Weighted estimating equations with nonignorably missing response data.

We propose weighted estimating equations for data with nonignorable nonresponse in order to reduce the bias that can occur with a complete case analysis. A survey concerning medical practice guidelines, malpractice litigation, and settlement provides the framework. The survey was sent to recipients in two waves: those who responded on the first or second wave are used to estimate a nonignorable nonresponse model, while the fraction of recipients who never responded is used to allow the percentage of missing data to change with each wave. We use the structure of the GEE of Liang and Zeger (1986, Biometrika 73, 13-22), adding weights equal to the inverse probability of being observed. We present simulations demonstrating the bias that can occur with an unweighted analysis and use the survey data to illustrate the methods.