatment choice. One useful method for this purpose utilizes variables, called instrumental variables, that can predict treatment choice but, conditional on the treatment received, do not affect patient outcome.

Use of such instrumental variables in the context of time-to-event outcomes has proved challenging. We present a Bayesian jointly specified semi-parametric model in this case. For treatment choice, it employs a linear or a probit model according as the treatment is continuous or binary. For the time-to-event outcome, we use a Cox proportional hazards regression with a nonparametric prior for the baseline hazard function. The two models are linked by jointly modeling the two error terms. Implementation of full Bayesian inference is illustrated via an example.