Why the MRC-BSU is a great place to learn your trade! Richard Nixon Advanced Quantitative Sciences | Economic Modeling David Ohlssen Integrated Information Science | Statistical Methodology Medical Research Council Conference on Biostatistics in celebration of the MRC Biostatistics Unit's Centenary Year Our backgrounds From MRC-BSU to Novartis Richard Nixon David Ohlssen MRC-BSU: Ph.D. with Stephen MRC-BSU: Ph.D. with Linda Duffy (3 years) • Applying Bayesian Random effects models to cluster randomized trials and evidence synthesis MRC-BSU: Post doc with Simon Thompson (6 years) • Statistical issues in health economic assessment Novartis: Economic modeling (7 years) • Decision Analysis • Health Economics • Structured Benefit-risk Sharples (3 years) • Applying Bayesian methods to assessment of healthcare providers MRC-BSU: Post doc with David Spiegelhalter (3 years) • Bayesian model diagnostics for DAGs Novartis: Statistical methodology (7 years) • Trial design (Bayesian and frequentist) • Dose response modeling • Advisory committee preparation | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Role and impact of biostatistics in drug development Shaping and influencing decision-making A successful statistician working in drug development is a translational scientist who • Understands a problem • Translates it to a model • Communicates back the results These skills go beyond the technical skills • Ability to think strategically • Ability to ask the right questions, probe, challenge, listen • Ability to influence decision-making of partners • Ability to work in a cross-functional team • Ability to communicate concisely internally and externally | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Our time and the MRC-BSU gave us in these skills The BSU sits at the sweet spot between methodology and application Generic methodology comes about from real world examples • Reoccurring issues are discovered when working on real problems • Robust statistical methodology developed to address real problems Many of the translational modeler skills, needed to work on real world application, are tacit • We learned from season experts how to approach a problem, and tools to solve it • Reading a polished solution in a paper hides the process of getting there | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Using Decision Analysis to choose a strategy for a trial interim adaptation Drug development is complex and quantitative There are many decisions which statistical methodology can support Drug development involves complex, high value decisions • Decisions are made in the context of uncertainty • Information comes from many different sources • A decision making team needs to structure and synthesize all this information People are good at “thinking fast”, and making decisions in the moment, but there are many physiological pitfalls when making complex decisions Decision Analysis gives a set of tools for structuring and analyzing decisions | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Components of Decision Quality1 What we can do? • Define a set of doable alternatives Decisions to be made What do we know? • Parameters describing the process we are modeling • Observable outcomes Uncertainties • Statistically these are random variables What do we want? • Clear values and trade-offs Values • Statistically these are utilities 1 Ron Howard. The Foundations of Decision Analysis Revisited, in Advances in Decision Analysis 2007 | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Problem statement and action taken Build a decision analysis model to assess protocol amendment Interim data suggests a post-marketing study is under powered. • Study was powered to demonstrate non-inferiority of new drug to standard-of-care with regard to an event rate. • Power calculations assumed the event rate per patient per year is 1.1. • Blinded interim data suggests event rate will 0.59 at the end of the study. This would reduce the power of the study to 57%. Build a decision model to assess different strategies for a protocol amendment. • Build a model to predict events from patient characteristics and seasonality. • Integrate information from interim data, study cost data and market forecasting model. • Assess the effect of different strategies on values. Sample size Exposure time Flexible exposure Patient enrichment | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Power Cost Time to LPLV eNPV Strategies Decision Analysis Begin with identifying representative alternative courses of action Sample size Exposure (years) Exposure Inclusion criteria Baseline 1 Baseline 2 Baseline CD Baseline 4 3500 1 Fixed 50 All All All 4000 1.5 Flexible 60 Severe (coded as 0) Yes Yes 4500 2 40 5000 5500 Pick one option from each column, e.g. • Increase sample size • Increase exposure to 1.5 years • Change inclusion criteria so must be treated with concomitant drug at baseline | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Probabilistic dependence Influence diagram Information Decisions Value Forecasting Patient share increase given success Event prediction model Interim # events (season, patient) Events Market size (region) Combined # events (season, patient) Inclusion criteria (new patients) Patient share (region) New event rate (season, patient) Recruitment Current recruit rate/site (region) New recruit rate/site (region) Power Interim person-years (region, season, pat) Person-years Comb person-years (region, season, pat) Number of sites (region) New recruit rate (region) Time LPLV New person-years (region, season, pat) Drop out rate Total sample size Exposure time (all patients) Cost/patient/month (region) | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Cost Incremental eNPV Event prediction model Pooled Phase III data is fitted by random effects Poisson regression i = patient, j=country, s = season Number of events Yis ~ Po( is ) Season effect Person-years Treatment group indicator Covariates m p k 1 l 1 log( is ) i j ( i ) s k Zik l X il log(Tis ) i j ~ N (0, 2 ) Patient random effects ~ N (0, c2 ) Country random effects Protocol plans to model data with a Negative Binomial distribution • This can be written as a Poisson distribution with a different mean for each patient, and a gamma random effect distribution between patients • The above parameterization is an approximation of this as it uses normal random effects | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 One way sensitivity analysis How event rate and power are affected by Decisions Increasing sample size by 70% has much more effect on power than doubling the exposure time Enrichment only increases power by a small amount | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Multi way sensitivity analysis Full sensitivity analysis on the four most influential decisions The current design is the top left panel • The power for a sample size of 3500 and exposure of 1 year is 57% Strategies that bring the power to 80% Sample size Exposure (years) Flexible exposure Inclusion criteria CD 6000 1 No All 4400 2 No All 4750 1 Yes All 5500 1 No Yes 4100 2 Yes All 4200 2 No Yes 3800 2 Yes Yes Other strategies to consider • Current design • Stop the study at 2500 patients • Just increasing exposure to 2 years • Just using flexible design | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Evaluate each strategy Value Which strategies are on the efficient frontier? Cost and time to LPLV are show on the axes, and power is given in () brackets Consider all the strategies with 80% power • Those in the red area are dominated by another strategy. i.e. another strategy is either cheaper for the same time, or quicker for the same cost, or both cheaper and quicker. Evaluate the strategies not in the red in terms of eNPV | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Net sales and incremental expected net present value (eNPV) Product share over time for the UK 2348 fails Product share over time in UK 2348 succeeds Treated patients patients over time for the UK in UK Treated over time 2200 2000 Product share Treated patients (1000's) 0.08 1800 0.06 0.04 0.02 1600 0.00 2010 2015 2020 Label change time 2010 2015 Year | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 2020 Year Sensitivity analysis How does % increase in net sales given study succeeds (shows noninferiority) affect eNPV Incremental eNPV = (Expected net sales – cost of study) – net sales if don’t do study. • If this is positive then the money spent on the study is more than compensated for in increased sales. The line at the top for a given (relative) % product share increase is the optimal strategy % Product share increase if successful Strategy 0 – 25 % Stop study 25 – 45% Flex >45% Sample size & flex | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Why the MRC-BSU is a great place to learn your trade! 1. Working with leading experts 2. Focus on real problems 3. Understanding a simple method before moving to a more complex one 4. Applying Bayesian statistics | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Exploring treatment effect heterogeneity using Funnel plots | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Funnel plot by health authority reviewer | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Alternative version | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Prediction from Bayesian models Thanks to Roland Fisch | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Introduction Objective and Problem Statement Design a study with a control arm / treatment arm(s) Use historical control data in design and analysis Ideally: smaller trial comparable to a standard trial Used in some of Novartis phase I and II trials Design options • Standard Design: “n vs. n” • New Design: “n*+(n-n*) vs. n” with n* = “prior sample size” How can the historical information be quantified? How much is it worth? | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 The Meta-Analytic-Predictive Approach Framework and Notation Y1 Y2 Y1,..,YH Historical control data from H trials YH 1,…, H Control “effects” (unknown) 2 ? ‘Relationship/Similarity’ (unknown) no relation… same effects 1 ? * H * Effect in new trial (unknown) Design objective: [ * | Y1,…,YH ] Y* Y* Data in new study (yet to be observed) | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Example – meta-analytic predictive approach to form priors Application Random-effect meta-analysis prior information for control group in new study, corresponding to prior sample size n* | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Bayesian setup-using historical control data Meta Analysis of Historical Data Study Analysis Drug Placebo Observed Control Response Rates Prior Distribution of Control Response Rate Historical Trial 1 Observed Control data Prior Distribution of drug response rate Observed Drug data Historical Trial 2 Historical Trial 3 Historical Trial 4 Historical Trial 5 MetaAnalysis Predictive Distribution of Control Response Rate in a New Study Bayesian Analysis Posterior Distribution of Control Response Rate Posterior Distribution of Drug Response Rate Historical Trial 6 Historical Trial 7 Posterior Distribution of Difference in Response Historical Trial 8 | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Utilization in a quick kill quick win PoC Design ... ≥ 70% ... ≥ 50% ... ≥ 50% 1st Interim 2nd Interim Final analysis Positive PoC if P(d ≥ 0.2)... Negative PoC if P(d < 0.2)... ... ≥ 90% ... ≥ 90% With N=60, 2:1 Active:Placebo, IA’s after 20 and 40 patients First interim Second interim ... > 50% Final Overall power Stop for efficacy Stop for futility Stop for efficacy Stop for futility Claim efficacy Fail 0 1.6% 49.0% 1.4% 26.0% 0.2% 21.9% 3.2% d = 0.2 33.9% 5.1% 27.7% 3.0% 8.8% 21.6% 70.4% d = 0.5 96.0% 0.0% 4.0% 0.0% 0.0% 0.0% 100.0% Scenario d= With pPlacebo = 0.15, 10000 runs | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 General Background: EMA Concept Paper on Extrapolation EMA produced a “Concept paper on extrapolation of efficacy and safety in medicine development”: A specific focus on Pediatric Investigation Plans : ‘Extrapolation from adults to children is a typical example ...’ Bayesian methods mentioned: • ‘could be supported by 'Bayesian' statistical approaches’ Alternative Approaches: - No extrapolation: full development program in the target population. - Partial extrapolation: reduced study program in target population depending on magnitude of expected differences and certainty of assumptions. - Full extrapolation: some supportive data to validate the extrapolation concept. | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Extrapolation and Validation Based on ideas from Bayesian model diagnostics Extrapolation step • Posterior predictive distributions (PPD): Predict outcomes of study regimens matching the ones in the available paediatric studies Validation step: Posterior Predictive Check (Full cross validation) • “confirm the predicted degree of similarity … in clinical response (efficacy, …)” (EMA Concept Paper on Extrapolation). • Overlay PPDs with observed incidence rates Priors Sensitivity and exploratory analyses 28 | Presentation Title | Presenter Name | Date | Subject | Business Use Only Adult data Bayesian meta-analytic predictive approach Model Mixed effect logistic regression model Yi ~ Binomial( Ni , πi ) logit( πi ) = μ + i + xi β Study i, Yi = number of events, Ni = number of patients, πi = event rate • μ: intercept • i ~ N(0, σ2): random study effect • xi : design matrix (Study level covariates) | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 DAG Adult data Bayesian meta-analytic predictive approach σ n * μ i x* yobs Yrep β ni YH yi | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 xi Summary why the MRC-BSU is a great place to learn your trade! 1. Working with leading experts 2. Focus on real problems 3. Understanding a simple method before moving to a more complex one 4. Applying Bayesian statistics | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 BACK UP | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Divide and conquer Break it down, understand it, and put it back together “The spirit of decision analysis is divide and conquer: decompose a complex problem into simpler problems, get one’s thinking straight on these simpler problems, paste these analyses together with logical glue, and come out with a program of action for the complex problem” -- Howard Raiffa | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 One way sensitivity analysis How time to LPLV and cost are affected by Decisions Increasing sample size has less effect on time to LPLV than increasing exposure, but costs more Changing the inclusion criteria to only recruit patients taking concomitant drug has the least effect on time to LPLV | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014 Multi-way sensitivity analysis Explore the interactions between the most influential decisions One way sensitivity analysis shows that increasing power while minimizing the effect on time to LPLV and cost is best achieved by • Increasing the sample size • Increasing the exposure time • Using a flexible exposure design • Enriching by including patients taking concomitant drug at baseline rather than by selecting patients on other baseline characteristics Explore the interactions between these four decisions in a multi-way sensitivity analysis | Why the MRC-BSU is a great place to learn your trade! | Richard Nixon & David Ohlssen | March 2014
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