Health economics

NICE and similar organisations use economic evaluation to learn about

• pharmaceuticals
• surgical procedures
• diagnostic technologies
• medical devices
• screening programmes
• interventions
• …

in order to best allocate the finite resources available.

Example: Cost-effectiveness

Investigating a new asthma drug

• Drug A (current standard) costs £1000 per patient per year
• Drug B (new drug) costs £1200 per patient per year

Evidence from a clinical trial suggests

• Patients on drug B had 30% more episode-free days than those on drug A.

If we have £200 per person to year to spend, we should opt for drug B.

Example: cost-effectiveness

But suppose

• we have limited funds
• there’s also a new drug that improves symptoms for sufferers of another disease.

Now we have new questions:

• How do we compare these new drugs?
• How do we compare the improvements they bring?
• How do we choose which drug to pay for?
• Which spending decision will achieve the ‘most health’?

We need a measure of health that applies to any possible health-spending decision.

The Rosser index and Alan Williams

The Rosser index attracted the attention of Prof. Alan Williams, a health economist who was seconded to the Treasury from 1966-1968

Alan Williams’s idea:

• To focus not on people’s clinical symptoms, but on how people live
• Seek the views of the ‘general public’, not just medics
• a single number that encompasses both
  • the value of additional life expectancy and
  • the value of improved quality of life

Alan Williams

The quality-adjusted life-year

So, a QALY value of 1 represents one year of perfect health, but it could also represent

• two years with a HRQoL of 0.5, or
• four years with a HRQoL of 0.25.

See Whitehead and Ali (2010) for some discussion and analysis around negative QALY values and the QALY generally.

Example: hip replacement

Expected value of health-related quality of life for patients following a hip replacement (from Fordham et al. (2012)).

Exercises

Suppose a patient has a chronic condition. With drug A, his health-related quality of life is 60% of that of a fully healthy person, and he has a life expectancy of five years (red area).

From the figures below:

1. Describe the effect of Drug B in terms of duration and health-related quality of life (HRQoL).
2. Calculate the gain in QALYs if the patient is switched to drug B (blue/green area).

Scenario 1

Scenario 1

Scenario 2

Scenario 2

How are HRQoL values elicited?

The health-related quality of life of a health state is not known or directly measurable

There are three main methods (broadly speaking)

• Visual analogue scale
• Time trade-off
• Simple gamble

The aim is to order health states by preference, and to assign HRQoL values to them.

Dimensions of the EQ-5D

The EQ-5D-5L defines health in terms of five dimensions:

• mobility
• self-care
• usual activities
• pain/discomfort
• anxiety/depression.

Each dimension is divided into five levels (in the EQ-5D-5L):

1. No problem
2. Slight problem
3. Moderate problem
4. Severe problem
5. Unable to / extreme problems

From this, there are 3125 possible health states.

EQ-5D questionnaire

The five dimensions of the EQ-5D-5L.

EQ-5D process

• The respondent answers the 5 dimension questions
  • This produces a 5-digit health state summary, eg. 31121
• The respondent places themselves on the visual analogue scale
  • “How would you describe your health state today?”
• The 5-digit health state summary can be converted into a single summary number reflecting the respondent’s HRQoL.
  • Uses a formula involving parameters (‘value sets’)
  • Different value sets available for different countries/regions
  • Value sets usually calibrated using representative samples and TTO method

Find out more:

EQ-5D and the EuroQol group: past, present and future, Devlin and Brooks (2017)
Comparing responsiveness of the EQ-5D-5L, EQ-5D-3L and EQ VAS in stroke patients, Golicki et al. (2015)

The ICER

The incremental cost-effectiveness ratio (ICER) for two options \(A\) and \(B\) is

\[ICER = \frac{Cost_A - Cost_B}{Outcome_A - Outcome_B}.\]

The extra cost per extra unit of health (eg. QALY).

Directly comparable to the willingness-to-pay threshold.

Notice that if

• \(Cost_A > Cost_B\) and \(Outcome_A < Outcome_B\) (ie. treatment \(A\) costs more than treatment \(B\) for worse results)
• \(Cost_A < Cost_B\) and \(Outcome_A > Outcome_B\) (ie. if treatment \(A\) costs less and has a better effect)

Then \(ICER < 0\). In both of these cases the outcome is obvious.

Incremental net benefit

The incremental net benefit is \[Z = \lambda\left(Outcome_A - Outcome_B\right)-\left(Cost_A - Cost_B\right)\] where

• \(\lambda\) is the willingness-to-pay threshold
• \(Z\) is measured in monetary units.

The larger \(Z\) is, the better our new treatment \(A\) is judged to be.

If \(Z<0\) then \(A\) is judged to be worse than \(B\).

The analysis: main steps:

1. Costing analysis to estimate the cost of U@Uni.
2. Within-trial analysis to estimate the short-term (6 month) cost-effectiveness of U@Uni
3. Economic modelling analysis to estimate the long-term (lifelong) cost-effectiveness.

The modelling involved

• Combining individual follow-up data with cross-sectional data on health behaviours
• Using this information to estimate the long-term effect.
• Using published data linking all four health behaviours to mortality risk.

Estimating the roll-out cost

Rolling U@Uni out to other universities would have a different cost:

• local development
• implementation
• Potentially more students

\[\text{Rollout cost per student} = \frac{\text{Cost of any local developement + implementation + monitoring cost}}{\text{Average number of new students}}\]

Cost-effectiveness: long term and rolled-out

Long term within trial cost per QALY around £22,844
Long term rolled-out cost per QALY around £1545

The long-term estimates of cost per QALY, with the threshold of £20,000 per QALY. Taken from Kruger et al. (2014).

If you’d like to read more about the details of the models used, see Kruger et al. (2014).

Uncertainty

In our examples so far we are reliant on various quantities:

• The costs of interventions / treatments
• The QALYs gained/lost in particular scenarios
• The proportion of people behaving/reacting in certain ways

In reality we are uncertain about these things.

Build a probabilistic model, capturing this uncertainty with distributions

what if we aren’t certain about \(p\)?

We are unlikely to know \(p\) exactly, so we model our uncertainty.

\[p\sim{Beta\left(\alpha, \beta\right)}\]

The Beta distribution with alpha=6, beta=34. The median is shown by the solid vertical lines and the 95% CI by the dashed lines.

Sampling infection numbers

We can now adopt a two-stage sampling process:

1. Sample a value for \(p\) from \(Beta\left(\alpha,\beta\right)\).
2. Sample a value for \(x\) from \(Bin\left(N, p\right)\)

Repeat this many times to generate a sample of \(x\) values that reflect our uncertainty about \(p\).

Parameter uncertainty, not structural uncertainty

Sampling infection numbers

We have repeated steps 1 and 2 a thousand times, for a population of 100 and \(p\sim{Beta\left(6,34\right)}\).

1000 samples of the number of people becoming infected in 100, sampling \(p\) from a Beta(6, 34) distribution.

Vaccination: cost

Vaccination is associated with a cost \(\psi_V\) per person, which we model by \(\psi_V \sim logN\left(1.95, 0.0606\right)\).

The total cost due to vaccination is \(\psi_V {N^V_V}\).

Vaccination: adverse effects

There are sometimes adverse effects from the vaccination, which we model using

\[\begin{align*} AE & \sim Bin\left(N^V_V, \beta_{AE}\right) \\ \beta_{AE} & \sim Beta\left(3.5, 31.5\right) \end{align*}\] and the loss of QALYs per person experiencing adverse effects is \[\begin{align*} \omega_{AE} & \sim{logN\left(-0.634, 0.0717\right)}. \end{align*}\]

The total loss of QALYs due to adverse effects from the vaccine is therefore \(\omega_{AE}AE\).

Infection parameters

The parameters \(\beta_I\) and \(\rho_v\) are modelled by

\[\begin{align*} \beta_I & \sim {Beta \left(13.01, 172.38\right)}\\ \rho_V & \sim{ logN \left(-0.374,0.00524\right)} \end{align*}\]

GP visits

Of those who are infected, some number visit their GP:

\[\begin{align*} GP^V & \sim Bin\left(I^V_{tot}, \beta_{GP}\right)\\ GP^0 & \sim Bin\left(I^0, \beta_{GP}\right) \end{align*}\]

where \(\beta_{GP}\sim{Beta\left(5.8, 13.80\right)}\). We model the cost per GP visit as \(\psi_{GP}\sim{logN\left(3, 0.0606\right)}\).

We calculate the total cost of GP visits as \(C_{GP}^V = GP^V\psi_{GP}\; \text{ and }\; C_{GP}^0 = GP^0\psi_{GP}.\)

Total costs and QALYs

We can now calculate the cost pp and QALYs lost pp for each cohort:

Cohort \(V\)

• \(\text{Cost} = \frac{1}{N}\left(\psi_VN^V_V + \psi_{GP}GP^V + \psi_HH^V\right)\)
• \(\text{QALYs lost} = \frac{1}{N}\left(\omega_{AE}AE^V + \omega_II_{tot}^V + \omega_PP^V + \omega_HH^V + \omega_DD^V\right)\)

Cohort 0

• \(\text{Cost} = \frac{1}{N}\left(\psi_{GP}GP^0 + \psi_HH^0\right)\)
• \(\text{QALYs lost} = \frac{1}{N}\left(\omega_II_{tot}^0 + \omega_PP^0 + \omega_HH^0 + \omega_DD^0\right)\)

We do this for each simulation.

In cost-effectiveness space

Red line: WTP threshold = £20000 / QALY Blue line: WTP threshold = £100 / QALY

## Warning: Removed 2 rows containing missing values (`geom_point()`).

Cost-effectiveness acceptability curve

Using the incremental net benefit

\[Z = \lambda\left(Outcome_A - Outcome_B\right)-\left(Cost_A - Cost_B\right)\]

We can plot the proportion of simulations that conclude the flu vaccine programme to be cost-effective (ie. for which \(Z>0\)) against \(\lambda\).

The red line is at 0.95.