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Dose-adaptive study designs offer benefits for proof-of-concept / Phase IIa clinical trials, as well as raise issues fo

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## Dose-adaptive study designs offer benefits for proof-of-concept / Phase IIa clinical trials, as well as raise issues fo

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**Dose-adaptive study designs offer benefits for**proof-of-concept / Phase IIa clinical trials,as well as raise issues for continued research OUTLINE: Dose-Adaptive Designs & Examples • Definition & Introduction (Jim) • Frequentist Designs, including Random Walk Designs (Jim) • 3+3 Design for cancer • Up&Down Design • Biased Coin Designs • Simulations of Up&Down Design for Dental Pain Clinical Trial • Bayesian-type Designs (Inna) • Continual Reassessment Method (CRM) • Bayesian D-optimal Design • Other related approaches • Bayesian 4-parameter logistic • Case Study (adaptive cross-over design) • CytelSim Software demo • Summary & Recommendations (Inna) • References Jim Bolognese & Inna Perevozskaya, Sept. 12, 2008**Continual Reassessment Method (CRM)**• Most known Bayesian method for Phase I trials • Underlying dose-response relationship is described by a 1-parameter function family • For a predefined set of doses to be studied and a binary response, estimates dose level (MTD) that yields a particular proportion (P) of responses • CRM uses Bayes theorem with accruing data to update the distribution of MTD based on previous responses • After each patient’s response, posterior distribution of model parameter is updated; predicted probabilities of a toxic response at each dose level are updated • The dose level for next patient is selected as the one with predicted probability closest to the target level of response • Procedure stops after N patients enrolled • Final estimate of MTD: dose with posterior probability closest to P after N patients • The method is designed to converge to MTD Innovative Clinical Drug Development Conference**Continual Reassessment Method (cont.)**Choose initial estimate of response distribution & choose initial dose Update Dose Response Model & estimate Prob. (Resp.) @ each dose Obtain next Patient’s Observation Next Pt. Dose = Dose w/ Prob. (Resp.) Closest to Target level Stop. EDxx = Dose w/ Prob. (Resp.) Closest to Target level Max N Reached? no yes**Escalation With Overdose Control (EWOC) Bayesian Design**• Assigns doses similarly to CRM, except for overdose control • predicted probability of next assignment exceeding MTD is controlled (Bayesian feasible design) • this distinction is particularly important in oncology • Assumes a model for the dose-response curve in terms of two parameters: • MTD • probability of response at dose D1 • EWOC updates posterior distribution of MTD based on this two-parameter model • Free software available here: • http://sisyphus.emory.edu/software_ewoc.php • Reference: • Z.Xu, M. Tighiouart, A. RogatkoEWOC 2.0: Interactive Software for Dose Escalation in Cancer Phase I Clinical Trials Drug Information Journal 2007 : 41(02) Babb, et al., 1998**Decision Theoretic Approaches**• Similar to CRM • Incorporates elements of Bayesian Decision Theory • Designed to study a particular set of dose levels D1, . . ., Dk • Two-parameter model for dose response with prior distributions on the parameters • Loss function minimizes asymptotic variance of dose which yields a particular proportion of responses • Posterior distribution estimates of the 2 parameters used to derive next dose, i.e., that estimated to have desired response level Whitehead, et al., 1995**Bayesian D-Optimal Sequential Design**• Based on formal theory of optimal design (Atkinson and Donev, 1992) • Similar to EWOC, a constraint is added to address the ethical dilemma of avoiding extremely high doses • Uses a two parameter logistic model for dose response curve • Slope & location • Binary endpoint • Minimum response rate fixed at 0%, maximum at 100% • Sequential procedure assigns dose at each stage which minimizes variance of posterior distribution of model parameters Haines, et al., 2003**Simulated Bayesian D-Optimal Design for ED50**(http://haggis.umbc.edu/cgi-bin/dinteractive/inna1.html) • Efficacy: Percent of patients with “Response” assumed underlying distribution Dose: 1 2 3 4 5 6 7 %Response: 30 40 55 65 75 75 75 • Prior estimates: ED25 between doses 1 and 2 ED50 between doses 2 and 3 • 6 patients in Stage 1 for seeding purposes • D-Optimal Design: 3 pts at dose 1, 2 at dose 3, 1 at dose 4 # responses: 1 1 1 • 24 subsequent patients (total 30 patients) entered sequentially at doses yielding minimum variance of model for ED50 estimate • Response / non-response assigned to approximate targeted %G/E distribution above**Simulated Bayesian D-Optimal Designfor ED50 – Results**(http://haggis.umbc.edu/cgi-bin/dinteractive/inna1.html)**Simulated Bayesian D-Optimal Designfor ED50 – Summary**• Results from a single implementation Dose: 1 2 3 4 5 6 7 assumed %Response: 30 40 55 65 75 75 75 #Responses: 4 - 2 1 8 - - #patients: 13 0 4 1 12 0 0 observed %Response: 31 - 50 100 67 - - • Bayesian estimated ED50 = dose 2.3 • However, few observations at other than 2 doses due to optimal design for particular dose-response model • Dose-Response curve between those two doses could be interpolated by the underlying fitted model • Should not extrapolate from model outside observed range • 2-parameter model (slope, location) forced through 0% and 100%**Bayesian Design for the 4-parameter Logistic model**• Underlying model: Available doses: Yijis (continuous) response of the j-th subject on the i-thdose, di is the vector of parameters of the distribution f • Patients are randomized in cohorts • Within each cohort, fixed fraction (e.g. 25%) is allocated to placebo, • For the remaining patients within cohort, dose is picked adaptively out of • Doses are picked so that QWV (Quantile Weighted Variance) utility function is minimized Developed by S. Berry for CytelSim (~2006)**Bivariate Models: Penalized Adaptive D-optimal Designs**• Addresses safety and efficacy simultaneously • Design is characterized by two dependent binary outcomes (efficacy and toxicity) • Similar to univariate model: involves dose-escalation and early stopping rules • Similar to Bayesian Sequential D-Optimal Design: • Model-based approach with formal optimality criteria: “maximize the expected increment of information at each dose” • Instead of Bayesian posterior update, Maximum Likelihood Estimates of current trial data used for next dose selection • “Penalized” design: Introduces various constraints that can be flexible to reflect ethical concerns, cost, sample size, etc. Dragalin, 2005**Bayesian-type DesignsPros (+) & Cons (-)**+ Minimize observations at doses of little interest (too small or large) + CRM assigns doses which migrate & cluster around EDxx - little info on dose-response away from targeted dose (e.g., ED50) + can compensate by targeting 2 or 3 response levels + Bayesian D-optimal design efficiently estimates model-based dose-response curve (& targeted EDxx) - yields most observations at 2 dose levels to optimally fit model - model restrictive - forced through 0% and 100% response levels - should not extrapolate response levels beyond observed doses**Bayesian-type DesignsPros (+) & Cons (-)**- Subjective nature of assignment of prior (starting) distribution - could take many observations to overcome an incorrect prior - Models underlying current methods not general enough for efficacy endpoints - 4-parameter model needed to estimate min & max response levels - Co-factors not included; could confound estimates + execute designs within important co-factor levels - Computations complex; little software available - Difficult to explain to clients - Not yet proven substantially better than up-and-down or t-statistic s designs when aim is estimation of dose-response curve**Logistics for Conduct of a Dose-Adaptive Designed Trial**• Response observable reasonably quickly • Increased statistical computations / simulations to justify dose-adaptive scheme in protocol • Need on-call person to assess previous response data and generate dose for next subject • For model-based dose-adaptive designs, need on-call unblinded statistician for associated analyses • OR, this could be automated via web-based interface (increases cost) • Rapid transfer of needed data • Need special packaging or unblinded pharmacist at site to package selected dose for each patient**Remarks (2)**• Logistics of implementation more complicated than usual parallel group design • Frequent data calls / brief simple analyses • Close contact with sites re: dose assignments • Special packaging (IVRS??) • Drug Supply – needed sufficiently for many possibilities • Tolerability rule(s) can be added for downward dose-assignment if pre-specified AE criteria are encountered • This has been studied in context of Bayesian dose-adaptive designs, but not in context of up&down designs • Number of placebo patients maintained as designed for intended precision vs. that group; could be down-sized, though**Dose-Adaptive DesignSummary**• Allocation of dose for next subject based on response(s) of previous subject(s) • Random Walk designs: only last subject’s response • T-statistic (frequentist) designs: all previous subjects’ responses • Bayesian-type designs: all previous subjects’ responses • High potential to limit subject allocation to doses of little interest (too high / too low) • Maximize information gathered from fixed N • Ethical advantage over fixed randomization • More attractive to patients / subjects • Inference conditional on doses assigned by design, but not overly important in early development • Requires more statistical up-front work (simulation) • No pre-specified allocation schedule; requires ongoing communication with site regarding allocation**Dose-Adaptive Design Summary**• Bayesian-type designs preferable to estimate dose-response curve; can also estimate a dose-response quantile of interest (e.g., EDxx) or (part of?) region of increasing dose-response • Complex; heavy computations • Random Walk & T-statistic Designs focus on quantile(s) of interest • Easy to understand & program • Consider as starting point for implementing dose-adaptive design • Let other design features guide towards other adaptive techniques based on particular experimental situation • Ongoing incomplete simulations have yet to identify major advantage of Bayesian-type designs over RW & T, unless prior information is important to consider. • Study, comparison, & refinement of these dose-adaptive designs continues**Dose-adaptive study designs offer benefits for**proof-of-concept / Phase IIa clinical trials,as well as raise issues for continued research OUTLINE: Dose-Adaptive Designs & Examples • Definition & Introduction (Jim) • Frequentist Designs, including Random Walk Designs (Jim) • 3+3 Design for cancer • Up&Down Design • Biased Coin Designs • Simulations of Up&Down Design for Dental Pain Clinical Trial • Bayesian-type Designs (Inna) • Continual Reassessment Method (CRM) • Bayesian D-optimal Design • Other related approaches • Bayesian 4-parameter logistic • Case Study (Bayesian and Adaptive cross-over designs) • CytelSim Software demo • Summary & Recommendations (Inna) • References Jim Bolognese & Inna Perevozskaya, Sept. 12, 2008**Case Study Example**Adaptive Dose-Ranging POC study By I. Perevozskaya and Y. Tymofyeyev**Study Background**• Development phase: Ib • Strategic objective: generate preliminary D-R info to optimize dose selection for Phase IIb study • Caveats: • Phase Ib will be run using surrogateendpoint • Future Phase IIb will be driven by clinical endpoint (chronic symptoms) • There is no formally established relationship between surrogate and clinical endpoints dose-response curves, but… • Dose selected as “sub-maximal” using surrogate endpoint D-R curve is believed to be “sub-therapeutic” for the clinical endpoint.**Study objectives**• (Broad) to demonstrate that a single administration of drug, compared with placebo, provides response that varies by dose • (Specific) • Find “sub-maximal” dose (e.g. ED75 defined as the dose yielding 75% of the placebo-adjusted maximal response ) • Meaningfully describe dose-response relationship • Demonstrate that at least one dose is significantly different from placebo**Study Design challenges and Adaptive design opportunity**• Easy to miss informative dose range with traditional design • Dose-response (D-R) can be relatively steep in the sloping part of the D-R curve • Dose-range & shape of curve = Unknown (and “unknowable” using PK) • Dose range to explore is very wide (6 active doses potentially considered) • Logistics: • Primary endpoint captured electronically within 1 day • The expected subject enrolment rate is not too high • Endpoint suitable for cross-over design • Following single-dose administration, 3-7 day washout is sufficient • 3-period (or even 4-period) cross-over could be reasonable**Bayesian Adaptive Design Description**• 6 active doses and placebo available • Design uses frequent looks at the data and adaptations (dose selections) are made after each IA • Patients are randomized in cohorts • Cohort is a small group of patients randomized between IAs • Within each cohort, fixed fraction (e.g. 25%) is allocated to placebo • For the remaining patients within cohort, dose is picked adaptively out of D1, ….D6. • Once endpoints for the whole cohort become available, decision is made about next cohort allocation using Bayesian algorithm (QWV utility function)**Bayesian Adaptive Design Description (cont.)**• The algorithm will try to cluster dose assignments around the “interesting” part of dose-response curve (e.g. ED75) • but there will be some spread around it (i.e. not all patients within cohort will go to the same dose). • The “target” will be moving for each cohort to be randomized • will depend on the trial information accumulated to the moment: • previous cohort’s dose allocations and responses.**Bayesian Adaptive Design for the 4-Parameter Logistic**Model: Details • Underlying model: Available doses: Yijis (continuous) response of the j-th subject on the i-thdose, di is the vector of parameters of the distribution f • Patients are randomized in cohorts • Within each cohort, fixed fraction (e.g. 25%) is allocated to placebo, • For the remaining patients within cohort, dose is picked adaptively out of • Doses are picked so that QWV (Quantile Weighted Variance) utility function is minimized Developed by S. Berry for CytelSim (~2006)**Implementation details of Bayesian Algorithm**• Developed by Scott Berry • Implemented in Cytel Simulation Bench software developed by Cytel in collaboration with Merck • Core idea: algorithm utilizes Bayesian updates of model parameters after each cohort • Components of ( , , ,) in 4-param. logistic model are treated as random with prior distribution (usually flat) placed upon them • After each cohort’s response, the (posterior) parameter distribution is updated and model D-R is re-estimated • The algorithm utilizes Minimum Weighted Variance utility function for decision making during adaptations • In our example, that translates into next cohort’s dose assignments are picked so that the variance of the response at the current estimate of ED75 is as small as possible**Flexible Modeling of Dose-Response With 4-Parameter Logistic**Model**Bayesian Adaptive Design Allocation Example**• Sample size modeled: N=120 • 10 cohorts of 12 patients in parallel design setting • Different dose allocations of 12 patients in each cohort are represented by different colors (dark blue is Pbo=D0, D1 is blue, …., brown is D6).**Bayesian Adaptive Design Example (Cont.)**Dose-response curve and Patient allocations to each dose at the end of this example trial • Assume the "true" max. effect dose (i.e., the dose to be "discovered" by the study) is "midpoint between Dose 2 and Dose 3 • D-R curve captured "Dose 3" as correct start of plateau. • Most patients were close to “Dose 3” • Few patients were on plateau**Bayesian Algorithm Allocation rule**• The algorithm clusters dose assignments around the “interesting” part of dose-response curve • With some “spread” around it (i.e. not all patients within cohort will go to the same dose). • The “target” is data-dependent and may change after each IA**Performance of Bayesian AD Under Various Dose-Response**scenarios • 8 different dose-response scenarios were studied, varying in: • Magnitude of maximum treatment effect • Location of the sloping part of the DR curve • Steepness of the sloping part of the DR curve • Allowing "true" ED75 to vary over the dose-range**Performance of Bayesian AD Under Various Dose-Response**scenarios (cont.) • Performance evaluated via simulations (using CytelSim Software) • Key criteria for evaluation included • Subject allocation pattern • Precision of picking “right dose” correctly • Power and Type I error for detecting dose-response • Precision of overall D-R estimation across all doses (measured by MSE)**Subject Allocation Pattern:ED75 centered within the dose**range (Curve ID 3)**Subject Allocation Pattern:ED75 shifted to the left of dose**range (Curve ID 5)**Subject Allocation Pattern:ED75 shifted to the right of dose**range (Curve ID 4)**Subject Allocation Pattern:Completely flat dose-response**(CurveID 8)**Power and Type I Error for Detecting Dose-Response*** *Power for D-R curve ID 1 is Type I error**MSE Efficiency Plots**Curve ID 3 (centered) Target dose is D3 Curve ID 5 (left-shifted) Target dose is between D2&D3**MSE Efficiency Plots (cont.)**Curve ID is 4 (right-shifted) target dose is D5 Curve ID is 8 (flat) target dose- NA**Summary of Bayesian Design Simulations**• In all 7 non-flat D-R scenarios, the design maximized allocations around the “true” ED75. • In case of flat D-R, most patients were allocated to max dose and placebo with very little in between • Type I error was preserved • Power to detect a dose-response is at least 90% • Power to detect a significant difference between the best dose and placebo is at least 89.5% • For all scenarios, AD design was uniformly more efficient than fixed design of the same sample size (measured by MSE ratio across doses )**Further Steps**• Simulations have shown that Bayesian AD design may adequately address the Ib study objectives: • A definitive single dose for Phase III was NOT needed • General idea about D-R needed: upper/lower plateau, sloping part • Due to absence of readily available software for crossover design, these computer simulations used N=120 in a parallel design setting • It was anticipated that similar results for power and Type 1 error could be obtained using N=30 subjects each contributing 4 measurements**Further Steps (cont.)**• Crossover-like framework preferable to parallel design framework • between/within subject variability => sample size considerations ( 30 vs. 120) • short drug half-life -> short washout period • Option 1: modify Bayesian design so that each subject can contribute multiple measurements • incorporate repeated-measures in modeling and simulations • Required involvement of external vendor and extra time to complete both simulator and randomizer • Option 2: consider true crossover design but change doses adaptively • Non-Bayesian approach • Could be accomplished in-house within approximately the same timeframe due to lower computational complexity • Can be reduced to “standard” crossover if no dose adjustment takes place**Adaptive Crossover Design Highlights**• Doses explored: {D1, …, D6} of Merck-X + pbo • Based on: 4 period crossover • Pbo + active doses A,B,C • Values of A, B, C are subset of {D1, …, D6} and change dynamically after each interim look (~twice weekly) • Time-to-endpoint + washout is 1 week • Decision rule: pick a subset of doses {A, B, C} from {D1, …, D6} based on (non-Bayesian) utility function • Utility function: cumulative score describing proximity of each dose to target ED75 according to current estimate of D-R • D-R estimation: based on isotonic regression model**Adaptive X-over Algorithm details: Score function**For each 3 dose combination, say {A,B,C}, the score is S(qA)+S(qB)+S(qC).**Adaptive X-over Algorithm details: Selection of 3-dose**combination Randomly select one of these 3 combinations and use until next adaptation.**Adaptive X-over Algorithm details: Interim D-R estimation**at usingisotonic regression 3 best dose combinations (based on proximity to ED75): 1. {3, 4, 5} 2. {3, 4, 6} 3. {3, 4, 7} Algorithm randomly choose one combination out of the 3 best combinations**Adaptive Cross-Over Design Performance Characteristics via**Simulations • Several D-R scenarios were explored • Allocation pattern: • similar to Bayesian design, the algorithm allocates subjects to the neighborhood of the effective and the highest sub-effective dose levels • N=60 patients adequate to achieve ~80% or better power for “best dose” vs. placebo comparison • Type I error is preserved • Caveat: • effect sizes were smaller than those explored for Bayesian AD • This contributed to sample size increase from N=30 (30 patients*4 obs.=120obs) for Bayesian AD to N=60 (60 patients*4 obs. =240 obs.) for the adaptive crossover design**Power for testing superiority of a dose level versus placebo**