A bi-endpoint expectation-maximisation algorithm for re-estimating sample size for the time-to-event endpoint under the blind condition

The expectation-maximisation (EM) algorithm can be used to adjust the sample size for the time-to-event endpoint without unblinding. Nevertheless, censoring or unreliable initial estimates may render inconsistent estimates by the EM algorithm. To address these limitations, we propose a bi-endpoint EM algorithm that incorporates the time-to-event endpoint and another endpoint, which can encompass various endpoint types and is not limited to efficacy indicators, during the EM iterations. Additionally, we suggest 2 approaches for choosing initial estimates. The application conditions are as follows: (i) at least one endpoint's initial estimate is reliable and (ii) the influence of this endpoint on the posterior distribution of the latent variable exceeds that of another endpoint.