Journal Article

FZJ-2026-00925

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png On the restricted maximum likelihood estimation in a two-arm randomized clinical trial for binary endpoints

Raseta, M. ; Bazarova, A. (Corresponding author)FZJ*

2024
[Verlag nicht ermittelbar] São Paulo

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Please use a persistent id in citations: doi:10.1214/24-BJPS613

Abstract: Optimal design of superiority, non-inferiority and equivalence two-arm clinicaltrials with binary endpoints remains a scientific topic of considerable theoretical and prac-tical interest. In their seminal paper Farrington and Manning (1990) demonstrate, uponsystematic simulation, the superiority of the design based on the conditional maximumlikelihood estimators (RMLE) to a number of viable alternatives. The approach based onthe RMLE is the most popular option among practitioners with more than 700 citationsup to date. They offer a closed form formula for the maximum likelihood estimator whichis claimed to be a unique root to a certain cubic polynomial in a specified parameter-dependent interval. We identify a number of instances where this formula is not well de-fined and thus not universally valid. More specifically still, for infinitely many parametercombinations, the formula suggested in Farrington and Manning (1990) involves divisionby 0 which is an ill-defined concept. In this manuscript we offer a full, mathematicallyrigorous theory of RMLE in this set-up, which has not been known to have been publishedpreviously. We thereby correct and extend the current results on the topic and provide aformula, which is indeed (universally) valid for all possible parameter combinations.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs) and Research Groups (POF4-511) (POF4-511)
2. Helmholtz AI Consultant Team FB Information (E54.303.11) (E54.303.11)

Appears in the scientific report 2024; 2025

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Database coverage:
; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Essential Science Indicators ; IF < 5 ; JCR ; National-Konsortium ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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