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Title: Bivariate mixed outcome-survival additive regression Authors:  Guillermo Briseno Sanchez - TU Dortmund University (Germany) [presenting]
Andreas Groll - Technical University Dortmund (Germany)
Abstract: A bivariate regression model is proposed where the response is given by a right-censored survival time and a binary outcome. The continuous survival time is modelled using the piecewise-exponential approach, i.e. a discrete-time survival model with a suitably augmented dataset is employed. The parameters of the bivariate distribution are modelled using additive predictors given by a linear combination of suitable representations of covariates $\mathbf{x}_{k,i}$ and regression coefficients $\boldsymbol{\beta}_k$, where $k = 1, \dots, K$ indexes the bivariate distribution parameters and $i = 1, \dots, n$ indexes the observations in the sample. The augmentation of the dataset required for a piecewise-exponential model results in a sequence of pseudo-observations of length $j = 1, \dots j(i)$ per individual $i$ in the sample. Therefore, the model for the survival marginal response consists of $n' > n$ rows, which makes the construction and evaluation of a likelihood function not possible. We derive the functions necessary to tackle the aforementioned issue. A joint bivariate density is then constructed using parametric copulae, allowing for the separate specification of the dependence structure and marginal distributions. Model fitting is carried out using trust-regions implemented as a custom extension of the R package GJRM.