| The proportional hazard Cox model is traditionally used in survival analysis to estimate the effect of several variables on the hazard rate of an event. Recently, neural networks were proposed to improve the flexibility of the Cox model. In this work, we focus on an extension of the Cox model, namely on a non-proportional relative risk model, where the neural network approximates a non-linear time-dependent risk function. We address the issue of the lack of time-varying variables in this model, and to this end, we design a deep neural network model capable of time-varying regression. The target application of our model is the waning of post-vaccination and post-infection immunity in COVID-19. This task setting is challenging due to the presence of multiple time-varying variables and different epidemic intensities at infection times. The advantage of our model is that it enables a fine-grained analysis of risks depending on the time since vaccination and/or infection, all approximated using a single non-linear function. A case study on a data set containing all COVID-19 cases in the Czech Republic until the end of 2021 has been performed. The vaccine effectiveness for different age groups, vaccine types, and the number of doses received was estimated using our model as a function of time. The results are in accordance with previous findings while allowing greater flexibility in the analysis due to a continuous representation of the waning function. |
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