JOINT MODELING OF TIME-TO-EVENT DATA AND MULTIPLE RATINGS OF A DISCRETE DIAGNOSTIC TEST WITHOUT A GOLD STANDARD by

Histologic tumor grade is a strong predictor of risk of recurrence in breast cancer. Nevertheless, tumor grade readings by pathologists are susceptible to intraand inter-observer variability due to its subject nature. Because of this limitation, histologic tumor grade is not included in the breast cancer stating system. Latent class models have been considered for analysis of such discrete diagnostic tests with regarding the underlying truth as a latent variable. However, the model parameters in latent class models are only locally identifiable, that is, any permutation on the categories of the underlying truth can lead to the same likelihood value. In many clinical practices, the underlying truth is known associated with the risk of a certain event in a trend. Here, we proposed a joint model with a Cox proportional hazards model for time-to-event data where the underlying truth is a latent predictor and a latent class model for multiple ratings of a discrete diagnostic test without a gold standard. With the known association between the underlying truth and the risk of an event in a trend, the proposed joint model not only fully identifies all model parameters but also provides valid assessment of the association between the diagnostic test result and the risk of an event. The modified EM algorithm was used for estimation with employing the survey-weighted Cox model in the M-step. To test whether the known trend imposed on model parameters can be assumed, we applied the Union-Intersection principle for the proposed joint model. The