FRANCESCO MARIANI

Dottore di ricerca

ciclo: XXXVII


supervisore: Stefania Gubbiotti
co-supervisore: Fulvio De Santis

Titolo della tesi: Random power and friends: hybrid Bayesian-frequentist approaches in clinical trials design

Expected values may fail in representing the distributions they summarize. This thesis investigates how this issue affects the evaluation of the design of an experiment, especially in clinical trials, when a hybrid Bayesian-frequentist approach is employed. We focus on the probability of success (PoS) of a test, which is originally (but not uniquely) defined as the expected value of the random power, ie the traditional power function of a test with respect to a design prior assigned to the parameter under scrutiny. We review and compare alternative definitions of PoS, we investigate the distributions they summarize (the random power and friends), and we provide a decision-theoretic look at the problem which leads to a unifying, uncontroversial quantification of success. We then go beyond clinical trials and hypothesis testing, and we study the Bayes risk as a synthesis of the random risk function in the point and set estimation classes of problems. Results, discussions and comparisons are supported by theoretical results and accompanied by biomedical examples and applications.

Produzione scientifica

11573/1733139 - 2025 - The distribution of the risk function for interval estimation
De Santis, Fulvio; Gubbiotti, Stefania; Mariani, Francesco - 04b Atto di convegno in volume
congresso: SIS 2024 - 52nd Scientific Meeting of the Italian Statistical Society (Bari)
libro: Methodological and Applied Statistics and Demography III - (978-3-031-64430-6)

11573/1734884 - 2025 - Recent results on the random probability of success of an experiment
De Santis, Fulvio; Gubbiotti, Stefania; Mariani, Francesco - 02a Capitolo o Articolo
libro: Methodological and Applied Statistics and Demography II. SIS 2024, Short Papers, Solicited Sessions - (978-3-031-64349-1)

11573/1692316 - 2024 - A dynamic power prior approach to non‐inferiority trials for normal means
Mariani, Francesco; De Santis, Fulvio; Gubbiotti, Stefania - 01a Articolo in rivista
rivista: PHARMACEUTICAL STATISTICS (Chichester, UK: Wiley.) pp. 242-256 - issn: 1539-1604 - wos: WOS:001101805100001 (2) - scopus: 2-s2.0-85176964822 (1)

11573/1719674 - 2024 - The distribution of power-related random variables (and their use in clinical trials)
Mariani, Francesco; De Santis, Fulvio; Gubbiotti, Stefania - 01a Articolo in rivista
rivista: STATISTICAL PAPERS (Heidelberg ; Berlin : Springer) pp. 5555-5574 - issn: 1613-9798 - wos: WOS:001315854100001 (0) - scopus: 2-s2.0-85204365936 (0)

11573/1722991 - 2024 - Toxicity Adaptive Lists Design: a practical design for Phase I drug combination trial in oncology
Russo, Massimiliano; Mariani, Francesco; Cleary, James M.; Shapiro, Geoffrey I.; Coté, Gregory M.; Trippa, Lorenzo - 01a Articolo in rivista
rivista: JCO PRECISION ONCOLOGY (Alexandria, VA : American Society of Clinical Oncology, [2017-]) pp. - - issn: 2473-4284 - wos: (0) - scopus: (0)

11573/1688601 - 2023 - On Bayesian power analysis in reliability
De Santis, Fulvio; Gubbiotti, Stefania; Mariani, Francesco - 04b Atto di convegno in volume
congresso: SEAS IN - Statistical Learning, Sustainability and Impact Evaluation (Ancona)
libro: Statistical Learning, Sustainability and Impact Evaluation, Book of the Short Papers, SIS 2023 - (9788891935618)

11573/1696303 - 2023 - On the Bayes risk induced by alternative design priors for sample size choice
De Santis, Fulvio; Gubbiotti, Stefania; Mariani, Francesco - 02a Capitolo o Articolo
libro: Optimization in Green Sustainability and Ecological Transition - (978-3-031-47686-0)

11573/1656190 - 2022 - A dynamic power prior approach to non-inferiority trials for normal means with unknown variance
Mariani, Francesco; De Santis, Fulvio; Gubbiotti, Stefania - 04b Atto di convegno in volume
congresso: SIS 2022 - 51esima Riunione Scientifica della Società Italiana di Statistica (Caserta)
libro: SIS 2022 Book of Short Papers - (9788891932310)

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