JDS Journal of Data Science 1683-8602 1680-743X 1680-743X School of Statistics, Renmin University of China JDS1008 10.6339/21-JDS1008 Statistical Data Science Spline Pattern-Mixture Models for Missing Data YangYeyeya@umich.edu1∗ LittleRoderick J.A.2 Center for Biologics Evaluation and Research, FDA, Silver Spring, MD, USA Department of Biostatistics, University of Michigan, Ann Arbor, MI, USA Corresponding author. Email: yeya@umich.edu. 20211022021 1917595 Supplementary Material

Please refer to the Supplementary Material document for:

1. A detailed description of the Gibbs sampling algorithm for the penalized spline prediction.

2. Results from all six simulation scenarios, including estimates from n=100 and n=400 and where λA=λT and λA≠λT .

3. R code and workspace for the simulations.

 112020 12021 2021 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2021 Open access article under the CC BY license.

We consider a continuous outcome subject to nonresponse and a fully observed covariate. We propose a spline proxy pattern-mixture model (S-PPMA), an extension of the proxy pattern-mixture model (PPMA) (Andridge and Little, 2011), to estimate the mean of the outcome under varying assumptions about nonresponse. S-PPMA improves the robustness of PPMA, which assumes bivariate normality between the outcome and the covariate, by modeling the relationship via a spline. Simulations indicate that S-PPMA outperforms PPMA when the data deviate from normality and are missing not at random, with minor losses of efficiency when the data are normal.

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