A Two-Latent-Class Model for Smoking Cessation Data with Informative Dropouts

Abstract

Non ignorable missing data is a common problem in longitudinal studies. Latent class models are attractive for simplifying the modeling of missing data when the data are subject to either a monotone or intermittent missing data pattern. In our study, we propose a new two-latent-class model for categorical data with informative dropouts, dividing the observed data into two latent classes; one class in which the outcomes are deterministic and a second one in which the outcomes can be modeled using logistic regression. In the model, the latent classes connect the longitudinal responses and the missingness process under the assumption of conditional independence. Parameters are estimated by the method of maximum likelihood estimation based on the above assumptions and the tetrachoric correlation between responses within the same subject. We compare the proposed method with the shared parameter model and the weighted GEE model using the areas under the ROC curves in the simulations and the application to the smoking cessation data set. The simulation results indicate that the proposed two-latent-class model performs well under different missing procedures. The application results show that our proposed method is better than the shared parameter model and the weighted GEE model.

Keywords:

• Area under ROC curve
• Informative dropout
• Latent class
• Tetrachoric correlation

Mathematics Subject Classification:

• Primary 62H30
• Secondary 62J12

Acknowledgment

This research was supported by National Institute on Drug Abuse R01 DA04174.

Notes

*Estimates are for the subjects who belong to η = 0.