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Μπευζιανης ➭ ε θ οδων στην οικονο ➭ ια της υγειας (thanks/blame mostly to Google Translate) Gianluca Baio University College London Department of Statistical Science g.baio@ucl.ac.uk http://www.ucl.ac.uk/statistics/research/statistics-health-economics/ http://www.statistica.it/gianluca https://github.com/giabaio Research Seminars Department of Statistics Athens University of Economics and Business, Athens Thursday 3 May 2018 Gianluca Baio (UCL) Bayesian methods in health economics Seminar AUEB, 3 May 2018 1 / 36

Outline 1. Health economic evaluation – What is it? – How does it work? 2. Statistical modelling – Individual-level vs aggregated data – The importance of being a Bayesian 3. Some examples — you get to choose... – Individual level & partially observed data – Survival analysis in HTA – Value of information 4. Conclusions Gianluca Baio (UCL) Bayesian methods in health economics Seminar AUEB, 3 May 2018 2 / 36

Outline 1. Health economic evaluation – What is it? – How does it work? 2. Statistical modelling – Individual-level vs aggregated data – The importance of being a Bayesian 3. Some examples — you get to choose... – Individual level & partially observed data – Survival analysis in HTA – Value of information 4. Conclusions Gianluca Baio (UCL) Bayesian methods in health economics Seminar AUEB, 3 May 2018 2 / 36

Outline 1. Health economic evaluation – What is it? – How does it work? 2. Statistical modelling – Individual-level vs aggregated data – The importance of being a Bayesian 3. Some examples — you get to choose... – Individual level & partially observed data – Survival analysis in HTA – Value of information 4. Conclusions Gianluca Baio (UCL) Bayesian methods in health economics Seminar AUEB, 3 May 2018 2 / 36

Outline 1. Health economic evaluation – What is it? – How does it work? 2. Statistical modelling – Individual-level vs aggregated data – The importance of being a Bayesian 3. Some examples — you get to choose... – Individual level & partially observed data – Survival analysis in HTA – Value of information 4. Conclusions Gianluca Baio (UCL) Bayesian methods in health economics Seminar AUEB, 3 May 2018 2 / 36

Health technology assessment (HTA) Objective : Combine costs & benefits of a given intervention into a rational scheme for allocating resources Gianluca Baio (UCL) Bayesian methods in health economics Seminar AUEB, 3 May 2018 3 / 36

Health technology assessment (HTA) Objective : Combine costs & benefits of a given intervention into a rational scheme for allocating resources Statistical model Estimates relevant population • parameters θ Varies with the type of • available data (& statistical approach!) Gianluca Baio (UCL) Bayesian methods in health economics Seminar AUEB, 3 May 2018 3 / 36

Health technology assessment (HTA) Objective : Combine costs & benefits of a given intervention into a rational scheme for allocating resources ∆ e = fe ( θ ) ∆ c = fc ( θ ) . . . Statistical Economic model model Estimates relevant population • Combines the parameters to obtain • parameters θ a population average measure for costs and clinical benefits Varies with the type of • available data (& statistical Varies with the type of available • approach!) data & statistical model used Gianluca Baio (UCL) Bayesian methods in health economics Seminar AUEB, 3 May 2018 3 / 36

Health technology assessment (HTA) Objective : Combine costs & benefits of a given intervention into a rational scheme for allocating resources ∆ e = fe ( θ ) ICER = g (∆ e, ∆ c ) ∆ c = fc ( θ ) EIB = h (∆ e, ∆ c ; k ) . . . . . . Decision Statistical Economic analysis model model Estimates relevant population Summarises the economic model • Combines the parameters to obtain • • parameters θ by computing suitable measures of a population average measure for “cost-effectiveness” costs and clinical benefits Varies with the type of • available data (& statistical Dictates the best course of Varies with the type of available • • approach!) actions, given current evidence data & statistical model used Standardised process • Gianluca Baio (UCL) Bayesian methods in health economics Seminar AUEB, 3 May 2018 3 / 36

Health technology assessment (HTA) Objective : Combine costs & benefits of a given intervention into a rational scheme for allocating resources Assesses the impact of uncertainty (eg in • parameters or model structure) on the Uncertainty economic results analysis Mandatory in many jurisdictions (including • NICE, in the UK) Fundamentally Bayesian! • ∆ e = fe ( θ ) ICER = g (∆ e, ∆ c ) ∆ c = fc ( θ ) EIB = h (∆ e, ∆ c ; k ) . . . . . . Decision Statistical Economic analysis model model Estimates relevant population Summarises the economic model • Combines the parameters to obtain • • parameters θ by computing suitable measures of a population average measure for “cost-effectiveness” costs and clinical benefits Varies with the type of • available data (& statistical Dictates the best course of Varies with the type of available • • approach!) actions, given current evidence data & statistical model used Standardised process • Gianluca Baio (UCL) Bayesian methods in health economics Seminar AUEB, 3 May 2018 3 / 36

1. (“Standard”) Statistical modelling — Individual level data Demographics HRQL data Resource use data Clinical outcome ID Trt Sex Age . . . u 0 u 1 . . . u J c 0 c 1 . . . c J y 0 y 1 . . . y J 1 1 M 23 . . . 0.32 0.66 . . . 0.44 103 241 . . . 80 y 10 y 11 . . . y 1 J 2 1 M 21 . . . 0.12 0.16 . . . 0.38 1 204 1 808 . . . 877 y 20 y 21 . . . y 2 J 3 2 F 19 . . . 0.49 0.55 . . . 0.88 16 12 . . . 22 y 30 y 31 . . . y 3 J . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . y ij = Survival time, event indicator (eg CVD), number of events, continuous measurement (eg blood pressure), . . . u ij = Utility-based score to value health (eg EQ-5D, SF-36, Hospital Anxiety & Depression Scale, . . . ) c ij = Use of resources (drugs, hospital, GP appointments, . . . ) Gianluca Baio (UCL) Bayesian methods in health economics Seminar AUEB, 3 May 2018 4 / 36

1. (“Standard”) Statistical modelling — Individual level data Demographics HRQL data Resource use data Clinical outcome ID Trt Sex Age . . . u 0 u 1 . . . u J c 0 c 1 . . . c J y 0 y 1 . . . y J 1 1 M 23 . . . 0.32 0.66 . . . 0.44 103 241 . . . 80 y 10 y 11 . . . y 1 J 2 1 M 21 . . . 0.12 0.16 . . . 0.38 1 204 1 808 . . . 877 y 20 y 21 . . . y 2 J 3 2 F 19 . . . 0.49 0.55 . . . 0.88 16 12 . . . 22 y 30 y 31 . . . y 3 J . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . y ij = Survival time, event indicator (eg CVD), number of events, continuous measurement (eg blood pressure), . . . u ij = Utility-based score to value health (eg EQ-5D, SF-36, Hospital Anxiety & Depression Scale, . . . ) c ij = Use of resources (drugs, hospital, GP appointments, . . . ) Compute individual QALYs and total costs as 1 J J ( u ij + u ij − 1 ) δ j � � � � with: δ j = Time j − Time j − 1 e i = and c i = c ij , 2 Unit of time j =1 j =0 1.0 0.8 Quality of life (scale 0-1) QALY i = “Area under the curve” 0.6 0.4 δj 0.2 uij + uij − 1 2 0.0 0 2 4 6 8 10 Time (years) Gianluca Baio (UCL) Bayesian methods in health economics Seminar AUEB, 3 May 2018 4 / 36

1. (“Standard”) Statistical modelling — Individual level data Demographics HRQL data Resource use data Clinical outcome ID Trt Sex Age . . . u 0 u 1 . . . u J c 0 c 1 . . . c J y 0 y 1 . . . y J 1 1 M 23 . . . 0.32 0.66 . . . 0.44 103 241 . . . 80 y 10 y 11 . . . y 1 J 2 1 M 21 . . . 0.12 0.16 . . . 0.38 1 204 1 808 . . . 877 y 20 y 21 . . . y 2 J 3 2 F 19 . . . 0.49 0.55 . . . 0.88 16 12 . . . 22 y 30 y 31 . . . y 3 J . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . y ij = Survival time, event indicator (eg CVD), number of events, continuous measurement (eg blood pressure), . . . u ij = Utility-based score to value health (eg EQ-5D, SF-36, Hospital Anxiety & Depression Scale, . . . ) c ij = Use of resources (drugs, hospital, GP appointments, . . . ) Compute individual QALYs and total costs as 1 J J ( u ij + u ij − 1 ) δ j � � � � with: δ j = Time j − Time j − 1 e i = and c i = c ij , 2 Unit of time j =1 j =0 (Often implicitly) assume normality and linearity and model independently 2 individual QALYs and total costs by controlling for baseline values e i = α e 0 + α e 1 u 0 i + α e 2 Trt i + ε ei [+ . . . ] , ε ei ∼ Normal (0 , σ e ) c i = α c 0 + α c 1 c 0 i + α c 2 Trt i + ε ci [+ . . . ] , ε ci ∼ Normal (0 , σ c ) Gianluca Baio (UCL) Bayesian methods in health economics Seminar AUEB, 3 May 2018 4 / 36