### Abstract

In biomedical and public health research, both repeated measures of biomarkers Y as well as times T to key clinical events are often collected for a subject. The scientific question is how the distribution of the responses [T, Y\X] changes with covariates X. [T\X] may be the focus of the estimation where Y can be used as a surrogate for T. Alternatively, T may be the time to drop-out in a study in which [V\X] is the target for estimation. Also, the focus of a study might be on the effects of covariates X on both T and Y or on some underlying latent variable which is thought to be manifested in the observable outcomes. In this paper, we present a general model for the joint analysis of [T, V\X] and apply the model to estimate [T\X] and other related functionals by using the relevant information in both T and Y. We adopt a latent variable formulation like that of Fawcett and Thomas and use it to estimate several quantities of clinical relevance to determine the efficacy of a treatment in a clinical trial setting. We use a Markov chain Monte Carlo algorithm to estimate the model's parameters. We illustrate the methodology with an analysis of data from a clinical trial comparing risperidone with a placebo for the treatment of schizophrenia.

Original language | English (US) |
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Pages (from-to) | 375-387 |

Number of pages | 13 |

Journal | Journal of the Royal Statistical Society. Series C: Applied Statistics |

Volume | 50 |

Issue number | 3 |

Publication status | Published - 2001 |

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### Keywords

- Informative drop-out
- Latent variable
- Longitudinal data analysis
- Markov chain Monte Carlo methods
- Regression
- Surrogate end point
- Survival analysis

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability