Alcohol and hospital admissions for injury and alcohol poisoning in West Sussex– a second order Monte Carlo simulation Ross Maconachie Public Health WSCC

Cost Effectiveness and ICERS Incremental economic evaluations are designed to answer the question: “What is the difference in costs and the difference in consequences of option A compared to option B?” Incremental Cost Effectiveness Ratio (ICER) is ICER = ∆C/∆E N S E W Threshold ICER Dominates Dominated CE Not CE NW quadrant is never cost effective SE quadrant is always cost effective NE depends on willingness to pay SW depends on willingness to accept

Decision Trees Used for short term costs and outcomes modelling, e.g. acute disease Probability of each branch of the tree is calculated from literature then costs and outcomes are “rolled back” to calculate difference in arms. Difference between the arms is used to calculate an Incremental Cost Effectiveness Ratio

Calculating Costs and Outcomes of Different Options Using a Decision Tree Rules Probabilities branching from each node must add up to 1 Costs and outcomes are placed at each node The probability of a given branch of a tree occurring is the product of all the probabilities along the branch

Exercise Decision to give Warfarin or not for patients with cardiomyopathy Patients have a probability to have an embolism, which is significantly reduced if they take warfarin but the drug produces a probability to have a bleeding incident Use the data below to calculate the difference in costs and QALYs between the warfarin and no warfarin arms of the trial Base case parameters ProbabilitiesP no warfarin probability of embolism0.09 warfarin probability of embolism0.017 warfarin probability of bleeding incident0.045 OutcomesQALY QALY for no warfarin embolism2.3 QALY for no warfarin no embolism4.5 QALY for warfarin embolism bleed1.8 QALY for warfarin no embolism bleed4 QALY for warfarin embolism no bleed2.3 QALY for warfarin no embolism no bleed4.5 NHS costs no warfarin no embolism100 no warfarin embolism1000 warfarin no embolism350 warfarin embolism1350 Bleed20

No embolism No warfarin Embolism Cardiomyopathy No bleed No embolism Bleed Warfarin No bleed Embolism Bleed Results ICER = (367.9 – 181) / (4.44 – 4.302) = £1,305 per QALY

Markov Models Appropriate when there is reoccurrence Can describe longer time horizons e.g. Disease process that evolves over time The progression of a chronic disease Estimate long term costs and life years gained

Markov Models Markov (health) States Should be mutually exclusive and exhaustive Markov cycle length: a fixed period of time e.g. one month/one year are common Transition Probabilities Transition from one state into another at the end of a single cycle Fixed transition probabilities out of each state adding up to 1 Markov Rewards Values assigned to each health state that represent the cost and utility of spending one cycle in that state (e.g. assign a cost for spending one unit of time in a ‘treatment’ state

Markov Models Notice the probability of staying dead once you enter the ‘dead’ state is 1.0!

Markov Models The example here is Motor Neurone Disease, a progressive neurodegenerative disorder

Markov Assumption For any individual, the probability of transition from any state to and state is independent of previous history Once in a health state, no memory of previous health state or timing E.g. it makes no difference a mild person if they have been moderate or severe before (or, indeed, how long they were ‘severe’ for) There are ways to relax this assumption but we won’t cover them here

Not all patients are the same! Monte Carlo Simulation (A bit more complex) Track the path of individual patients by 1 st order Monte Carlo:- Generating a random number to determine starting health state Continue generating random numbers to determine which health states the patient transitions to cycle to cycle Record costs and outcomes for every cycle in the stated time horizon and repeat 10,000 times to obtain means and distributions of results Probabilistic Sensitivity Analysis (Second Order Monte Carlo):- Randomly (based on an appropriate distribution) vary all transition probabilities, costs and outcomes in the model simultaneously and repeatedly resample Deterministic Sensitivity Analysis Vary this data to pre-specified extremes or specific scenarios

Alcohol model – Barbosa et al 2010 Assess the effect of a medium term intervention on LTCs associated with alcohol use Does not include admissions due to external causes (injuries) or alcohol poisoning Probability of death in any state is state-modified age/sex mortality rate

West Sussex Model Steps Rebuild Barbosa model structure as the “control group” Add intervention to the model structure – in this case patients have the chance to refer themselves to psychosocial counselling every time they transition into a state of harmful drinking Obtain new probabilities and cost data from published sources

Data in the model Treatment referral probability calculated from prevalence of harmful users vs. numbers referring to treatment per year (about 3.5%) Costs of “being an alcoholic” calculated by obtaining total costs from SUS database, applying harmful user attributable from literature estimate divided by number harmful users for male and female Costs of treatment were taken as the average attendances at the average cost (incl training etc.) Assumptions Men are double as likely to be high risk drinkers as women but total prevalence is still roughly 6.75% (GHS 2009) Men have 3% below the mean abstinence rate and women 3% above (GHS 2009) Unsuccessful treatment completions are transferred equally into hazardous and harmful (lack of data) Treatment success is equal between males and females (no data) Transition probabilities between states (other than treatment referral) do not differ between men and women (as assumed in Barbosa et al. 2010) Probability of dying while in treatment is equal to Ex-harmful (lack of data) Simpson's rule is applied to utilities because they occur incrementally through the cycles but as costs are attached to discrete events simpsons rule has not been applied

The Results TypeOptionCost (£)QALYsInc CostInc QALYs ICER (£/QALY) Deterministic Alc Male/Alc Male Treat£ £ £3, Deterministic Alc Female/Alc Female Treat£ £ £4, When only costs of hospital admissions for injuries and poisoning are included, the treatment costs £3k per QALY for men and £5k per QALY for women. The difference is due to the cost of men being in ‘harmful’ states being higher, meaning that the intervention is more valuable.

Second Order Monte Carlo Remember – not all patients will be the same and there is uncertainty around most of our parameters (modelled using standard errors). Probability distributions are constructed from the mean and standard error of each parameter. For example, attendances at counselling had a mean of 15 and a standard deviation 4.5 so a normal distribution of attendances might look like this: N Lots of people will attend close to 15 sessions but a few will attend as little as 6 and some as many as 24 (95% of people are within this range – anyone know why?)

Second Order Monte Carlo Probabilities and utilities were varied on a beta distribution Costs were varied on a gamma distribution (except unit cost of treatment which was fixed) Due to uncertainty around underlying prevalence estimates for treatment referral the s.e. was set equal to the mean Random numbers are generated for all parameters simultaneously and the resulting values, sampled from their distribution are used as the parameters for that ‘run’ of the model This re-sampling process is repeated 1000 times in order to obtain a distribution of results Let’s have a look at the Monte Carlo in action! Demonstration Now we have 1000 different ICERs to work with

SE quadrant – dominant, NW quadrant Dominated, NE and SW depend on threshold ICER (willingness-to-pay)

Results of PSA TypeOptionICER (£/QALY) Prob Cost effective at £20k/QALYEVPI £20k/QALY (WSx) PSAAlc Male/Alc Male Treat£2, £64, PSAAlc Female/Alc Female Treat£5, £73, PSA Alc Male/Alc Male Treat (Disc 6/1.5)£2, £62, PSA Alc Female/Alc Female Treat(Disc 6/1.5)£4, £74, In the mean case, the intervention remains cost effective in both men and women and is not sensitive to changes in discount rate The probability that the intervention is cost effective is about 80% for men and 70% for women (great similarity between the costs of states for women led to greater uncertainty)