Utility Model¶

In LEAP, we quantify the health-related quality of life of individuals with asthma using health state utilities, which range from 0 to 1, where 1 represents perfect health and 0 represents death.

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. Each dimension has five levels of severity, ranging from no problems to extreme problems.

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

After processing the EQ5D data, leap/processed_data/eq5d_canada.csv, 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 health state 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.

Since the EQ-5D-5L data described above only covers individuals aged 18 and older, the utility values for ages 0 to 17 are interpolated. We assume that utility decreases linearly from a value of 1 (perfect health) at age 0 to the observed EQ-5D value at age 18, \(u_{18}\), separately for each sex:

\[u_{\text{age}} = 1 - \dfrac{1 - u_{18}}{18} \times \text{age}, \quad \text{age} \in [0, 17]\]

Since these values are derived rather than directly observed, the standard deviation sd for ages \(< 18\) is set to 0.

Disutility Due to Asthma Exacerbations¶

The health state utility values stratified by exacerbation severity come from [Yaghoubi, 2020], in Table I, originally sourced from [Lloyd, 2007] and [Campbell, 2010]:

Variable	Value
Utility of mild exacerbation	0.57
Utility of moderate exacerbation	0.45
Utility of severe exacerbation	0.39 (see note below)
Utility of very severe exacerbation	0.33

Note

In [Yaghoubi, 2020], severe exacerbations are equivalent to our definition of very severe exacerbations. Thus, we are missing the utility of severe exacerbations. We defined the utility of a severe exacerbation as the arithmetic mean of the utilities of moderate and very severe exacerbations:

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

We need to convert these health state utilities to disutilities due to exacerbations. According to [Lloyd, 2007], the mean EQ-5D utility for asthma patients with no exacerbation was 0.89; we use this as the baseline. Thus, the disutility due to asthma exacerbations is given by:

\[d_E(S) = 0.89 - u_E(S)\]

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 \(S\)
\(S \in \{\text{mild}, \text{moderate}, \text{severe}, \text{very severe}\}\) is the asthma exacerbation severity level

Exacerbation Severity	Utility	Disutility
Mild	0.57	0.32
Moderate	0.45	0.44
Severe	0.39	0.50
Very Severe	0.33	0.56

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 [Aldington, 2007]. To convert these values we need the weekly disutility:

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

Exacerbation Severity	Annual Disutility	Exacerbation Duration	Weekly Disutility	Disutility per Exacerbation
Mild	0.32	7 days	0.00615	0.00615
Moderate	0.44	14 days	0.00846	0.01692
Severe	0.50	14 days	0.00962	0.01923
(Very) Severe	0.56	14 days	0.01077	0.02154

Disutility Due to Asthma Control Levels¶

The health state utility values stratified by asthma control level come from a discrete choice experiment of 157 adult patients with asthma in Canada [McTaggart-Cowan, 2008], as reported in Table 3 of [Einarson, 2015]:

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 age 15 as the baseline age, consistent with the minimum age (15 years) of the target population in [Yaghoubi, 2020]. According to the EQ5D data, the baseline utility for a 15-year-old is 0.9. Thus, the disutility stratified by asthma control is given by:

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

where:

\(d_C(k)\) is the disutility due to asthma control level \(k\)
\(u_C(k)\) is the utility due to asthma control level \(k\)
\(k \in \{\text{well-controlled}, \text{partially-controlled}, \text{uncontrolled}\}\) is the asthma control level

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¶

Exacerbation disutility is applied per exacerbation event, i.e. it is incurred each time agent \(i\) has an exacerbation of the corresponding severity. Control level disutility is 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 \(k\). The net utility is given by the formula:

\[\begin{split}\small u^{(i)} = \begin{cases} u_{\text{age}, \text{sex}}^{(i)} & \text{if agent } i \text{ does not have asthma} \\[6pt] \max\left(0,\ u_{\text{age}, \text{sex}}^{(i)} - \left( \sum_{S=1}^{4} n_E^{(i)}(S) \cdot d_E(S) + \sum_{k=1}^{3} P(y^{(i)} = k) \cdot d_C(k) \right)\right) & \text{if agent } i \text{ has asthma} \end{cases}\end{split}\]

where:

\(u_{\text{age}, \text{sex}}^{(i)}\) is the baseline utility for agent \(i\), of the given age and sex (without asthma)
\(n_E^{(i)}(S)\) is the number of exacerbations at severity level \(S\) in a time interval, for agent \(i\)
\(d_E(S)\) is the disutility due to an asthma exacerbation of severity level \(S\)
\(S \in \{\text{mild}, \text{moderate}, \text{severe}, \text{very severe}\}\) is the asthma exacerbation severity level
\(P(y^{(i)} = k)\) is the probability of agent \(i\) being at asthma control level \(k\)
\(d_C(k)\) is the disutility due to being at asthma control level \(k\)
\(k \in \{\text{well-controlled}, \text{partially-controlled}, \text{uncontrolled}\}\) is the asthma control level