Utility Model¶

In economics, the utility is a number that represents how satisfied a person is with a certain situation. In the context of the LEAP model, it is used to quantify the health-related quality of life of individuals with asthma.

Datasets¶

EQ5D¶

The EQ5D is a standardized instrument used to measure health-related quality of life. It consists of five dimensions: mobility, self-care, usual activities, pain/discomfort, and anxiety/depression. The EQ5D is widely used in health economics and clinical trials to assess the impact of diseases and treatments on quality of life.

We use the EQ5D values to calculate the baseline utility for an individual of a given age and sex. For example, suppose we have a 30-year-old female with asthma. We can use the EQ5D values to calculate her baseline utility (her utility if she didn’t have asthma), and then we can compute her net utility by subtracting the utility loss due to asthma.

The EQ5D data was obtained from Table 3 in the paper Canada population norms for the EQ-5D-5L [Yan, 2024].

After processing the EQ5D data, our dataset is formatted as follows:

Column	Type	Description
`age`	`int`	A person's age in years, range `[0, 110]`
`sex`	`str`	F = Female, M = Male
`eq5d`	`float`	The baseline utility for a person of a given age and sex. Range `[0, 1]`.
`sd`	`float`	The standard deviation of the utility value, used to account for uncertainty in the utility value. Standard deviation for `age < 18` is set to 0 since those EQ5D values were interpolated.

Disutility Due to Asthma Exacerbations¶

As in the Asthma Control Model, we used the study [Yaghoubi, 2020], in Table I:

Variable	Value
Utility of exacerbation by severity: mild	0.57
Utility of exacerbation by severity: moderate	0.45
Utility of exacerbation by severity: (very) severe	0.33

Note

In the paper, severe exacerbations are equivalent to our definition of very severe exacerbations. Thus, we are missing the utility of severe exacerbations. To account for this, we defined the utility of a severe exacerbation as:

\[\begin{split}\text{utility}(\text{severe}) &= \dfrac{ \text{utility}(\text{moderate}) + \text{utility}(\text{very severe}) }{2} \\ &= \dfrac{0.45 + 0.33}{2} = 0.39\end{split}\]

Now, these are utility values, but we want disutility. Since the study [Yaghoubi, 2020] starts at age 15, we set that as the baseline age. According to the EQ5D data, the baseline utility for a 15-year-old is 0.9. Thus, the disutility due to asthma exacerbations is given by:

\[d_E(S) = 0.9 - u_E(S)\]

where:

\(d_E(S)\) is the disutility due to an asthma exacerbation of severity level \(S\)
\(u_E(S)\) is the utility due to an asthma exacerbation of severity level \(S\)
\(S \in \{1, 2, 3, 4\}\) is the asthma exacerbation severity level (1 = mild, 2 = moderate, 3 = severe, 4 = very severe)

Exacerbation Severity	Utility	Disutility
Mild	0.57	0.33
Moderate	0.45	0.45
Severe	0.39	0.51
Very Severe	0.33	0.57

Now, the values listed in this table are the disutility for having an asthma exacerbation of a given severity for an entire year. We assume that a mild asthma exacerbation lasts for 7 days, while all the other severity levels last for 14 days. To convert these values we have the weekly utility:

\[d_{\text{weekly}} = d_{\text{annual}} \times \dfrac{1}{52}\]

Exacerbation Severity	Annual Disutility	Exacerbation Duration	Weekly Disutility	Disutility per Exacerbation
Mild	0.33	7 days	0.00633	0.00633
Moderate	0.45	14 days	0.00865	0.01731
Severe	0.51	14 days	0.00981	0.01962
(Very) Severe	0.57	14 days	0.01096	0.02192

Disutility Due to Asthma Control Levels¶

We used Table 3 in the study [Einarson, 2015] to obtain the utility values stratified by asthma control level:

Control	Author	Instrument	Baseline (Mean)	SD
Well controlled	McTaggart-Cowan et al.	EQ-5D	0.840	0.200
Adequate	McTaggart-Cowan et al.	EQ-5D	0.810	0.220
Not controlled	McTaggart-Cowan et al.	EQ-5D	0.800	0.210

As with the exacerbation severity, we want to convert these utility values to disutility values. We use the baseline utility for a 15-year-old of 0.9. Thus, the disutility stratified by asthma control is given by:

\[d_C(L) = 0.9 - u_C(L)\]

where:

\(d_C(L)\) is the disutility due to asthma control level \(L\)
\(u_C(L)\) is the utility due to asthma control level \(L\)
\(L \in \{1, 2, 3\}\) is the asthma control level (1 = well-controlled, 2 = partially-controlled, 3 = uncontrolled)

Asthma Control Level	Utility	Disutility
Well-Controlled	0.84	0.06
Partially-Controlled	0.81	0.09
Uncontrolled	0.80	0.10

Model: Calculating Utility¶

The net utility is given by the formula:

\[u := u_{\text{baseline}} - A \cdot \left( \sum_{S=1}^{4} d_E(S) \cdot n_E(S) + \sum_{L=1}^{3} d_C(L) \cdot C(L) \right)\]

where:

\(u_{\text{baseline}}\) is the baseline utility for a person of a given age and sex (without asthma)
\(d_{E}(S)\) is the disutility due to an asthma exacerbation of severity level \(S\)
\(n_E(S)\) is the number of asthma exacerbations of severity level \(S\) in a year
\(S \in \{1, 2, 3, 4\}\) is the asthma exacerbation severity level (1 = mild, 2 = moderate, 3 = severe, 4 = very severe)
\(d_{C}\) is the disutility due to having asthma at control level \(L\)
\(C(L)\) is the proportion of the year spent at asthma control level \(L\)
\(L \in \{1, 2, 3\}\) is the asthma control level (1 = well-controlled, 2 = partially-controlled, 3 = uncontrolled)
\(A\) is a boolean indicating whether the person has asthma