Designing a Bayesian randomised controlled trial in osteosarcoma. How to incorporate historical data?

Transcription

1 Designing a Bayesian randomised controlled trial in osteosarcoma: How to incorporate historical data? C. Brard, L.V Hampson, M-C Le Deley, G. Le Teuff SCT - Montreal, May 18th 2016 Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 1

2 Setting: Osteosarcoma Osteosarcoma A rare disease (estimated incidence: /million/year in Europe) Persistent dismal prognosis of patients with metastases or poor histological response to neoadjuvant chemotherapy Need of new treatments MTP-PE: Already evaluated in osteosarcoma in INT-0133 randomised trial by the Children Oncology Group (COG) Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 1

3 COG trial: a phase III trial Factorial design: chemotherapy +/- ifosfamide, +/- MTP-PE Trial analysed separately: localised and metastatic osteosarcoma Results pretty homogeneous between both strata, Localised osteosarcoma (Meyers et al. 2008): Overall survival: HR = 0.71, p = 0.03 Event-free survival: HR = 0.80, p = 0.08 Metastatic osteosarcoma (Chou et al. 2009): Overall survival: HR = 0.72, p = 0.27 Event-free survival: HR = 0.72, p = 0.23 No clear consensus of the key opinion leaders because of - a possible interaction ifosfamide* MTP-PE (Meyers et al. 2005) - a separate analysis of both strata No market authorisation in France French authorities requested additional data Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 2

4 New trial in France: MEPACT trial Randomised phase II trial in high risk osteosarcoma (metastatic disease or poor histological response): Endpoint: event-free survival (EFS) Comparison: one-sided alpha = 10% 50 2 patients feasible over 3 years With this sample size (51 events), the protocol specifies a 80%-power for a relative treatment effect (HR) of 0.54 Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 3

5 New trial: MEPACT Motivation for using historical data Rare disease: need to increase the power Individual data on control arm from the French OS2006 trial: Including similar patients in control arm of MEPACT trial (similar backbone chemo., same centres, same disease conditions) Published MTP-PE relative treatment effect (HR) from COG trial (INT-0133) Bayesian approach in addition to the standard frequentist approach Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 4

6 Objectives To define how to incorporate these historical data To evaluate the impact of the weight allocated to historical data To compare frequentist and Bayesian approaches Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 5

7 Historical data Available information Number of events Estimated parameters OS2006 trial (high risk pts) 73 β 0H = (sd = 0.143) Individual data Weibull σ H = (sd = 0.109) COG trial 330 β 1H = ln(0.786) (sd = 0.110) MTP-PE treatment effect β 1H : Meta-analysis of both strata, localised and metastatic osteosarcoma Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 6

8 Bayesian Weibull model Posterior distribution using power 1 and mixture 2 prior π(β 0, σ, β 1 D, D 01, D 02, α 0, ω 1 ) L(β 0, σ, β 1 D) L(β 0H, σ H D 01 ) α 0 π 0 (β 0H ) π 0 (σ H ) ω 1 N(β 1H, sd 2 ) + (1 ω 1 ) N(0, ) Control arm parameters β 0 N and σ IG Down-weight prior using power prior α 0 control the impact of historical data α 0 [0 1] Treatment effect parameter β 1 N Down-weight prior using mixture prior ω 1 control the impact of historical data ω 1 [0 1] 1. Ibrahim, Statistical Science Bernardo, Wiley 1994 ; Schmidli, Biometrics 2014 Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 7

9 Bayesian Weibull model Posterior distribution using power 1 and mixture 2 prior π(β 0, σ, β 1 D, D 01, D 02, α 0, ω 1 ) L(β 0, σ, β 1 D) L(β 0H, σ H D 01 ) α 0 π 0 (β 0H ) π 0 (σ H ) ω 1 N(β 1H, sd 2 ) + (1 ω 1 ) N(0, ) Control arm parameters β 0 N and σ IG Down-weight prior using power prior α 0 control the impact of historical data α 0 [0 1] Treatment effect parameter β 1 N Down-weight prior using mixture prior ω 1 control the impact of historical data ω 1 [0 1] 1. Ibrahim, Statistical Science Bernardo, Wiley 1994 ; Schmidli, Biometrics 2014 Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 7

10 Bayesian Weibull model Posterior distribution using power 1 and mixture 2 prior π(β 0, σ, β 1 D, D 01, D 02, α 0, ω 1 ) L(β 0, σ, β 1 D) L(β 0H, σ H D 01 ) α 0 π 0 (β 0H ) π 0 (σ H ) ω 1 N(β 1H, sd 2 ) + (1 ω 1 ) N(0, ) Control arm parameters β 0 N and σ IG Down-weight prior using power prior α 0 control the impact of historical data α 0 [0 1] Treatment effect parameter β 1 N Down-weight prior using mixture prior ω 1 control the impact of historical data ω 1 [0 1] 1. Ibrahim, Statistical Science Bernardo, Wiley 1994 ; Schmidli, Biometrics 2014 Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 7

11 Simulation study: data generation EFS distribution Weibull(β 0, σ) Censoring rate (5%) Uniform distribution For each scenario: replications Control arm Treatment effect Optimist Historical Pessimist β 1p = ln(0.54) β 1H = ln(0.786) 0.5 β1 1H = ln(0.886) Historical: β 0H, σ H S1 S2 S3 Worse: β 0H, σ H S4 S5 S6 Better: β 0H +, σ H + S7 S8 S9 Historical data for the control arm (OS2006 trial): β 0H, σ H : point estimate of the frequentist Weibull model β, σ 0H H : 95% CI lower bound (worse outcome than historical) β, σ 0H + H + : 95% CI upper bound (better outcome than historical) Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 8

12 Simulation study: Analysis Three types of modelling were considered: - Bayesian Weibull model - Frequentist Weibull and Cox model For Bayesian analyses, ( MC with burn-in) we down-weighted historical data: - Control group parameters, using α 0 = 0, 0.3, 0.6, 1 - Treatment effect parameter, using ω 1 = 0, 0.025, 0.07, 0.15, 0.3, 0.6, 1 Decision rule: We concluded a benefit if We evaluated Power P (β 1 < 0) > value {97.5% ; 95% ; 90%} Bias in the estimation of β 1 Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 9

13 Impact of incorporating historical data on control only (ω 1 = 0) Treatment effect = Historical treatment effect = ln(0.786) If control arm = historical data S2: β 0, σ = β 0H, σ H Limited impact of historical data on the power No bias Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 10

14 Impact of incorporating historical data on control only (ω 1 = 0) Treatment effect = Historical treatment effect = ln(0.786) If control arm = historical data S2: β 0, σ = β 0H, σ H Limited impact of historical data on the power No bias More pessimistic, S5: β 0, σ = β 0H,σ H Decrease in power with increasing α 0 Increase in bias: Underestimation of the treatment effect Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 10

15 Impact of incorporating historical data on control only (ω 1 = 0) Treatment effect = Historical treatment effect = ln(0.786) If control arm = historical data S2: β 0, σ = β 0H, σ H Limited impact of historical data on the power No bias More pessimistic, S5: β 0, σ = β 0H,σ H Decrease in power with increasing α 0 Increase in bias: Underestimation of the treatment effect More optimistic, S8: β 0, σ = β 0H +, σ H + Increase in power with increasing α 0 Overestimation of the treatment effect Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 10

16 Impact of incorporating historical data on treatment effect only (α 0 = 0) Control arm parameters = Historical control parameters Treatment effect = historical data S2: β 1 = β 1H = ln(0.786) Major increase in power by incoporating historical data, even with small ω 1 No bias Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 11

17 Impact of incorporating historical data on treatment effect only (α 0 = 0) Control arm parameters = Historical control parameters Treatment effect = historical data S2: β 1 = β 1H = ln(0.786) Major increase in power by incoporating historical data, even with small ω 1 No bias More pessimistic, S3: β 1 = 0.5 β 1H Large increase in power Slight overestimation of the trt effect Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 11

18 Impact of incorporating historical data on treatment effect only (α 0 = 0) Control arm parameters = Historical control parameters Treatment effect = historical data S2: β 1 = β 1H = ln(0.786) Major increase in power by incoporating historical data, even with small ω 1 No bias More pessimistic, S3: β 1 = 0.5 β 1H Large increase in power Slight overestimation of the trt effect More optimistic, S1: β 1 = β 1p = ln(0.54) Increase in power persists, although prior less optimistic than the true trt effect Underestimation of the treatment effect Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 11

19 Scenario 2: The ideal situation, β 1 = β 1H Control arm parameters = Historical (β 0, σ = β 0H, σ H ) Increase in power, but limited impact of historical data on the control arm No bias Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 12

20 Discussion Incorporating historical data on the treatment effect: Increase in power Even if treatment effect is better than historical treatment effect With acceptable bias Historical data on control arm: Limited impact on the power With major bias if baseline outcome differs from the historical data Unexpected results Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 13

21 Discussion Possible explanation We have assumed that historical data follow a Weibull model Questionable modelling Perspectives Ongoing work incorporating OS2006 data using a flexible parametric modelling Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 14

22 Conclusion In rare diseases, Bayesian approach is very appealing However, with time-to-event data, incorporating individual historical data on control arm remains tricky Maybe due to uncertainty about the correct specification of baseline survival distribution Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 15

23 Thank you Acknowledgements: Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 15

24 References Goodman S.N, Sladky J.T. A Bayesian approach to randomized controlled trials in children utilizing information from adults : the case of Guillain-Barre Clin Trials, 2 : 305, 2005 Ibrahim JG, Chen MH. Power prior distributions for regression models Stat Sci, 15 : 46 60, 2000 Schmidli H, Gsteiger S, Roychoudhury S, et al. Robust Meta-Analytic-Predictive Priors in Clinical Trials with Historical Control Information Biometrics, 70, , 2014 Dec Viele K, Berry S, Neuenschwander B, et al. Use of historical control data for assessing treatment effects in clinical trials Pharmaceut Statist, , 2014 Brard et al. Designing a Bayesian randomised controlled trial in osteosarcoma 15