# The Use of a Probabilistic Sensitivity Analysis for Decision Making: The example of Drug- Eluting Stents

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1 The Use of a Probabilistic Sensitivity Analysis for Decision Making: The example of Drug- Eluting Stents Mark Sculpher, PhD Professor Centre for Health Economics University of York, UK Seminar at Harvard Clinical Research Institute, 17 th August 2004

2 Outline Rationale for probabilistic sensitivity analysis Overview of methods of PSA Case study drug eluting stents

3 Policy background Cost-effectiveness analysis increasingly used for health service decision making Important role for decision modelling Compare all relevant interventions Synthesise available evidence Extrapolation Generalisation Decision models can identify: Best option given available evidence Probability of making the wrong decision Value of additional research Part of the new NICE Reference Case

4 Uncertainty and variability Overall variability between patients 1 st order uncertainty Reflected in standard deviations associated with a mean value Parameter uncertainty 2 nd order uncertainty Uncertainty in mean parameter values Reflected in standard error of the mean Sub-group heterogeneity Base-line characteristics explain a proportion of overall variability between patients (e.g. age, sex) Generate mean parameter values per sub-group Variability within sub-group will remain Structural uncertainty Uncertainty regarding modelling assumptions

5 Parameter uncertainty Why probabilistic sensitivity analysis? Numerous parameters in decision models Each estimated with uncertainty Standard sensitivity analysis unwieldy Need to propagate joint parameter uncertainty in terms of decision uncertainty Quantification of decision uncertainty provides starting point for assessing the value of additional research In non-linear models, probabilistic models provide the only unbiased estimate of mean cost-effectiveness

6 Probabilistic sensitivity analysis Steps in the process Identify sources of parameter uncertainty Characterise uncertain parameters as probability distributions Define correlations as appropriate: Patient-level data Use of regression methods Propagate uncertainty through model using Monte Carlo simulation

7 Monte Carlo simulation Second order simulation (1) p Costs 1-p Costs Distribution of mean costs

8 Monte Carlo simulation Second order simulation (2) Live p1 C(L) ADE No ADE p2 1-p2 C(ADE) Costs: 300 Effects: 40 Costs: 220 Effects: 35 Costs: 420 Effects: 42 Costs: 380 Effects: 38 Costs: 250 Effects: 49 Die 1-p1 Costs: 290 Effects: 46 Costs: 350 Effects: 42 C(D)

9 Selecting distributions Universe of possible distributions available Often criticised as arbitrary But choice for a given distribution is relatively small Parametric choices are frequently made in statistics

10 Selecting distributions Commonly used distributions Parameters Probabilities Costs Utilities Relative risks Distribution Beta Log-normal Gamma Beta Gamma (1 U) Log-normal Details Between 0 and 1 Ranging from 0 to Minus to 1 Ratios Additive on log scale

11 Case-study study - background 2,100 deaths per million from coronary artery disease in UK one of the highest in the world 1.4 million suffer from angina in the UK Percutaneous coronary interventions (PCI) provide a major therapeutic option in patients resistant to medical therapy About 85% of PCIs now undertaken using coronary stents in the UK Restenosis is a common problem with PCI Drug eluting stents have been shown to reduce restenosis Can their acquisition cost be justified?

12 Case-study study - objectives To assess the cost-effectiveness of sirolimus-eluting stent (CYPHER TM ) compared to bare metal stents Based on treatment effects taken from three randomised trials Express health benefits in terms of quality-adjusted lifeyears Assess variation in cost-effectiveness by patient characteristics Use probabilistic sensitivity analysis to assess decision uncertainty

13 Key methods Base-case assumption of no differential effect on mortality QALY decrement through restenosis: symptomatic time waiting for further revascularisation Time horizon of 12 months based on trial follow-up Health service (payer) perspective

14 Source of data on treatment effects Trial characteristic Ravel E-SIRIUS SIRIUS Sample size Diabetes mellitus (%) Multi-vessel disease (%) Reference vessel diameter (mm, mean ± SD) 2.62 ± ± ± 0.47 Length of lesion (mm, mean ± SD) 9.58 ± ± ± 5.8

15 Key data inputs treatment effects Input RAVEL E-SIRIUS SIRIUS Sirolimus Bare metal Sirolimus Bare metal Sirolimus Bare metal Further procedures (target lesions) - PCI 1/120 (0.008) 18/118 (0.153) 8/175 (0.046) 42/177 (0.237) 40/533 (0.075) 130/525 (0.248) - CABG 1/120 (0.008) 0/118 (0.000) 1/175 (0.006) 4/177 (0.023) 8/533 (0.015) 16/525 (0.030) MI 4/120 (0.033) 6/118 (0.051) 8/175 (0.046) 4/177 (0.023) 16/533 (0.030) 18/525 (0.034)

16 Other key data inputs Input Value Cost of Sirolimus-eluting stent 1,762 Cost of bare metal stent 1,145 Cost of PCI 2,984 Cost of CABG 6,450 Utility without symptoms 0.84 ± 0.16 Utility with symptoms 0.69 ± 0.20 Waiting times for revascularisation (Days) 196

17 Base-case results Input RAVEL E-SIRIUS SIRIUS Difference in costs Difference in QALYs ICER 15,198 3,181 7,461

18 Probabilistic sensitivity analysis RAVEL Trial Ravel - Equal Death Ravel - Equal Death Incremental QALYs Standard Sirolimus-Eluting Probability Cost-Effective Sirolimus-Eluting Standard Incremental cost Monetary Value of a QALY

19 Probabilistic sensitivity analysis E-SIRIUS Trial esirius - Equal Death esirius - Equal Death Incremental QALYs Standard Sirolimus-Eluting Probability Cost-Effective Sirolimus-Eluting Standard Incremental cost Monetary Value of a QALY

20 Probabilistic sensitivity analysis SIRIUS Trial Sirius - Equal Death Sirius - Equal Death Incremental QALYs Standard Sirolimus-Eluting Probability Cost-Effective Sirolimus-Eluting Standard Incremental cost Monetary Value of a QALY

21 Further sub-group analysis Sub-Groups Sub-group 1 Diabetics Non-diabetics Sub-group 2 Long lesions Non-long lesions Sub-group 3 Small vessel disease Non-small vessel disease ICERs 2,848 10,432 30,864 DES dominates 5,569 8,746

22 Alternative assumptions about mortality Ravel - Equal Death Ravel - Cardiac Death Probability Cost-Effective Sirolimus-Eluting Standard Probability Cost-Effective Sirolimus-Eluting Standard Monetary Value of a QALY Monetary Value of a QALY ICER = 15,198 ICER = 1,674

23 Conclusions Based on 12-month trial data, reduction in restenosis results in cost offset to acquisition of DES Reduction in restenosis has a impact of quality of life Waiting times for procedures one way to capture these effects DES appears cost-effective based on standard NICE thresholds Decision uncertainty: 0.8 to 0.42 depending on trial and assuming equal mortality ICERs (and uncertainty) sensitive to assumptions about mortality

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