A stochastic variant of the EM algorithm to fit mixed (discrete and continuous) longitudinal data with nonignorable missingness

Abstract

In longitudinal studies data are collected on the same set of units for more than one occasion. In medical studies it is very common to have mixed Poisson and continuous longitudinal data. In such studies, for different reasons, some intended measurements might not be available resulting in a missing data setting. When the probability of missingness is related to the missing values, the missingness mechanism is termed nonrandom. The stochastic expectation-maximization (SEM) algorithm and the parametric fractional imputation (PFI) method are developed to handle nonrandom missingness in mixed discrete and continuous longitudinal data assuming different covariance structures for the continuous outcome. The proposed techniques are evaluated using simulation studies. Also, the proposed techniques are applied to the interstitial cystitis data base (ICDB) data.

Keywords:

• Interstitial cystitis data
• longitudinal data
• maximum likelihood
• missing data
• parametric fractional imputation
• stochastic EM

Acknowledgments

The authors are very grateful the editor, the associate editor for their cooperation and support. The authors also are very grateful for anonymous reviewers for their helpful comments that improve the article significantly. The authors would like to thank Professor Kathleen Joy Propert at University of Pennsylvania, School of Medicine for providing guidelines about how to obtain the ICDB data. The ICDB data reported here were supplied by the National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK) Central Repositories. This manuscript does not necessarily reflect the opinions or views of the NIDDK Central Repositories, or the NIDDK.