Probiotic responder identification in cross-over trials for constipation using a Bayesian statistical model considering lags between intake and effect periods

Recent advances in microbiome research have led to the further development of microbial interventions, such as probiotics and prebiotics, which are potential treatments for constipation. However, the effects of probiotics vary from person to person; therefore, the effectiveness of probiotics needs to be verified for each individual. Individuals showing significant effects of the target probiotic are called responders. A statistical model for the evaluation of responders was proposed in a previous study. However, the previous model does not consider the lag between intake and effect periods of the probiotic. It is expected that the lag exists when probiotics are administered and when they are effective. In this study, we propose a Bayesian statistical model to estimate the probability that a subject is a responder, by considering the lag between intake and effect periods. In synthetic dataset experiments, the proposed model was found to outperform the base model, which did not factor in the lag. Further, we found that the proposed model could distinguish responders showing large uncertainty in terms of the lag between intake and effect periods. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This work was supported by JSPS/MEXT KAKENHI (Grant Number JP19J20117 to SH, JP20H00624, JP19H01152, and JP18KT0016 to MH). ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: The randomized controlled trial whose dataset was used in this study was conducted with the approval of the clinical trial ethics review committee of Chiyoda Paramedical Care Clinic. I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable. Yes