Workshop on Patient Level Simulation Modelling

1. Workshop on Patient Level Simulation Modelling Welcome and Introduction Sheffield Experiences of Patient Level Simulation Alan Brennan and Jim Chilcott, HEDS, ScHARR, CHEBS

2. Purpose of Today / Focus Fortnight • When do we need a “patient level model” rather than a “simpler cohort model”? • How many simulations? • patient level (“1st order”) for convergence; • To investigate parameter uncertainty in probabilistic sensitivity analysis (“2nd order”) • When are ‘emulators’ helpful e.g. to replace the computationally expensive patient level simulation model with an analytic formula

3. Speakers • 10.30 Alan Brennan and Jim Chilcott • 11:00 Ruth Davies, Warwick “5 minute” break • 12:00 Steve Chick, INSEAD 1pm Lunch Break • 2:00 Pelham Barton, Birmingham • 3:00 Simon Eggington, ScHARR, Sheffield • 3:30 Marc Kennedy, Sheffield 4pm Round Up Discussion Questions throughout Slides on www….

4. Health Economics Context • Assess value of policies / health technologies • Compare mean utility gain (QALYs) versus current care for population • Calculate incremental cost per QALY gained • Choose option with max expected net benefit (threshold * Q – C) • Assess uncertainty by varying parameters

5. Influences on model structure (‘in real’) • Conceptual model of disease + patient pathways • Published evidence on epidemiology, effectiveness, utilities, costs • Often defines health states • Form of available data e.g. • Individual level time in each health state • Cross sectional ‘census’ of numbers • Average ‘response’ or ‘relative risk’ plus confidence intervals • Tool-kit available to the analyst

6. Sheffield Experience of Patient Level Simulation • Service Planning Models e.g. • East Anglia Ambulances • Call arrival rates, Ambulances crew roster, • Travel and service times • Performance by ‘zone’ over a week (8 mins target) • Theatre ~ Bed Simulation • Weekly theatre schedule by case mix • Minutes in theatre/recovery and days in hospital bed • % theatre over-run and % over bed capacity

7. Health Economic Models (1) Osteoporosis • Complex pathway and time dependent prognosis • Future risk of fracture dependent on …previous hip, wrist, vertebral, other fractures, age, sex, duration on treatment, duration since fracture • ‘feedback’ i.e. risks increase given events • Utility dependent also on nursing home admission • Expected discounted Lifetime Cost and QALYs • Annual time periods and probabilities of transtion to next health states • Stevenson et al. HTA report(s) + Journal of OR Society • Some Markov ‘competitor’ models

8. Health Economic Models (2) Rheumatoid Arthritis • Sequences of treatment, tracking of disability score • Future disability dependent on … • extent of improvement given treatment, • duration of successful response, • response to next line therapy in a sequence etc ….. • Mortality risk may depend on disability score • Expected discounted Lifetime Cost and QALYs • 6 monthly. Probabilities of response /withdrawal • Rheumatology 2003;42:1–13. Modelling the cost-effectiveness of etanercept in adults with rheumatoid arthritis in the UK. A. Brennan, N. Bansback, A. Reynolds and P. Conway • Some Markov (drug / disability band) , some patient level ‘competitor’ models

9. Health Economic Models (3) Type II Diabetes • Multiple disease states, sequences of treatment and time dependent prognosis • Future risk of heart disease, stroke, retinopathy, neuropathy and renal disease dependent on …previous events, Hba1c over past years, cholesterol, blood pressure, age, sex, improvement given treatment, persistence or withdrawal, adherence ….. • Expected discounted Lifetime Cost and QALYs • Annual time periods and probabilities of transition to next health states in 5 parallel disease models • Chilcott JB, Whitby SM, Moore R. Clinical impact and health economic consequences of posttransplant type 2 diabetes mellitus. Transplantation Proceedings 2001 Aug;33(5A Suppl):32S-39S • Mostly patient level ‘competitor’ models

10. Diabetes: Interaction between metabolic variables + co-morbidities Nephropathy Hypertension Blood pressure Stroke Coronary Heart Disease Total Cholesterol Neuropathy Hyperglycaemia (blood sugar) Hba1c Retinopathy

11. Simplified Algorithm Algorithm includes therapy targets

12. Rationale for Patient-Level Diabetes Model (1) • Type 2 diabetes affects a wide range of patients, i.e. use policy model for subgroup analysis • diagnosed at 40 or 60, • existing cardiovascular disease, • Smoker v non smoker, • some have large metabolic disorders, • others are newly diagnosed, • Substantial evidence on risk of complications, e.g. • UKPDS CHD risk engine (logistic regression model) • Eastman risk equations for retinopathy

13. Rationale for Patient-Level Diabetes Model (2) • Risk is not linear with risk factors – most relationships are exponential (some strongly) • Covariance between some of the characteristics, • older patients more likely to have diabetes for longer duration • metabolic abnormalities tend to cluster • blood pressure varies according to gender • Interaction between metabolic variables and size of response to therapy • RESULT : the average of risks is not same as the risk for the patient with ‘average’ characteristics

14. Health Economic Models (4) Others • Patient Level • Venous Leg Ulcers • Breast Cancer • Deep Vein Thrombosis • Cohort • Multiple Sclerosis • Bowel Cancer Screening • Carotid Stenosis Assessment • Anti-platelet therapy

15. When do we need a “patient level model” issues • We are refining the question this fortnight e.g. • Discrete time individual patient simulation versus discrete event (continuous time) individual but interacting patient simulation • More than one way to represent Markovian behaviour in a “simpler cohort model” • Other model frameworks e.g. systems dynamics flows • Some criteria are easy • Interacting time dependent patient prognosis • Competing for resources and undergoing waiting time • Explosion of hundreds of thousands of states

16. When do we need a “patient level model” issues • Markov criteria mean must have • Probability of transition depends only on current state • Constant rate of transition per period, implying exponential survival time in state • Note, there are rules for appropriate cycle length • But there is some Markov flexibility • Merged states or phasing can help generalise beyond exponential survival time in state • Many models have time dependent transition probabilities i.e. different in period 1 to period 2

17. When do we need a “patient level model” issues • The hardest question (for me anyway) • OK, there is the concept that complex event histories with prognosis depending on the accumulated history means that a patient level model is necessary. • But …… What if you simplify • e.g. use Markov assumptions knowing they may be wrong but thinking it ‘will all come out in the wash’ • Can you know a priori when such simplification will work i.e. give the correct (same) decision as the full individual level model

18. When do we need a “patient level model” issues • And what about hybrids? • In fact all 3 models above have some level of individual variability built in • But … some parameters attached to the simulated individual are estimates of population means e.g • utility of diabetic health states • Annual cost associated with Rheumatoid disability score • .

19. How many simulations? issues • In practice, we use 10,000 patients (1st order) because it seems enough to reduce variability in mean QALY • However, when treatments are close (i.e. QALY difference is small) we have used more

20. How many simulations? issues • In health economic modelling Probabilistic sensitivity Analysis (PSA) is usually done using 1,000 or 10,000 simulations allowing the uncertain parameters to vary across their plausible ranges by Monte Carlo sampling from their defined prior distributions • So do we need 1,000 (2nd order) x 10,000 (1st order) = 10 million model runs to get a CEAC ? • The mathematics of the optimum balance between 1st order and 2nd order is under investigation by Tony O’Hagan (does not like the terminology 1st and 2nd order)

21. Emulators • The challenge of undertaking PSA for the Osteoporosis model that led us to Emulators and Gaussian Processes • The process involved …. • Producing 100 or 200 runs of the model with 10,000 simulated patients in each (i.e. 100 hours). • Allowing Jeremy Oakley to fit a Gaussian Process emulator to approximate the results of the individual patient level model for any set of input parameters • Programming the function into EXCEL, then doing 10,000 runs over uncertain parameters to undertake PSA and draw the CEAC • Stevenson et al. Medical Decision Making 2003

22. Software we have used • Visual Basic (VBA) with EXCEL front end • Simul8 • R

23. Aside: Bayesian Clinical Trial Programme Simulation • Given current therapy uncertainty you can model • patients in a clinical trial of sample size n • simulated trial outputs and the decision algorithm for moving to next stage e.g. phase II • Phase II probability of success conditional on previous stage success etc. • Similarly Phase III and hence regulatory approval

24. Recommendations • Attend this workshop…….. • Join the OR Society ! • Read Pidd, Law and Kelton • Go to the conferences