Bayesian Joint Modeling of Skew-Positive Longitudinal-Survival Data Using Birnbaum-Saunders Distribution

There has been a great interest in joint modeling of longitudinal and survival data in recent two decades. Joint models have less restrictive assumptions in multivariate modeling and could address various research questions. This has led to their wide applications in practice. However, earlier models had normality assumption on the distribution in longitudinal part that is usually violated in real data. Hence, recent research have focused on circumventing this issue. Using various skewed distributions has been proposed and applied in the literature. Nevertheless, the flexibility of the proposed methods is limited especially when the data are skew positive.

In this paper, we introduce the use of Birnbaum-Saunders (BS) distribution in joint modeling context. BS distribution is more flexible and could cover a wide range of skew, kurtotic or bimodal data.

We analyzed publicly available ddI/ddC data both with normal and BS distributions in Bayesian setting and compared their fit by Widely Applicable Information Criterion (WAIC). The joint BS model showed a better fit to the data.

We introduced and applied BS distribution in joint modeling of longitudinal-survival data. Using multi-parameter distributions such as BS in Bayesian setting could improve the fit of models without limitations that arise in transformation of data from original scale.