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    Bayesian nonparametric bivariate survival regression for current status data
    (International Society for Bayesian Analysis, 2024-01-01)
    We consider Bayesian nonparametric inference for event time distributions based on current status data. We show that under dependent censoring conventional mixture priors, including the popular Dirichlet process mixture prior, lead to biologically uninterpretable results as they unnaturally skew the probability mass for the event times toward the extremes of the observed data. Simple assumptions on dependent censoring can fix the problem. We then extend the discussion to bivariate current status data with partial ordering of the two outcomes. In addition to dependent censoring, we also exploit some minimal known structure relating the two event times. We design a Markov chain Monte Carlo algorithm for posterior simulation. Applied to a recurrent infection study, the method provides novel insights into how symptoms-related hospital visits are affected by covariates.
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    Bayesian quantile regression models for heavy tailed bounded variables using the No-U-Turn sampler
    (Springer Science and Business Media Deutschland GmbH, 2025-07-01)
    When we are interested in knowing how covariates impact different levels of the response variable, quantile regression models can be very useful, with their practical use being benefited from the increasing of computational power. The use of bounded response variables is also very common when there are data containing percentages, rates, or proportions. In this work, with the generalized Gompertz distribution as the baseline distribution, we derive two new two-parameter distributions with bounded support, and new quantile parametric mixed regression models are proposed based on these distributions, which consider bounded response variables with heavy tails. Estimation of the parameters using the Bayesian approach is considered for both models, relying on the No-U-Turn sampler algorithm. The inferential methods can be implemented and then easily used for data analysis. Simulation studies with different quantiles (q=0.1, q=0.5 and q=0.9) and sample sizes (n=100, n=200, n=500, n=2000, n=5000) were conducted for 100 replicas of simulated data for each combination of settings, in the (0, 1) and [0, 1), showing the good performance of the recovery of parameters for the proposed inferential methods and models, which were compared to Beta Rectangular and Kumaraswamy regression models. Furthermore, a dataset on extreme poverty is analyzed using the proposed regression models with fixed and mixed effects. The quantile parametric models proposed in this work are an alternative and complementary modeling tool for the analysis of bounded data.
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