Diagnostics for a two-stage joint survival model

Abstract

A two-stage joint survival model is used to analyze time to event outcomes that could be associated with biomakers that are repeatedly collected over time. A Two-stage joint survival model has limited model checking tools and is usually assessed using standard diagnostic tools for survival models. The diagnostic tools can be improved and implemented. Time-varying covariates in a two-stage joint survival model might contain outlying observations or subjects. In this study we used the variance shift outlier model (VSOM) to detect and down-weight outliers in the first stage of the two-stage joint survival model. This entails fitting a VSOM at the observation level and a VSOM at the subject level, and then fitting a combined VSOM for the identified outliers. The fitted values were then extracted from the combined VSOM which were then used as time-varying covariate in the extended Cox model. We illustrate this methodology on a dataset from a multi-center randomized clinical trial. A multi-center trial showed that a combined VSOM fits the data better than an extended Cox model. We noted that implementing a combined VSOM, when desired, has a better fit based on the fact that outliers are down-weighted.

Keywords:

• Down-weighting
• Extended Cox model
• Outlier detection
• Time-varying covariate
• Two-stage survival model
• Variance shift outlier model

Acknowledgement(s)

We thank the Training in HIV-related Non-communicable Disease Complications Program in Malawi (NIH Fogarty grant D43TW009609) and Fogarty International Center of the National Institutes for Health, under Award Number D43TW010559 for funding the project. We thank the Newton Fund, The Academy of Medical Sciences, UK for partial funding. We thank the Mayosi Research Group, Department of Medicine, University of Cape Town for providing the data for the study.

Disclosure statement

The content of this manuscript is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health and co-funders.

Additional information

Funding

This project has been supported by the Training in HIV-related Non-communicable Disease Complications Program in Malawi (NIH Fogarty grant D43TW009609) and Fogarty International Center of the National Institutes for Health, under Award Number D43TW010559. The project has also been partially funded by the Newton Fund of The Academy of Medical Sciences, UK.