Extensions of the Penalized Spline Propensity Prediction Method of Imputation.

Abstract

Little and An (2004) proposed a penalized spline propensity prediction (PSPP) method of imputation of missing values that yields robust model-based inference under the missing at random assumption. The propensity score for a missing variable is estimated and a regression model is fit with the spline of the propensity score as a covariate. The predicted marginal mean of the missing variable is doubly robust (DR) under the misspecification of the imputation model. In the first part of the thesis, we study properties of a simplified version of the PSPP that does not center the regressors prior to including them in the prediction model. We then extend the PSPP to multivariate data so as to yield consistent estimates of both marginal and conditional means. The extended PSPP method is compared with the PSPP method and simple alternatives in a simulation study. For the second part of the thesis, we compare the PSPP method with several other DR estimators. The PSPP method uses a spline of propensity score to impute the missing values and the resulting estimates have a double robustness property. The DR property can also be achieved by modeling the relationship parametrically, such as the linear in the weight method and calibration method (Firth and Bennett, 1998; Robins, Rotnitzky and Zhao, 1994). We compare root mean square error (RMSE), width of confidence interval and non-coverage rate of these methods under different mean functions and propensity score functions. We also study the effects of sample size and misspecification of the propensity scores. The PSPP method yields estimates with smaller RMSE and width of confidence interval compared with other methods under most situations. It yields estimates with non-coverage rates close to the 5% nominal level. For the third part of the thesis, we extend the PSPP methods to the monotone missing data. We propose to impute the missing values based on a stepwise PSPP procedure. We illustrate the proposed method by applying it to an online weight loss study conducted by Kaiser Permanente. We finish the thesis with a short discussion and future work.