Cost Model

Data

Cost Due to Asthma Exacerbations

The data used in the cost model comes from the study [Yaghoubi, 2020], in Table I.

Variable

Value

Direct costs of mild exacerbation

$130 USD

Direct costs of moderate exacerbation

$594 USD

Direct costs of severe exacerbation

$2425 USD (see note below)

Direct costs of very severe exacerbation

$9900 USD

Note

In [Yaghoubi, 2020], severe exacerbations are equivalent to our definition of very severe exacerbations. Thus, we are missing the cost of severe exacerbations. To account for this, we defined the cost of a severe exacerbation as the geometric mean of the costs of moderate and very severe exacerbations, i.e. the average of the two costs on the log-scale:

\[\begin{split}\text{cost}_E(\text{severe}) &= \exp\left(\dfrac{ \text{log}(\text{cost}_E(\text{moderate})) + \text{log}(\text{cost}_E(\text{very severe})) }{2}\right) \\ &= \$2425 \text{ USD}\end{split}\]

Cost Due to Asthma Control Levels

The data used for background cost by asthma control level also comes from the same study [Yaghoubi, 2020], in Table I:

Variable

Value

Annual direct costs of well-controlled asthma

$2372 USD

Annual direct costs of not-well-controlled asthma

$2965 USD

Annual direct costs of uncontrolled asthma

$3127 USD

Currency Conversion

The costs reported in [Yaghoubi, 2020] above, for both exacerbations and asthma control levels, are in USD, reported in September 2018 price year. To match the target price year of our model, all costs are converted to 2023 CAD in two steps:

  1. Inflation adjustment: 2018 USD are converted to 2023 USD using the Consumer Price Index (CPI) Inflation Calculator from the U.S. Bureau of Labor Statistics:

    \[1 \text{ USD (Sept 2018)} = 1.22 \text{ USD (Sept 2023)}\]

  2. Exchange rate conversion: 2023 USD are converted to 2023 CAD using the Bank of Canada’s annual average exchange rate:

    \[1 \text{ USD (2023)} = 1.36 \text{ CAD (2023)}\]

Combining these two factors gives the overall USD-to-CAD conversion rate used in the model:

\[\text{exchange_rate_usd_cad} = 1.22 \times 1.36 \approx 1.66\]

The conversion rate is applied to obtain the 2023 CAD costs used in the model:

Direct costs (2023 CAD)

Variable

Value

Mild exacerbation

$216 CAD

Moderate exacerbation

$986 CAD

Severe exacerbation

$4026 CAD

Very severe exacerbation

$16434 CAD

Well-controlled asthma (annual)

$3938 CAD

Not-well-controlled asthma (annual)

$4922 CAD

Uncontrolled asthma (annual)

$5191 CAD

Model

Exacerbation costs are applied per exacerbation event, i.e. an agent incurs this cost each time they have an exacerbation of the corresponding severity. Control level costs are weighted by \(P(y^{(i)} = k)\), which per the Asthma Control Model represents the proportion of the time interval agent \(i\) spends at control level \(k\):

\[\text{cost}^{(i)} = \sum_{S=1}^4 n_E^{(i)}(S) \cdot \text{cost}_E(S) + \sum_{k=1}^3 P(y^{(i)} = k) \cdot \text{cost}_C(k)\]

where:

  • \(n_E^{(i)}(S)\) is the number of exacerbations at severity level \(S\)

  • \(\text{cost}_E(S)\) is the cost of an exacerbation at severity level \(S\)

  • \(P(y^{(i)} = k)\) is the probability of agent \(i\) being at asthma control level \(k\)

  • \(\text{cost}_C(k)\) is the cost of being at asthma control level \(k\)