Anytime-Valid A/B Testing of Counting Processes

Michael Lindon, Nathan Kallus
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:3529-3537, 2025.

Abstract

Motivated by monitoring the arrival of incoming adverse events such as customer support calls or crash events from users exposed to an experimental product change, we consider sequential hypothesis testing of continuous-time counting processes. Specifically, we provide a multivariate confidence process on the cumulative rates $(\Lambda^A_t, \Lambda^B_t)$ giving an anytime-valid coverage guarantee $\mathbb{P}[(\Lambda^A_t, \Lambda^B_t) \in C^\alpha_t \, \forall t >0] \geq 1-\alpha$. This provides simultaneous confidence process on $\Lambda^A_t$, $\Lambda^B_t$ and their difference $\Lambda^B_t-\Lambda^A_t$, allowing each arm of the experiment and the difference between them to be safely monitored throughout the experiment. We extend our results by constructing a closed-form $e$-process for testing the equality of rates with a time-uniform Type-I error guarantee at a nominal $\alpha$. We characterize the asymptotic growth rate of the proposed $e$-process under the alternative and show that it has power 1 when the average rates of the two process differ in the limit.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-lindon25a, title = {Anytime-Valid A/B Testing of Counting Processes}, author = {Lindon, Michael and Kallus, Nathan}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {3529--3537}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/lindon25a/lindon25a.pdf}, url = {https://proceedings.mlr.press/v258/lindon25a.html}, abstract = {Motivated by monitoring the arrival of incoming adverse events such as customer support calls or crash events from users exposed to an experimental product change, we consider sequential hypothesis testing of continuous-time counting processes. Specifically, we provide a multivariate confidence process on the cumulative rates $(\Lambda^A_t, \Lambda^B_t)$ giving an anytime-valid coverage guarantee $\mathbb{P}[(\Lambda^A_t, \Lambda^B_t) \in C^\alpha_t \, \forall t >0] \geq 1-\alpha$. This provides simultaneous confidence process on $\Lambda^A_t$, $\Lambda^B_t$ and their difference $\Lambda^B_t-\Lambda^A_t$, allowing each arm of the experiment and the difference between them to be safely monitored throughout the experiment. We extend our results by constructing a closed-form $e$-process for testing the equality of rates with a time-uniform Type-I error guarantee at a nominal $\alpha$. We characterize the asymptotic growth rate of the proposed $e$-process under the alternative and show that it has power 1 when the average rates of the two process differ in the limit.} }
Endnote
%0 Conference Paper %T Anytime-Valid A/B Testing of Counting Processes %A Michael Lindon %A Nathan Kallus %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-lindon25a %I PMLR %P 3529--3537 %U https://proceedings.mlr.press/v258/lindon25a.html %V 258 %X Motivated by monitoring the arrival of incoming adverse events such as customer support calls or crash events from users exposed to an experimental product change, we consider sequential hypothesis testing of continuous-time counting processes. Specifically, we provide a multivariate confidence process on the cumulative rates $(\Lambda^A_t, \Lambda^B_t)$ giving an anytime-valid coverage guarantee $\mathbb{P}[(\Lambda^A_t, \Lambda^B_t) \in C^\alpha_t \, \forall t >0] \geq 1-\alpha$. This provides simultaneous confidence process on $\Lambda^A_t$, $\Lambda^B_t$ and their difference $\Lambda^B_t-\Lambda^A_t$, allowing each arm of the experiment and the difference between them to be safely monitored throughout the experiment. We extend our results by constructing a closed-form $e$-process for testing the equality of rates with a time-uniform Type-I error guarantee at a nominal $\alpha$. We characterize the asymptotic growth rate of the proposed $e$-process under the alternative and show that it has power 1 when the average rates of the two process differ in the limit.
APA
Lindon, M. & Kallus, N.. (2025). Anytime-Valid A/B Testing of Counting Processes. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:3529-3537 Available from https://proceedings.mlr.press/v258/lindon25a.html.

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