A Review of Bayesian Perspectives on Sample Size Derivation for Confirmatory Trials.

Funder: Biometrika TrustSample size derivation is a crucial element of planning any confirmatory trial. The required sample size is typically derived based on constraints on the maximal acceptable Type I error rate and minimal desired power. Power depends on the unknown true effect and tends to be calculated either for the smallest relevant effect or a likely point alternative. The former might be problematic if the minimal relevant effect is close to the null, thus requiring an excessively large sample size, while the latter is dubious since it does not account for the a priori uncertainty about the likely alternative effect. A Bayesian perspective on sample size derivation for a frequentist trial can reconcile arguments about the relative a priori plausibility of alternative effects with ideas based on the relevance of effect sizes. Many suggestions as to how such "hybrid" approaches could be implemented in practice have been put forward. However, key quantities are often defined in subtly different ways in the literature. Starting from the traditional entirely frequentist approach to sample size derivation, we derive consistent definitions for the most commonly used hybrid quantities and highlight connections, before discussing and demonstrating their use in sample size derivation for clinical trials

Concert recording 2017-10-11

[Track 1]. Fantasy on Acteon / J.B. Arban -- [Track 2]. Fantasiestücke. I. Zart und mit Ausdruck [Track 3]. II. Lebhaft, leicht / Robert Schumann -- [Track 4]. El Moncayo / Jan Hadermann -- [Track 5]. Concerto for tuba. I. Allegro moderato / John Williams -- [Track 6]. Sonata in F minor. I. Triste [Track 7]. II. Allegro / G.F. Telemann -- [Track 8]. Suite no. 3 for solo cello, BWV 1009. Prelude / J.S. Bach -- [Track 9]. Fantasy for tuba / Malcolm Arnold -- [Tracks 10-12]. Sonata in F major / Benedetto Marcello

A review of Bayesian perspectives on sample size derivation for confirmatory trials

Sample size derivation is a crucial element of the planning phase of any confirmatory trial. A sample size is typically derived based on constraints on the maximal acceptable type I error rate and a minimal desired power. Here, power depends on the unknown true effect size. In practice, power is typically calculated either for the smallest relevant effect size or a likely point alternative. The former might be problematic if the minimal relevant effect is close to the null, thus requiring an excessively large sample size. The latter is dubious since it does not account for the a priori uncertainty about the likely alternative effect size. A Bayesian perspective on the sample size derivation for a frequentist trial naturally emerges as a way of reconciling arguments about the relative a priori plausibility of alternative effect sizes with ideas based on the relevance of effect sizes. Many suggestions as to how such `hybrid' approaches could be implemented in practice have been put forward in the literature. However, key quantities such as assurance, probability of success, or expected power are often defined in subtly different ways in the literature. Starting from the traditional and entirely frequentist approach to sample size derivation, we derive consistent definitions for the most commonly used `hybrid' quantities and highlight connections, before discussing and demonstrating their use in the context of sample size derivation for clinical trials

Concert recording 2015-04-29a

[Track 01]. Brook green suite. Prelude ; [Track 02]. Dance / Gustav Holst ; translated by Akira Yodo -- [Track 03]. Pastorale / Eric Ewazen -- [Track 04]. Glyder landscape. Twll du ; [Track 05]. Cantilever / Peter Smalley -- [Track 06]. The window opens toward the ocean / Jiro Censhu -- [Track 07]. Piano trio no. 1 in D minor, op. 49. Molto allegro agitato ; [Track 08]. Finale : Allegro assai appassionato / Felix Mendelssohn

Concert recording 2017-11-27

[Track 1]. Concert prelude / Derek Bourgeois -- [Track 2]. Tuba concerto / Edward Gregson -- [Track 3]. Cyberspace / Peter Graham -- [Track 4]. Concert piece no. 1 / Rodger Vaughan -- [Track 5]. Rhapsody for euphonium / Jerry Brubaker -- [Track 6]. Concerto, K. 191. I. Allegro / W.A. Mozart -- [Track 7]. The green hill / Bert Appermont -- [Track 8]. Suite / Vaclav Nelhybel -- [Track 9]. Brides of the waves / Herbert L. Clarke -- [Track 10]. Fantasy / Philip Sparke -- [Track 11]. Concerto for euphonium. I. Allegro moderato / Philip Wilby

Concert recording 2014-04-27

[Track 01]. Introduction and dance / J.E. Barat -- [Track 02]. Three miniatures. Allegro / Anthony Plog -- [Track 03]. Three miniatures. Adagio / Anthony Plog -- [Track 04]. Three miniatures. Allegro / Anthony Plog -- [Track 05]. Concerto. Introduction-allegro / Corrado Maria Saglietti -- [Track 06]. Concerto. Adagio / Corrado Maria Saglietti -- [Track 07]. Suite for unaccompanied tuba. March / Walter Hartley -- [Track 08]. Suite for unaccompanied tuba. Valse / Walter Hartley -- [Track 09]. Suite for unaccompanied tuba. Sarabande / Walter Hartley -- [Track 10]. Suite for unaccompanied tuba. Galop / Walter Hartley -- [Track 11]. Sonata for euphonium and piano childs play / Barbara York -- [Track 12]. Apres un Reve / Gabriel Faure ; translated by Mead -- [Track 13]. Concerto in one movement / Alexei Lebedev -- [Track 14]. Tuba suite. Prelude / Gordon Jacob -- [Track 15]. Tuba suite. Hornpipe / Gordon Jacob -- [Track 16]. Tuba suite. Sarabande / Gordon Jacob -- [Track 17]. Tuba suite. Bouree / Gordon Jacob -- [Track 18]. Tuba suite. Intrada ; Mazurka / Gordon Jacob -- [Track 19]. Fantasia di concerto / Eduardo Boccalari

Concert recording 2015-11-19

[Track 01]. Partita. Prelude ; [Track 02]. Capriccio ; [Track 03]. Sarabande ; [Track 04]. Bourree ; [Track 05]. Schezo / Arthur Butterworth -- [Track 06]. Introduction and dance / J.E. Barat -- [Track 07]. Concert pierce no. 1 / Joseph Turrin -- [Track 08]. Sonata. Allegro ; [Track 09]. Aria / Bruce Broughton -- [Track 10]. Variations on the Carnival of Venice / J.B. Arban -- [Track 11]. Concerto for bass tuba. Allegro moderato ; [Track 12]. Romanza / Ralph Vaughan Williams -- [Track 13]. Concerto, op. 114 / Derek Bourgeois -- [Track 14]. Milori blue. Simply ; [Track 15]. Presto / Jonathan Newman

Concert recording 2015-04-09a

[Track 01]. Five pieces in folk style. With humor ; [Track 02]. Not fast, but freely ; [Track 03]. Not too fast / Robert Schumann ; arr. Paul Droste -- [Track 04]. Suite no. 1 for tuba and piano, Effie. Effie joins the carnival ; [Track 05]. Effie goes folk dancing ; [Track 06]. Effie sings a lullaby / Alec Wilder -- [Track 07]. Sonata. Andante sostenuto / Trygve Madsen -- [Track 08]. Concerto. Non troppo allegro / Phillip Wilby -- [Track 09]. In bel di / Giaccomo Puccini -- [Track 10]. Ave Maria / Franz Schubert ; arr. Baadsvik -- [Track 11]. Concerto. Allegro moderato / John Williams -- [Track 12]. Fantaisie concertante / Jacques Castéréde