Propensity score adjustment with several followups

Abstract Propensity score weighting adjustment is commonly used to handle unit nonresponse. When the response mechanism is nonignorable in the sense that the response probability depends directly on the study variable, a followup sample is commonly used to obtain an unbiased estimator using the framework of two-phase sampling, where the follow-up sample is assumed to respond completely. In practice, the followup sample is also subject to missingness. We consider propensity score weighting adjustment for nonignorable nonresponse when there are several follow-ups and the final follow-up sample is also subject to missingness. We propose two methods, one using calibration weighting and the other using a conditional likelihood using a so-called reverse conditional probability. Both methods provides consistent estimates under correct specification of the response model. A limited simulation study is used to compare the estimators. The proposed methods are applied to the real data example in a Korean household survey of employment.