Joint analysis of longitudinal and survival AIDS data with a spatial fraction of long‐term survivors: A Bayesian approach

A typical survival analysis with time-dependent covariates usually does not take into account the possible random fluctuations or the contamination by measurement errors of the variables. Ignoring these sources of randomness may cause bias in the estimates of the model parameters. One possible way for overcoming that limitation is to consider a longitudinal model for the time-varying covariates jointly with a survival model for the time to the event of interest, thereby taking advantage of the complementary information flowing between these two-model outcomes. We employ here a Bayesian hierarchical approach to jointly model spatial-clustered survival data with a fraction of long-term survivors along with the repeated measurements of CD4+ T lymphocyte counts for a random sample of 500 HIV/AIDS individuals collected in all the 27 states of Brazil during the period 2002-2006. The proposed Bayesian joint model comprises two parts: on the one hand, a flexible model using Penalized Splines to better capture the nonlinear behavior of the different CD4 profiles over time; on the other hand, a spatial cure model to cope with the set of long-term survivor individuals. Our findings show that joint models considering this set of patients were the ones with the best performance comparatively to the more traditional survival approach. Moreover, the use of spatial frailties allowed us to map the heterogeneity in the disease risk among the Brazilian states.

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