American Statistical Association New York City Metropolitan Area Chapter Memorial Sloan-Kettering Cancer Center Biostatistics Seminar

We consider estimating the mean of a variable Y subject to missing values, with the aid of a set of fully-observed predictors X, assuming the data are missing at random. We compare a number of estimators that combine information from a model relating Y to X (the prediction model) and a model relating the propensity to respond to X (the propensity model). These methods all have a double robustness (DR) property, namely, they yield a consistent estimate if either the mean structure of the prediction model or the propensity model is correctly specified. One method is to include the inverse of the propensity score as a linear term in the imputation model (Firth and Bennett, 1998; Scharfstein, Rotnitzky and Robins, 1999; Bang and Robins, 2005). Another method is to calibrate the predictions from a parametric model by adding the mean of the weighted residuals (Robins, Rotnitzky and Zhao, 1994; Scharfstein, Rotnitzky and Robins, 1999). The Penalized Spline Propensity Prediction (PSPP) method achieves double robustness by including the propensity score in the prediction model nonparametrically (Little and An, 2004; Zhang and Little, 2005). All these methods are consistent and have good asymptotic properties, but here we study their efficiency and confidence coverage over a range of sample sizes. Simulations tend to favor the PSPP method, suggesting in particular that calibration does not improve the inference when the relationship between Y and the estimated propensity is modeled using a flexible spline model. Extensions to inferences other than the mean are also discussed.