Modelling and simulation in the pharmaceutical industry Reflections

Modelling and simulation in the pharmaceutical industry Reflections from a statistician’s and engineer’s perspective Carl-Fredrik Burman, Ph. D, Assoc Prof Senior Principal Scientist Astra. Zeneca R&D Mölndal

Agenda • Seven theses about good modelling 1. It is about making better decisions 2. It is driven by the underlying question 3. It is based on applied sciences 4. It uses a diversity of information sources 5. It is not made unnecessarily complicated 6. It is a continuous process 7. It facilitates communication • Some thoughts on simulation • Concluding remarks 2 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Seven theses about good modelling • Based on Burman & Wiklund (Pharm Stat 2011) • The seven theses are partly overlapping • The intention is rather prescriptive than descriptive 3 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Are theses just saying the obvious? 4 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

1. Good modelling is about making better decisions

Don’t model unless you see which decision could be improved by your model 6 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Value of Modelling (Cf. Value of Information) • Data, information, models may have a larger or smaller value depending on the situation • • X D M V available data decision “modelling” value (in e. g. Swiss franc, or total patient benefit) • Value of Modelling = Vo. M = E[ V( D(X, M) ) ] E[ V( D(X) ) ] • Value only(? ) through changing the decision 7 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Value of Modelling A simple example • Value of Modelling = Vo. M = E[ V( D(X, M) ) ] E[ V( D(X) ) ] • Say that we have a pure go / no go (dichotomous!) phase III investment decision • If it’s pretty obvious that we should “go”, modelling doesn’t help • However, if this is a tough decision, modelling (e. g. predicting through biomarker-clinical endpoint relation, extrapolating over time and population) may be very valuable. • Frontload: Start modelling ph III before ph II investment 8 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Value of Modelling Example (cont’d) • Value of Modelling = Vo. M = E[ V( D(X, M) ) ] E[ V( D(X) ) ] • Say that we face a phase III investment decision that is not purely dichotomous, but concerns - Go / No Go - Dose selection - Population - Sample size • Then, all these may add more or less to the overall value • Highly dependent on specific situation 9 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Decision focus Don’t necessarily have to be one single decision • Useful to update model continuously (Thesis 6) • Series of decisions • Adaptive Programmes • Cross-over to new projects • Obvious for same indication • But trial data for one drug can sometimes help to give useful background information for completely different indications (variability, disease progression) 10 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

“Soft” but important? • (Too) many modellers have been vague about the aim of their work - Describe the system - Improve understanding - Write scientific papers -. . . • Modelling can be used for summarising information, predicting, gaining insights, etc. • However, the benefits of e. g. a ‘gained insight’ will be realised when the insight is reflected in an actual decision. 11 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Industry vs. Academia • I think the luxury of “non-purpose” modelling should sometimes be allowed - Cf. pure mathematics - but more often in academia 12 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

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2. Good modelling is driven by the underlying question

“All models are wrong, some are useful” George Box 15 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Don’t search for the ultimate model • “All models are wrong. . . ” A model cannot incorporate all available information and be capable of answering all relevant project questions. • “. . . some are useful” The usefulness depends on the purpose of modelling, on which decision we set out to support. • Fit for purpose The model should thus be tailored to the concrete project question (Thesis 5). 16 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Different objectives different models needed • Example 1: Testing overall placebo-controlled efficacy • Example 2: Is the drug less efficacious than a competitor drug in elderly? If so, where’s the cut-off? • Example 3: Dose adjustment possible based on age or pharmacokinetic exposure (that correlates with age) 17 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Need to understand the real question • Common consultancy experience: - Clients may ask the wrong question • The modeller should try to understand the overall context 18 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

3. Good modelling is based on applied sciences

Be a scientist, not a narrow-minded statistician! 20 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Modelling “Reality” Mathematics To me, modelling is about translating from the real problem to mathematics, and going back from a mathematical solution to a practical solution. 21 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

• Note! Modelling in my narrow sense is not about solving the mathematical problem! • Modelling process: - Understand the project problem - Formulate objective - Map reality onto mathematic - Solve mathematical problem - Translate back to give decision support - Check robustness - Communicate 22 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Good modelling requires the utilisation of several scientific areas, not only statistics • Statisticians often have excellent skill-sets for modelling work. • However, we may need to transcend traditional roles and eagerly seek to understand the essence of the project’s problem. • Think and act as scientists in a wider sense, focussed on providing useful decision support, irrespectively of what kind of methods that are needed. • Avoid “He that is skilled with a hammer tends to think everything’s a nail” • Collaborate! 23 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

4. Good modelling uses a diversity of information sources

Combining different information sources Several pieces to the puzzle • Often, we need several components, e. g. - Dose-response Time dependence Biomarker – clinical endpoint Variability (between patients, over time, day-to-day, measure-to-measure) • to build a useful model • Information needed will often come from different sources 25 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Different information sources • In-house randomised clinical trials • Pre-clinical data • Competitor data • Observational studies • Literature information • Expert knowledge • . . . 26 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Combining different information sources … to estimate a common parameter • Scientific insights needed to see the relevance of information • In principle, the Bayesian framework is readily applicable as it treats all types of uncertainties in the same way. • In-house design decisions can be guided by Bayesian decision theory, even if regulators and other costumers require frequentist analyses 27 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

5. Good modelling is not made overly complicated

Not overly complicated Ockham’s razor: “Pluralitas non est ponenda sine neccesitate” (“Entities should not be multiplied unnecessarily'‘) William of Ockham, 1285– 1347/49 “A model should be as simple as possible and yet no simpler” Albert Einstein, 1879 -1955 29 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Efficiency of modelling work • Don’t spend time on modelling that likely have ignorable impact on the decision problem. • The first question to ask is whether modelling is worthwhile, i. e. to assess whether the net ‘Value of Modelling’ is positive. 30 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Marginal Value of Modelling • How much effort to put into modelling? • Engineering: Quick and dirty! • Value of Modelling Vo. M = E[ V( D(X, M) ) ] E[ V( D(X) ) ] 31 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Example • Pharmacokinetics / pharmacodynamics (PK/PD) modelling can give great benefits. • However, if it’s clear that one single dose is sought, the PK component will typically not be important. • Why estimate f(PK(d)), when you only need f(d)? 32 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

6. Good modelling is a continuous process

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Continuous learning • A model made for one decision point can often be re-used, updated and applied to a later decision. • The ‘Learning Loop’ provides a description of the continuous modelling process and the interaction with (design) optimisations and information retrieval. • The greatest benefits will likely be achieved with ’model-based drug development’, where modelling is fully integrated in the process. 35 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

7. Good modelling facilitates communication

Transparency • Modelling is not a concern only for the quantitative scientists. • Modelling is not replacing the decisionmakers, but supporting them. 37 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Decision support • Present not only the optimal solution, but also • Assumptions • Robustness checks. • The ideal is that the decision-makers can challenge assumptions and interactively study the consequences of altering them. • Successful modelling processes provide major benefits in transparency within the teams regarding underlying assumptions, and facilitate communication with governance bodies and decision-makers. 38 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Some thoughts about simulation

Simulation A piece of cake? • We are considering “simple” clinical trial simulation, not e. g. MCMC • For most statisticians, it is trivial to simulate a simple clinical trials, with sufficient precision • However, many modelling problems are more complicated, including - a range of scenarios - multidimensional optimisation. • In our experience, simulation studies are often ineffective, leading to inadequate precision in results. 40 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Give confidence intervals for simulation results! 41 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Simulation Alternatives • Consider alternatives to simulation - analytic solutions - Numerical analysis - Approximations • In many cases, parts of the problem can be solved by such means, leaving a much simpler problem to stochastic simulations. 42 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Simulation Simplify • Don’t make your simulation model overly complicated! • Simulate sufficient statistics, not individual data • Approximate. E. g. central limit theorem. 43 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Simulation Reduce simulation variability • Simulations are often applied to compare the efficiency of competing designs, e. g. of a dose-finding trial. • Two designs with different doses can effectively be compared by using the same simulated residuals for both designs. • This can greatly reduce the variance of a difference of estimates. • A similar trick can be used when the doses are the same but different allocations (e. g. larger placebo group) are considered. 44 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Remember: Confidence intervals! 45 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Concluding remarks

The role of the pharma statistician • An arguably conservative attitude has served us well - Appropriate in the traditional core area: the analysis of (confirmatory) clinical trial data. • However, time they are a-changing. - An increasing importance on complex issues in programme design and decision support • To more effectively add value, statisticians need to adopt a more flexible mindset and be willing to embrace new, useful methodology. 47 Carl-Fredrik Burman | 13 Sept 2012 Global Medicines Development | Biometrics & Information Science

Which designs are possible? Alternative designs What do we know already? Modelling Where do we want to go? Optimise design, based on model & objectives Simulations / Computations Objectives

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