23º SINAPE - Simpósio Nacional de Probabilidade e Estatística

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Joint models for longitudinal and time-to-event data are a powerful tool that take
into account these two data types simultaneously into a single model, allowing to
infer about the dependence and association between the longitudinal biomarker (e.g.
prostate-specific antigen, PSA) and time-to-event, for a better assessment of the effect
of a treatment. These models are useful for studies in the field of health that aim at
understanding the disease (e.g. prostate cancer), considering its development over
time and the amount of time until the patient reaches the absorbent state (e.g. death).
The most used joint models, that result from a combination of a longitudinal model
and a survival analysis, do not allow to monitor the link between the longitudi-
nal biomarker and the transitions between the multiple states of the disease until it
reaches the absorbent state. In order to better understand this link between the lon-
gitudinal biomarker and the transitions between the multiple states, in this paper we
use a joint model that combines the longitudinal model and the multi-state Markov
model. An application is presented where a data set from prostate cancer is consid-
ered. The parameters of the model are estimated by maximum likelihood, which is
performed in two stages: (i) in the first stage the fixed and random effects are esti-
mated based on the longitudinal biomarker PSA; and (ii) in the second stage those
estimates are used to link the longitudinal model with the multi-state Markov model,
allowing the measurement of the impact for the risk of death, considering demo-
graphic covariables, in each transition between the states of the disease along time.
In this way, the model is able to assess the biomarker’s trajectory, to define the risks
of transitions between health states, and to quantify the impact of the PS


Joint model; Longitudinal model; Muti-state Markov model; Prostate cancer


Análise de Sobrevivência


Felipe Emanoel Barletta Mendes, Omar Cléo Neves Pereira , Paulo Canas Rodrigues, Isolde Terezinha Previdelli