Gene set analysis evaluates the collective impact of groups of genes on an outcome of interest, such as disease occurrence. By incorporating biological knowledge through predefined gene sets, this approach enhances the interpretability of results and improves statistical power compared with gene-wise analyses. In the context of time-to-event data, existing methods are limited and fail to account for potentially strong correlations within gene sets. Given the strong performance of the Generalized Berk-Jones (GBJ) statistic, which effectively incorporates correlation within the test statistic, we adapted this method to the time-to-event framework using a Cox model. We then compared its performance with established methods, including the Cauchy, Harmonic Mean, Wald test, global test, and global boost test. We further benchmarked these methods in two different real-world datasets: gliomas and breast cancer. Our proposed method, sGBJ, shows an overcontrol of Type I error, leading to reduced statistical power compared with other methods in numerical studies particularly when the number of genes is greater than or equal to the number of observations. The Wald test and global boost test generally exhibited the highest power, except in very high-correlation settings for the global boost test, while the Wald test could not adjust for confounders in current implementations.

In this work, we aimed at forecasting the number of SARS-CoV-2 hospitalized patients at 14 days to help anticipate the bed requirements of a large scale hospital using public data and electronic health records data. Previous attempts led to mitigated performance in this high-dimension setting; we introduce a novel approach to time series forecasting by providing an alternative to conventional methods to deal with high number of potential features of interest (409 predictors). We integrate Reservoir Computing (RC) with feature selection using a genetic algorithm (GA) to gather optimal non-linear combinations of inputs to improve prediction in sample-efficient context. We illustrate that the RC-GA combination exhibits excellent performance in forecasting SARS-CoV-2 hospitalizations. This approach outperformed the use of RC alone and other conventional methods: LSTM, Transformers, Elastic-Net, XGBoost. Notably, this work marks the pioneering use of RC (along with GA) in the realm of short and high-dimensional time series, positioning it as a competitive and innovative approach in comparison to standard methods.