Statistical Heresy ? Response Adaptive Randomization in Clinical - PowerPoint PPT Presentation

Statistical Heresy ? Response Adaptive Randomization in Clinical Trials Mi-Ok Kim Associate Professor of Pediatrics Div. of Biostatistics and Epidemiology CCHMC, UC College of Medicine Supported by CCTST Method Grant June 17 th , 2011

When info. is available, • Shall we use it? – Yes. • What about if the information is from an ongoing clinical trial and we consider using the information to change some aspects of the trial under way? – No.

A Dilemma Faced by Dr. Chmielowski • Mr. McLaughlin: the experimental drug stopped the growth of the tumor. • Mr. Ryan: chemotherapy, priori known ineffective, could not hold back the tumors. • Mr. Ryan is highly likely to benefit from the experimental drug yet would not be allowed to switch as it would muddy the trial’s results.

Conflicts of Convent. Design w Ethics • Why wouldn’t Mr. Ryan be allowed to cross- over to the experimental drug? • Why hadn’t Mr. Ryan be given a greater than 50:50 chance of being assigned to the experimental drug?

Outline • Response Adaptive Design – Frequentist/Bayesian Approach • Early Immunomodulator Trt Use in Pediatric Ulcerative Colitis Patients – Motivation – Logistical & Statistical Issues – Simulation Results • Conclusion

Response Adaptive Randomization (RAR) • Skews alloca. prob. away from equal alloca. over the course of a trial to favor the better or best performing trt arm adaptively based on resp. data accrued thus far w/o undermining the validity and integrity of the trial • Allocation prob. are adapted “by design”, not on “ad hoc” basis. • Same inference procedure works as with a fixed (non-adaptive) design

Randomized Play-the-Winner Failure Success Success

Doubly Biased Coin Design • Pick a target allocation – E.g) Minimizing the expected total # of failures p T  p p T C • True unknown. p , T p C • Use estimates based on available data successively over the course of a trial.

How to compare different designs? Suppose a target allocation probability is given & the sample size is fixed: The power increases as the variance of the sample allocation ratio gets smaller (Hu & Rosenberger, 2003)

Ped. U Colitis Pts • Current trt regimens are far from optimal. – Up to 45% on corticosteroid (CS) 1yr after Dx. – Up to 26% receiving colectomy within 5yrs post Dx – No guidance as to who shall receive IM therapy, not 5-ASA monotheray, the least toxic UC drug • PROTECT: observational study that aims to – Est. the success rate of standardized therapeutic protocol – Develop a prediction model

Early IM Trt Use in Ped. U Colitis Pts Control Low Likelihood Steroid Group Early IM Free Remission at 1 yr Enrollment Success Control High Likelihood Group Early IM 2ndary Outcome: Remission by day 30

Doubly Biased Coin Design • Pick a target allocation  1 p – Urn model  C 58 . 3 %    ( 1 ) ( 1 ) p p T C p , T p • Estimate the unknown based on C available data

Issues in Implementing an RAR Design 1. Delay in the response • Okay. Update when resp. become available. • DABCD (Hu et al., 2007), Urn model (Bai et al., 2002; Hu and Zhang, 2005), Drop-the-loser rule (Zhang, et. al., 2007) 2. Heterogenous pt population • Okay. • DABCD (Duan and Hu, 2007), Urn model (Bai & Hu, 1999, 2005), Drop-the-loser rule (Zhang, et. al., 2007)

Issues in Implementing an RAR Design 1. Delay in the response • Use the Kaplan-Meier estimator to incorporate the delayed (or unavailable) responses & to update based on all available data. 2. Heterogenous pt population • Use the short-term Seconndary endpoint as a strata variable.

Proposed Method 1. “Standard” Method: Primary Only / Primary + Secondary 2. K-M Method: Primary Only / Primary + Secondary Heterogeneous delays are okay Simulation – Use the Ped. IBD Collaborative Research Group Registry (n=353)

Low Likelihood Group, Long Delay 0.60 Mean % Patients assigned to the TRT group 0.55 0.50 "Standard" method K-M method 0.45 0 50 100 150 200 Patient number in the order of entry

High Disk, Short Delay, n=228 Low likelihood Group, Short Delay 0.60 Percentage of patients assigned to the treatment group 0.55 0.50 Standard method Proposed method K-M method 0.45 0 50 100 150 200 Patient number in the order of entry

"Standard" Method, Long Delay 0.8 0.7 % Patients assigned to the TRT group 0.6 0.5 0.4 0.3 Primary only 0.2 1 9 19 31 43 55 67 79 91 104 119 134 149 164 179 194 209 Patient number in the order of entry

"Standard" Method, Long Delay 0.8 0.8 0.7 0.7 % Patients assigned to the TRT group 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 Primary only Primary+Secondary 0.2 0.2 1 1 9 9 19 19 31 31 43 43 55 55 67 67 79 79 91 91 104 104 119 119 134 134 149 149 164 164 179 179 194 194 209 209 Patient number in the order of entry

Results (2000 simulated data replicates) N ≈ 228 Primary Only Primary + Secondary (0.5 vs 0.3) Fixed “Standard” K-M “Standard” K-M 90.8 (80.7%) 93.1 (80.3%) 94.7 (80.7%) 92.9 (78.8%) 94.8 (79.5%) 99.7 (91.6%) 103.4 (88.7%) 101.8 (94.0%) 104.7 (93.5%)

Bayesian Approach • Prior knowledge about parameters + Data = Posterior knowledge about parameters • Prior for rate of success stratified by the secondary endpoint. • Require more extensive pre-trial research to appropriately design the approach with acceptable operating characteristics

Bayesian Approach • When the priors are appropriately specified, may perform better.

When Bayesian approach may help? • When there exist sufficient priori info. on which to base a relatively strongly informative prior – may bring substantially greater gain. • Continuous assessment of trt effects is natural. Easier to incorporate early stopping rules and multiple hypotheses. • Testing a drug in genetically defined many sub- patient populations • Testing many drugs with limited resources

Conclusion • Response adaptive randomization is a well- established randomization method that increases pt benefit without undermining the validity or integrity of clinical trials. • RAR can be applied for delayed responses, while maintaining the benefits of the adaptive design. • Bayesian approach can be more beneficial

• Ms. Chunyan Liu (DBE) • Dr. Jack J. Lee (MD Anderson) • Dr. Feifang HU (Univ. of Virginia) • Dr. Lee Denson (Direct Inflammatory Bowel Disease Center at CCHMC) • the Ped. IBD Collaborative Research Group • Dr. Lili Ding (DBE) – Adaptive Dose Finding • Ms. Yangqing Hu – Covariate Adaptive Randomization Design

References • Hu, F. and Rosenberger, W.F. (2003). Optimality, variability, power: Evaluating response-adaptive randomization procedures for treatment comparisons. Journal of the American Statistical Association, 98, 671- 678. • Hu, F. F., L. X. Zhang, et al. (2008). Doubly adaptive biased coin designs with delayed responses. Canadian Journal of Statistics-Revue Canadienne De Statistique 36(4): 541-559. • Bai, Z., Hu, F. and Rosenberger, W.F. (2002). Asymptotic properties of adaptive designs for clinical trials with delayed response. Ann. Statist . Vol 30, No 1, 122-139. • Hu, F. and Zhang, L.X. (2004). Asymptotic normality of adaptive designs with delayed response. Bernoulli. 10, 447-463. • Zhang, L.-X., Chan, W.S., Cheung, S.H., Hu, F. A generalized drop-the-loser urn for clinical trials with delayed responses. (2007) Statistica Sinica , 17 (1), pp. 387-409.

References • Duan, L. L. and F. F. Hu (2009). Doubly adaptive biased coin designs with heterogeneous responses. Journal of Statistical Planning and Inference 139(9): 3220-3230. • Bai, Z. D. and Hu, Feifang (1999) Asymptotic theorems for urn models with nonhomogeneous generating matrices. Stochastic Processes and their applications, Vol. 80, 87-101. • Bai, Z. D. and F. F. Hu (2005). Asymptotics in randomized URN models. Annals of Applied Probability 15(1B): 914-940. • Hu, F. and W. F. Rosenberger (2006). The theory of response-adaptive randomization in clinical trials. Hoboken, N.J., Wiley-Interscience.