  Survival analysis or time-to-event analysis aims to model and predict the
time it takes for an event of interest to happen in a population or an
individual. In the medical context this event might be the time of dying,
metastasis, recurrence of cancer, etc. Recently, the use of neural networks
that are specifically designed for survival analysis has become more popular
and an attractive alternative to more traditional methods. In this paper, we
take advantage of the inherent properties of neural networks to federate the
process of training of these models. This is crucial in the medical domain
since data is scarce and collaboration of multiple health centers is essential
to make a conclusive decision about the properties of a treatment or a disease.
To ensure the privacy of the datasets, it is common to utilize differential
privacy on top of federated learning. Differential privacy acts by introducing
random noise to different stages of training, thus making it harder for an
adversary to extract details about the data. However, in the realistic setting
of small medical datasets and only a few data centers, this noise makes it
harder for the models to converge. To address this problem, we propose
DPFed-post which adds a post-processing stage to the private federated learning
scheme. This extra step helps to regulate the magnitude of the noisy average
parameter update and easier convergence of the model. For our experiments, we
choose 3 real-world datasets in the realistic setting when each health center
has only a few hundred records, and we show that DPFed-post successfully
increases the performance of the models by an average of up to $17\%$ compared
to the standard differentially private federated learning scheme.
