Jim Bolognese, Cytel Inc. 05Nov2015

Transcription

1 Modified Toxicity Probability Intervals (mtpi), Bayesian Logistic Regression Modeling (BLRM), Continual Reassessment Method (CRM) via EAST6.3.1 vs. T-statistic (Tstat) Design via COMPASS for finding MTD Jim Bolognese, Cytel Inc. 05Nov2015

2 Motivation mtpi is appealing and popular for adaptive dose-finding of Maximum Toxicity Dose (MTD) Easy to implement (fixed pre-stated algorithm) efficient versus competitor designs (CRM, BLRM) much better than traditional 3+3 design T-statistic design is appealing and popular with some for adaptive dose-finding of Target Dose Easy to implement (requires simple calculation after each cohort) Efficient versus competitor designs (Bayesian 4PL, Emax, NDLM) Better than fixed-randomized designs

3 Dose-Response Curves Simulated (MTD = dose with probability of response = 0.3) DR1 EAST6.1.3 default linear DR3 left-shifted DR2 right-shifted DR4 extreme high DR5 extreme low

4 Design Parameters 7 doses (1,2,3,4,5,6,7) Total N=30 subjects 10 sequential cohorts of 3 subjects each 1 st cohort at Dose1 Each subsequent cohort assigned a single dose per adaptive design Target Toxicity Level 0.3 #simulations of each DR curve scenario mtpi - 10K (EAST default) Tstat 1K (some needed computations easier in EXCEL)

5 mtpi Parameters Toxicity Intervals Under dosing: <0.25 On-Target dosing: Over dosing: >0.35 Prior on TRUE toxicity probability at each dose ~ Beta(1,1) Over-Dosing Exclusion Rule Prob(Pi>Pt data) > [to yield full sample size] Pi = Prob(toxicity at dose i) Pt = Target probability of toxicity = 0.3 Similar results for EAST default Prob > 0.95 (not shown) Prob>0.6 also simulated and summarized No Under-dosing exclusion rule used

6 mtpi Design Parameters (1)

7 mtpi Design Parameters (2)

8 mtpi optimization 2 levels of early stopping posterior probability required (0.95 and 0.80). 2 toxicity probability ranges: +/-"05" range +/-"20" range under dosing 0 to to 0.10 target dosing 0.25 to to 0.50 over dosing 0.35 to to 1.00 beta(1,2) prior to yield estimate of ~0.3 for probability of toxicity at each dose since the target toxicity level is 0.3 beta(1,1) also run; it yields estimate 0.5

9 T-stat Parameters (1) T = (Pi-0.3)/sqrt( (Pi*(1-Pi)/n ) Pi = isotonic estimated proportion of toxicity at Dose i Dose escalation / de-escalation rules: T < -2 up 2 dose increments -2 T < -0.1 up 1 dose increment -0.1 T < 0.1 repeat dose 0.1 T < 2 down 1 dose increment 2 T down 2 dose increments

10 T-stat Parameters (2) T = (Pi-0.3)/sqrt( (Pi*(1-Pi)/n ) Pi = isotonic estimated proportion of toxicity at Dose i Dose escalation / de-escalation rules: T < -2 up 2 dose increments -2 T < -1 up 1 dose increment -1 T < 1 repeat dose 1 T < 2 down 1 dose increment 2 T down 2 dose increments NOTE: T-stat may have unfair advantage over dose esc. designs since it can skip a dose in extreme cases (i.e., T >2)

11 Tstat Design Parameters (1)

12 Tstat Design Parameters (2)

13 Tstat optimization Stop dose Di and all doses > Di when: Prob(toxicity Di > 0.35 observed isotonic estimate) > 0.8 Prob(toxicity Di > 0.50 observed isotonic estimate) > 0.8 Simulated for each of Tstat(1) and Tstat(2) Also considered NO dose-stopping MANY THANKS to Jaydeep Bhattacharyya for programming the early stopping into CytelSim

14 BLRM Parameters (Bayesian Logistic Regression Modeling) Toxicity Intervals Under dosing: <0.25 Target toxicity: Excessive toxicity: Unacceptable toxicity: >0.45 Prior Distribution: Bivariate Lognormal for the 2 logistic parameters Prior on Lowest Dose and MTD Prob.(DLT) at D1 = 0.05 Estimated MTD = 4 # Beta Samples = 1000 (Direct Sampling; default settings) Probability(Overdosing) < 0.25 No Early Stopping

15 BLRM Design Parameters

16 BLRM Optimization 3 priors for logistic regression model, per Neuenschwander(2008) Doses with EWOC OD post.prob > 0.5, 0.7, 0.9 evaluated 9 combinations in all.

17 BLRM Priors (Neuenschwander, 2008) bivariate normal prior for means of log(alpha) and log(beta) in the Bayesian logistic linear regression model: mean(alpha) = logit(p-star)=log(0.3/0.7)=-0.847, where p-star is the target toxicity level mean(beta) = 0, SD(alpha) = 2, SD(beta) = 1, correlation = 0 setting prior probabilities of (1) exceeding the minimum unacceptable toxicity proportion at the lowest dose, and (2) falling below the maximum under-dosing toxicity proportion at the highest dose at, e.g., then deriving corresponding multivariate normal parameters. For Prob(p1>0.6)=0.05 and Prob(pK<0.2=0.05), the corresponding 5 multivariate normal parameters (m1,m2,s1,s2,rho) are (-0.376, , 0.853, 0.931, ). Flatter prior: mean(alpha)=-1.025, mean(beta)=-1.091, SD(alpha)=0.893, SD(beta)=1.147, corr=

18 CRM Parameters (Continual Reassessment Method) Target Probability of Toxicity = 0.3 Toxicity Probability Upper Limit = 0.3 Model Type = Logistic (c=-7) Distribution = Lognormal [ ln(θ) ] mu=1, sigmasquared = 1 Doses: D1 D2 D3 D4 D5 D6 D7 Prob(tox): Overdoseing rule: Prob(Pi>Pt data) > 0.6 No Early Stopping

19 CRM Design Parameters

20 CRM Optimization Permit skipping doses since Tstat dose so Permit dose escalation if a prior subject experienced a toxicity Three priors (CRM1,2,3) chosen for similarity to the priors for BLRM plus a very-close-to-flat prior (CRM4) for one-parameter power model: all use gamma(1,1) as prior for the power parameter D1 D2 D3 D4 D5 D6 D7 CRM1 uses toxicity prob: 0.02, 0.05, 0.1, 0.2, 0.4, 0.6, 0.8 CRM2 uses toxicity prob: 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6 CRM3 uses toxicity prob: 0.05, 0.07, 0.1, 0.15, 0.2, 0.3, 0.4 CRM4 uses toxicity prob: 0.27, 0.28, 0.29, 0.3, 0.31, 0.32, 0.33 Plus 2 upper toxicity probability limits for the EAST default oneparameter logistic model 6 CRM configurations in all

21 Remarks on mtpi vs BLMR vs CRM vs Tstat Tstat design looks like a competitor to mtpi, BLRM, CRM for toxicity dose-finding trials Based on Performance criteria: Probability of identifying correct target ID, probability of assigning subjects to doses > target, # toxicities observed Early indications are that Tstat is competitive with mtpi, BLRM, CRM in consideration of a spectrum of TRUE underlying DR curves mtpi, BLRM, CRM could be optimized better than Tstat design for particular individual (or like) DR curves BLRM & CRM seem better than mtpi for estimating target dose, but might assign more subjects to higher doses

22 Performance Characteristics mtpi vs BLRM vs CRM vs T-stat mtpi (1) mtpi (.6) mtpiopt % correct MTD mtpi 20, 95 BLRMdf BLRMopt BLRM 1OD 50 default linear rightshifted leftshifted extreme high extreme low BLRMopt confined to BLRMprior1 & BLRMprior2 since prior3 increases assignment to doses with toxicity levels too much CRM df CRM opt CRM 2 Tstat (1) Tstat (2)

23 Performance Characteristics mtpi vs BLRM vs CRM vs T-stat mtpi (1) mtpi (.6) mtpiopt % of subjects assigned dose > MTD* mtpi 20,95 BLRM df BLRM 1OD 50 BLRMopt CRM2 default linear rightshifted n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a leftshifted extreme high extreme low n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a CRM df CRM opt *assigned dose > dose1 for extreme high DR curve Tstat (1) Tstat (2)

24 default linear rightshifted leftshifted extreme high extreme low mtpi (1) mtpi (.6) Performance Characteristics mtpi vs BLRM vs CRM vs T-stat mtpiopt Estimated Number of DLT's per Trial mtpi 20,95 BLRM df BLRMopt BLRM 1OD 50 CRM df CRMopt CRM 2 Tstat Tstat (1) (2) BLRMopt confined to BLRMprior1 & BLRMprior2 since prior3 increases assignment to doses with toxicity levels too much

25 Performance Characteristics mtpi vs BLRM vs CRM vs T-stat % correct MTD mtpiopt BLRMop t CRM opt Tstat opt Tstat(1) Tstat(2) T1,35,8 0 T1,50,8 0 T2,35,8 0 T2,50,8 0 default linear rightshifted left-shifted extreme high extreme low

26 Performance Characteristics mtpi vs BLRM vs CRM vs T-stat % of subjects assigned dose > MTD* default linear rightshifted mtpiopt BLRMop t CRM opt Tstat opt Tstat(1) Tstat(2) T1,35,80 T1,50,80 T2,35,80 T2,50, n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a left-shifted extreme high extreme low n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a *assigned dose > dose1 for extreme high DR curve

27 Performance Characteristics mtpi vs BLRM vs CRM vs T-stat average # DLT's per trial mtpiopt BLRMop t CRMopt Tstat opt Tstat(1) Tstat(2) T1,35,80 T1,50,80 T2,35,80 T2,50,80 default linear rightshifted left-shifted extreme high extreme low

28 One Way to Rank the Designs Across the Five DR Curves & 3 Performance Criteria 3 criteria: Probability of identifying correct target dose ID Probability of assignment to doses above target dose Average number of toxicities / simulated trial Weight them 50:25:25, since 2 nd & 3 rd criteria both assess limiting safety 1 st criteria is the primary objective Compute relative difference from optimal for each DR curve for each design: (Max.%correct %correct)/(max. Min.%correct) (Prob.Assgn>Tgt Min.Prob.)/(Max. Min.Prob.Assgn>Tgt) (Avg#tox Min.Avg#tox)/(Max. Min.Avg#tox) Then compute weighted average across all DR curves Values closer to 0 indicate closer to optimal design Values closer to 1 indicate closer to worst design Values = 0.5 indicate mid-way between optimal and worst designs

29 One Way to Rank the Designs Across the Five DR Curves & 3 Performance Criteria Design Overall Average Relative Difference from Optimal Design Overall Average Relative Difference from Optimal mtpiopt 0.27 Tstat opt 0.34 Tstat(1) 0.52 CRMopt 0.41 Tstat(2) 0.52 BLRMopt 0.44 T1,35, T2,50, mtpi(1) 0.56 mtpi20, mtpi(.6) 0.57 BLRMdf 0.47 CRMdf 0.64 T2,35, BLRM1OD T1,50, CRM2 0.77

30 Tstat as easy as mtpi to implement Number of T-Statistic Design for Target Toxicity Level = 0.3 modify yellow-highlighted cells to modify design spec's Number of Subjects Observed Toxicities

31 Tstat as easy as mtpi to implement (spreadsheet computes table in previous slide) Dose Selection Rules Values of T Dose from to Increment -infinity infinity -2

32 Remarks on mtpi vs BLMR vs CRM vs Tstat Tstat design looks like a competitor to mtpi, BLRM, CRM for toxicity dose-finding trials Based on Performance criteria: Probability of identifying correct target ID, probability of assigning subjects to doses > target, # toxicities observed Early indications are that Tstat is competitive with mtpi, BLRM, CRM in consideration of a spectrum of TRUE underlying DR curves mtpi, BLRM, CRM could be optimized better than Tstat design for particular individual (or like) DR curves BLRM & CRM seem better than mtpi for estimating target dose, but might assign more subjects to higher doses

33 Next Steps re: Tstat for toxicity dose-finding Consider adding Tstat to EAST among adaptive dose escalation designs Consider other ranking mechanisms Evaluate additional design configurations to optimize Consider investigating Ivanova(2012) Bayesian Isotonic Adaptive Dose-Finding design vs mtpi, CRM, BLRM, Tstat Not sure if methodology extends to binary endpoints Consider employing isotonic estimates with mtpi Validate these results Other?? [DISCUSSION]

34 REFERENCES Ivanova A, Bolognese J, Perevozskaya I. Adaptive design based on T-statistic for dose-response trials. Statistics in Medicine, 2008 May 10;27(10): EAST6.3.1 User Manual, Cytel Inc., Cambridge, MA 2014 COMPASS User Manual, Cytel Inc., Cambridge, MA, 2012 Ivanova A, Xiao C, Tymofyeyev Y. Two-stage designs for Phase 2 dose-finding trials. Statist. Med. 2012; 31: Ji Y, Liu P, Li Y, and Bekele N (2010). A modified toxicity probability interval method for dose finding trials. Clinical Trials, 7: Neuenschwander B, Branson M, and Gsponer T (2008). Clinical aspects of the Bayesian approach to phase I cancer trials. Statistics in Medicine, 27:

35 EXTRA SLIDES follow this one (duplicate info: subsets of info in previous slides)

36 Remarks (all designs targeted to 0.2) 3+3 vs mtpi vs BLRM vs CRM vs T-stat 3+3 generally identifies the correct target dose less frequently than the other designs In some cases, much less frequently 3+3 assigns greater percent of patients at target dose in some cases, but never materially fewer However, since N=6 limit, this comparison seems not informative

37 Performance Characteristics mtpi vs BLRM vs CRM vs T-stat mtpi (1) mtpi (.6) mtpiopt mtpi 20, 95 mtpi- SAS % correct MTD mtpi- ISO BLRM df BLRM opt BLRM 1OD 50 CRM df CRM opt CRM 2 Tstat Tstat (1) (2) default linear rightshifted leftshifted extreme high extreme low BLRMopt confined to BLRMprior1 & BLRMprior2 since prior3 increases assignment to doses with toxicity levels too much

38 Performance Characteristics mtpi vs BLRM vs CRM vs T-stat mtpi (1) mtpi (.6) mtpiopt % of subjects assigned dose > MTD* mtpi 20,95 mtpi- SAS mtpi- ISO BLRM df BLRM opt BLRM 1OD 50 default linear rightshifted n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a leftshifted extreme high extreme low n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a CRM df CRM opt *assigned dose > dose1 for extreme high DR curve CRM 2 Tstat (1) Tstat (2)

39 Performance Characteristics (all 0.2 target) mtpi vs BLRM vs CRM vs T-stat % correct MTD mtpi(1) mtpi(.6) 3+3 BLRM CRM Tstat(1) Tstat(2) default linear right-shifted left-shifted extreme high extreme low

40 Performance Characteristics (all 0.2 target) mtpi vs BLRM vs CRM vs T-stat % of subjects assigned dose > MTD* mtpi(1) mtpi(.6) 3+3 BLRM CRM Tstat(1) Tstat(2) default linear right-shifted left-shifted extreme high extreme low n/a n/a n/a n/a n/a n/a n/a *assigned dose > dose1 for extreme high DR curve