Description: the new statistical inference framework "Safe Anytime-Valid Inference" (SAVI) based on so-called e-values promises to improve efficiency of statistical inferences. That is, in contrast to traditional p-values, e-values allow multiple analyses of accumulating data without adjusting for multiplicity while still maintaining Type I error rate control. While the theoretical properties of SAVI methods are to some extent understood through the proliferation of research articles in mathematical statistics in recent years, it is unclear whether these properties translate into actual benefits for clinical researchers. The aim of this thesis is to perform a neutral comparison of e-values with traditional methods for sequential analysis in clinical trials, such as group sequential designs and alpha-spending functions. To this end, traditional and SAVI methods will be summarized and applied to case studies from clinical trials. Based on these case studies, a neutral simulation study will be designed to better understand how the properties of SAVI methods compare to traditional methods under realistic conditions.

References:
Grünwald, P., de Heide, R., Koolen, W. (2024). Safe testing, Journal of the Royal Statistical Society Series B: Statistical Methodology, 86(5):1091-1128. https://doi.org/10.1093/jrsssb/qkae011
Ly, A., Boehm, U., Grünwald, P., Ramdas, A., van Ravenzwaaij, D. (2024). Safe Anytime-Valid Inference: Practical Maximally Flexible Sampling Designs for Experiments Based on e-Values. https://doi.org/10.31234/osf.io/h5vae
Ramdas, A., Grünwald, P., Vovk, V., Shafer, G. (2023). Game-Theoretic Statistics and Safe Anytime-Valid Inference. Statistical Science. 38(4):576-60. https://doi.org/10.1214/23-STS894
Turner, R., Ly, A. (2022). safestats: Safe Anytime-Valid Inference. https://CRAN.R-project.org/package=safestats
Lakens, D., Pahlke, F., Wassmer, G. (2021). Group Sequential Designs: A Tutorial. https://doi.org/10.31234/osf.io/x4azm
Pallmann, P., Bedding, A.W., Choodari-Oskooei, B. et al. (2018). Adaptive designs in clinical trials: why use them, and how to run and report them. BMC Medicine. 16:29. https://doi.org/10.1186/s12916-018-1017-7
Wassmer, G., Brannath, W. (2016). Group sequential and confirmatory adaptive designs in clinical trials. https://doi.org/10.1007/978-3-319-32562-0
Wassmer, G., Pahlke, F. (2024). rpact: Confirmatory Adaptive Clinical Trial Design and Analysis. https://CRAN.R-project.org/package=rpact.
Morris, T.P., White, I.R., Crowther M.J. (2019). Using simulation studies to evaluate statistical methods. Statistics in Medicine. 38(11):2074-2102. https://doi.org/10.1002/sim.8086
Siepe, B.S., Bartoš, F., Morris, T.P., Boulesteix, A.-L., Heck, D.W., Pawel, S. (2024). Simulation Studies for Methodological Research in Psychology: A Standardized Template for Planning, Preregistration, and Reporting. Psychological Methods. https://doi.org/10.1037/met0000695 https://doi.org/10.31234/osf.io/ufgy6 https://www.overleaf.com/latex/templates/ademp-prereg-simulation-study-template/dkhtxjtmpbfj