1. Copyright © 2015 Actelion Pharmaceuticals Ltd CONFIDENCE INTERVALS FOR FUNCTIONS Anne Kümmel, Actelion Pharmaceuticals Ltd. 2015 – 07 – 16 BaselR

2. © 2015 Actelion Pharmaceuticals Ltd  Scenario: –Dose response is sigmoidal –All parameters have a variability of 0.2 s.d. (log-normal)  At which dose range will I observe a response of 50% of the maximal? OFTEN, THE RESULT OF A SIMULATION, NOT THE PARAMETER VALUE ITSELF IS THE KEY INTEREST MOTIVATION 14 Jul 2015 2

3. © 2015 Actelion Pharmaceuticals Ltd  Parameter estimation is a key tool for pharmacometric analysis of clinical data  Estimation software usually provides estimation error for the parameter estimates  How uncertain are the model predictions?  Implementation of a R framework to calculate confidence intervals for model functions –Different CI calculation methods –Single function for parameter estimation and confidence interval calculation –Any user-specified, closed-form models SUMMARY 3 14 Jul 2015

4. © 2015 Actelion Pharmaceuticals Ltd …. IS ONLY THE FIRST STEP UNCERTAINTY OF PARAMETER ESTIMATES 4 14 Jul 2015 ParameterEstimateRSE (%) E00.2971.9 Emax0.02632.3 EC507.4798.2  (hill coeffcient) 1.8791.9 Estimation error usually provided by estimation software Often based on the Fisher Information matrix to calculate the parameter variance- covariance matrix 

5. © 2015 Actelion Pharmaceuticals Ltd DIFFERENT METHODS FOR CI CALCULATION 5 14 Jul 2015

6. © 2015 Actelion Pharmaceuticals Ltd IMPLEMENTATION IN A SINGLE R FRAMEWORK 6 14 Jul 2015 Input parameters for parameter estimation and confidence calculation:  Error model ( errmod )  Estimation method ( estmethod )  Initial parameter estimates ( init )  Confidence interval (CI) calculation method ( CImethod )  Vector of independent variable values for which to calculate CI ( xsupport )

7. © 2015 Actelion Pharmaceuticals Ltd parameter.estimation() 1) Parameter estimation2) Confidence calculation3) Visualization R FRAMEWORK SETUP 7 14 Jul 2015 parameter.estimation.nls() parameter.estimation.nlm() CI.boot() CI.delta() CI.sim() CI.MC() plot.data.CI() calc.jacobian() calc.VarFun() est.nls() est.nlm()

8. © 2015 Actelion Pharmaceuticals Ltd EXAMPLE: ESTIMATION OF CI FOR DOSE RESPONSE CURVE 8 14 Jul 2015

9. © 2015 Actelion Pharmaceuticals Ltd COMPARISON OF DIFFERENT METHODS 9 14 Jul 2015 MethodCalculation time (s) Delta method0.32 Simulation (k=1000)0.92 MC simulation-estimation (k=1000)212.60 Bootstrap (k=1000)224.53

10. © 2015 Actelion Pharmaceuticals Ltd SINGLE-INTERFACE FRAMEWORK FOR DATA FITTING, CONFIDENCE AND PREDICTION INTERVAL CALCULATION SUMMARY 10 14 Jul 2015 Possible extensions: ODE model, function for prospective analysis, link to PFIM model library Alternatives which you are using?

11. © 2015 Actelion Pharmaceuticals Ltd THANK YOU. 11 14 Jul 2015