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The use of Bayesian designs for trials in rarecancers: application to the LINES trial
Peter Dutton30 November 2015
th
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BackgroundPhase II trial of Linsitinib in patients with
relapsed and/or refractory Ewing's Sarcoma
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Ewing's SarcomaPrevalence: Two patients per million per yearPopulation: Childhood cancer, with average age 15 at diagnosisFive year overall survival rate: 60%
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Relapsed/refractory settingPrevalence: 0.6 patients per million per yearFive year overall survival rate: less than 10%
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LinsitinibOne of a number of IGF inhibitors to be tested in Ewing's patientsDual inhibitor blocking the IGF-1 and IGF-1R cell level pathwaysExtensive phase I testing performed in a general cancer settingFailed Phase II and III trials in a number of more common cancers
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Main ProblemVery rare setting (target recruitment is 30 patients per year)Known toxicity profile is not Ewing's sarcoma specific
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Trial design constraintsAim to recruit around 40 patients in 18 monthsSingle arm trialTwo co-primary endpoints; response and toxicityFrequent interim analyses
, , , = 0.2pR0 = 0.35pR
1 = 0.3pT0 = 0.1pT
1
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Possible DesignsFrequentist Bryant and Day two stage designBayesian posterior probability designBayesian posterior predictive designBayesian decision theory designHybrid designs
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Bryant and Day's two stage design (Bryant and Day 1995)This is an extension of Simon's two stage design to incorporate two endpoints.
Using alpha=0.1 and power=0.8 the designs are:
Design Sample size at analysis
Single stage 44
Bryant and Day (optimal) 20, 50
Bryant and Day (minmax) 24, 41
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Posterior probabilityProbabilistic summary of the posterior distribution
P(R > |data,prior)pR0
P(R < |data,prior)pR1
Bayesian approachPrior ∗ Data ∝ Posterior
Both endpoints are BinomialUses the conjugate Beta priorChosen a non-informative Beta prior, Beta(1,1)
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Bayesian sample size (Whitehead et al. 2008)Whitehead et al. proposed imposing the following restrictions on the posterior
probability of the trialEfficacy: P(R > |X = − 1) > ηpR
0 xn
Futility: P(R < |X = ) > ζpR1 xn
The smallest Bayesian sample size is the smallest n such that there exists which satisfies the above inequalities
xn
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Frequentist sample sizeMinimise n such that there exists
satisfying:xn
P(X ≥ |R = ) > powerxn pR1
P(X ≥ |R = ) < αxn pR0
Bayesian sample sizeMinimise n such that there exists
satisfying:xn
P(R < |X = ) > ζpR1 xn
P(R > |X = − 1) > ηpR0 xn
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Initial designAfter the first 10 patients and for every cohort of five:
If , then recommend stopping for toxicity.If , then recommend stopping for futility.
P(T > 0.3|prior,data) > 0.8P(R < 0.2|prior,data) > 0.8
After the first 20 patients and for every cohort of five:If , then recommend stopping for efficacy.P(R > 0.35|prior,data) > 0.9
After closing the trial with 40 patients:If , then recommend further research.P(R > 0.35|prior,data) > 0.5
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Initial design
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Initial design
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Initial design
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Modified designAfter the first 10 patients and for every cohort of five:
If , then recommend stopping for toxicity.If , then recommend stopping for futility.
P(T > 0.1|prior,data) > 0.95P(R < 0.35|prior,data) > 0.95
After the first 20 patients and for every cohort of five:If , then recommend stopping for efficacy.P(R > 0.2|prior,data) > 0.95
After closing the trial with 40 patients:If , then recommend further research.P(R > 0.2|prior,data) > 0.9
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Modified design
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Modified design
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Modified design
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Hybrid Posterior Probability ApproachProposal
Adjust the levels of the posterior probabilities ( and ) using a Lan-DeMets(1995) style alpha spending function
η ζ
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Motivation for alpha spending
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(t) = 1 − f(t, )ηRαR αR
(t) = 1 − f(t, )ζRαR αR
Hybrid Posterior Probability Approacht = =Current information
Total informationncurrent
nmaximum
O'Brien-Fleming (1979) alpha spending function: f(t, α) = 2 − 2Φ ( )α/2)t√
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Why is the trial BayesianNo prior information so no added valueAny future trial after LINES would include the data from LINES in the prior
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Potential further research1. No literature on frequentist Lan-DeMets for multiple endpoints2. Combining the endpoints in the Bayesian posterior probability based approach
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R packageAll the sample size programs are available from CRAN in the EurosarcBayes
package.
The research leading to these results has received funding from the EuropeanUnion Seventh Framework Programme (FP7/2007-2013) under grant agreement
number 278742 (Eurosarc).