Conceptual framework

The method involves the estimation of indirect cost associated with measles-related deaths among children aged 0–14 years in Somalia. The paper used a macroeconomic model of cost-of-illness (COI) within the framework of recommendations of reporting economic evaluations according to the WHO guideline for identifying the economic consequences of disease and injury [16]. This paper computed undiscounted productive years of life lost (UDPYLL), discounted productive years of life lost (DPYLL) and conflict and growth-adjusted non-health gross domestic product per capita (^aNHGDPPC) associated with measles-related deaths. This information was then used to estimate the present value of the non-health gross domestic product loss (NHGDPLoss) associated with measles-related deaths among children aged 01–14 years. Previous studies have used similar approaches to estimate the impact of deaths associated with a disease on non-health components of the future gross domestic product (GDP) [14]. The impact of deaths associated with disease on the non-health components of GDP is the ‘quantity of interest’ when estimating the indirect cost [16–Reference Kirigia18]. The use of health services or goods does not generate utility or welfare per se [Reference Grossman19]. GDP, which is the total value of all marketed final goods and services produced in an economy during a year, is regarded as one of the measures of the market production forgone due to disease death. While medical care and health expenditures actually form part of GDP [Reference Kirigia18, Reference Kirigia20], a more appropriate quantity of interest would be the impact of disease or injury on the non-health components of GDP [Reference Chisholm17].

Total non-health macroeconomic loss of measles model and specification

This paper follows the general framework of previous studies [16, Reference Kirigia18–Reference Kirigia20] in measuring the indirect cost by computing the present value of NHGDPLoss due to disease death. In particular, this paper follows the approach of allowing a finite and stable upper limit growth component to NHGDPPC by assuming that NHGDPPC cannot exceed GDP per capita (GDPPC) in any given year in the future [Reference Da'ar21]. However, while providing a specific context of disease burden in a conflict and fragile health system, the present study augments previous approaches by adjusting the NHGDPPC for conflict and fragility conditions. Conflict and fragility conditions affect the macroeconomic fundamentals of health systems [Reference Martin and Evans22].

The NHGDPLoss associated with measles-related deaths among children aged 0–14 years is the product of the total number of DPYLL above the minimum employment age lost, the NHGDPPC and the estimated total number of deaths associated with measles in that age group (ETMD_0–14). ETMD_0–14 is calculated from the proportion of total measles deaths of children aged 0–14 years (PTMD_0–14) out of the total measles deaths reported of the population aged <65 years.

The number of productive years of life lost (PYLL) for children aged 0–14 years was calculated by subtracting the sum of the average age at death (AAD_0–14) and years remaining to attain the minimum age of employment i.e. the average years lost at the death of a child before attaining the age of employment (YEL) from life expectancy (LE) at birth. In 2015, LE at birth in Somalia was 56.6 years for females and 53.5 for males according to health data we gleaned from WHO updates, World Bank and United Nations for Population [23]; or for simplicity, 57 and 54 years were used. AAD_0–14 is the simple average age at death for age group 0–14, which equals to 0 plus 14 years divided by 2 (0 + 14/2) = 7. A simple average was used since available evidence of measles deaths did not indicate the distribution by age. The legal minimum age of employment is 15 years according to Article II of the International Labour Organisation (ILO) convention [24]. From AAD_0–14, YEL is 15 − 7 = 8. Thus, the number of future PYLL equals LE minus 15 years. In 2015, the PYLL for female children aged 0–14 years in Somalia was 42 years, i.e. LE of 57 years minus the sum of AAD (7 years) and YEL (8 years). Similarly, the PYLL for male children aged 0–14 years was 39 years:

(1a)$${\rm PYL}{\rm L}_{{\rm F}(0-14)} = {\rm L}{\rm E}_{\rm F}-{\rm AAD}-{\rm YEL} = \lsqb {57-7-8} \rsqb = 42$$

(1b)$${\rm PYL}{\rm L}_{{\rm M}(0-14)} = {\rm L}{\rm E}_{\rm M}-{\rm AAD}-{\rm YEL} = \lsqb {54-7-8} \rsqb = 39$$

where PYLL, LE, AAD and YEL are defined in the preceding section. The present value of NHGDPLoss to the country due to measles-related deaths among children aged 0–14 years is given by

(2)$${\rm pv}{\rm N}_{0-14} = {\rm pv}{\rm N}_{{\rm F}(0-14)} + {\rm pv}{\rm N}_{{\rm M}(0-14)}$$

where pvN₀₋₁₄is the present value of total non-health GDP loss due to measles deaths among children aged 0–14 years, disaggregated by gender according to equations (3) and (4):

(3)$$\eqalign{& {\rm NHGDPLos}{\rm s}_{{\rm F}(0{\rm \ndash} 14)} = \cr & \displaystyle{1 \over {{\lpar {1 + r} \rpar }^1}} \times \left( {G-\alpha^t\left[ {{\textstyle{1 \over \beta}} \lpar {G-\lpar {G-H} \rpar } \rpar } \right]} \right)_1 \times D_{{\rm F}(014)} \cr & + \displaystyle{1 \over {{\lpar {1 + r} \rpar }^2}} \times \left( {G-\alpha^t\left[ {{\textstyle{1 \over \beta}} \lpar {G-\lpar {G-H} \rpar } \rpar } \right]} \right)_2 \times D_{{\rm F}(014)} \cr & + \displaystyle{1 \over {{\lpar {1 + r} \rpar }^3}} \times \left( {G-\alpha^t\left[ {{\textstyle{1 \over \beta}} \lpar {G-\lpar {G-H} \rpar } \rpar } \right]} \right)_3 \times D_{{\rm F}(014)} \cr & \vdots \cr & + \displaystyle{1 \over {{\lpar {1 + r} \rpar }^T}} \times \left( {G-\alpha^t\left[ {{\textstyle{1 \over \beta}} \lpar {G-\lpar {G-H} \rpar } \rpar } \right]} \right)_T \times D_{{\rm F}(014)} \cr \cr = & \sum\limits_{t = 1}^T {\left\{ {\displaystyle{1 \over {{\lpar {1 + r} \rpar }^t}} \times {\left( {G-\alpha^t\left[ {\displaystyle{1 \over \beta} \lpar {G-\lpar {G-H} \rpar } \rpar } \right]} \right)}_t \times D_{{\rm F}(0{\rm \ndash} 14)}} \right\}}} $$

and

(4)$$\eqalign{& {\rm NHGDPLos}{\rm s}_{{\rm M}(0{\rm \ndash} 14)} = \cr & \displaystyle{1 \over {{\lpar {1 + r} \rpar }^1}} \times \left( {G-\alpha^t\left[ {{\textstyle{1 \over \beta}} \lpar {G-\lpar {G-H} \rpar } \rpar } \right]} \right)_1 \times D_{{\rm M}(014)} \cr & + \displaystyle{1 \over {{\lpar {1 + r} \rpar }^2}} \times \left( {G-\alpha^t\left[ {{\textstyle{1 \over \beta}} \lpar {G-\lpar {G-H} \rpar } \rpar } \right]} \right)_2 \times D_{{\rm M}(014)} \cr & + \displaystyle{1 \over {{\lpar {1 + r} \rpar }^3}} \times \left( {G-\alpha^t\left[ {{\textstyle{1 \over \beta}} \lpar {G-\lpar {G-H} \rpar } \rpar } \right]} \right)_3 \times D_{{\rm M}(014)} \cr & \vdots \cr & + \displaystyle{1 \over {{\lpar {1 + r} \rpar }^T}} \times \left( {G-\alpha^t\left[ {{\textstyle{1 \over \beta}} \lpar {G-\lpar {G-H} \rpar } \rpar } \right]} \right)_T \times D_{{\rm M}(014)} \cr = & \sum\limits_{t = 1}^T {\left\{ {\displaystyle{1 \over {{\lpar {1 + r} \rpar }^t}} \times {\left( {G-\alpha^t\left[ {\displaystyle{1 \over \beta} \lpar {G-\lpar {G-H} \rpar } \rpar } \right]} \right)}_t \times D_{{\rm M}(0{\rm \ndash} 14)}} \right\}}} $$

where

• • NHGDPLoss_0–14 is the net present value of conflict- and growth-adjusted total non-health GDP loss due to measles-related deaths among children aged 0–14 years;

• • G is the GDP per capita;

• • H is the health expenditure per capita;

• • D is the estimated total measles deaths (ETMD) that occur among children aged 0–14 years;

• • G-H is the non-health GDP per capita;

• • α is a growth adjustment parameter depicting the proportion of non-health GDP per capita to GDP per capita;

• • $\alpha = \displaystyle{{G_T-H_t} \over {G_T-H_{t-1}}};\;{\rm and \; 0} \lt; \alpha \lt; 1$, by assumption;

• • $\beta$ Z is a conflict and fragility-adjustment parameter;

• • $\beta = {\rm CF}{\rm I}_{{\rm SOM}}/{\rm CF}{\rm I}_{{\rm MAX}} \; {\rm and \; 0} \lt \beta \lt 1$, by assumption;

• • $1/(1 + r)^t$ Zis the discount factor;

• • $\sum\nolimits_{t = 1}^T {}$ Zdepicts the summation from year t to T; t represents the first year of life lost to measles and T is the terminal year, i.e. the final year of all future PYLL per measles death as defined earlier.

Discounting

The present value of the NHGDPLoss due to measles-related deaths is the sum of NHGDPLoss_F(0–14) and NHGDPLoss_M(0–14). The NHGDPLoss for each group was estimated by multiplying the total number of DPYLL (which is equivalent to the sum of the discount factors) by the ^aNHGDPPC and the ETMD_(0–14) in that age group. Future costs diminish the more distant in the future they occur, hence society generally value them less than the present costs. This underscores the premise of discounting, which necessitates the need to adjust for the time value of losses occurring in different periods. Discounting future health outcomes have been addressed in previous studies [Reference Chapman and Elstein25, Reference Torgerson and Raftery26]. Discounting future costs and benefits is performed because of time preference, which refers to the desire to realise benefits in the present while deferring any negative effects of doing so [Reference Torgerson and Raftery26]. Failure to discount effects even when costs are counted for can lead to inconsistent or misleading results [Reference Weinstein and Stason27]. Failing to discount future costs also has the effect of dampening the present benefits of reducing burden, potentially slowing interventions to be more cost-effective than they would otherwise seem.

Sensitivity analysis

This paper then conducted a sensitivity analysis to assess the impact of a range of values of a set of epidemiologic and economic factors on the indirect cost associated with measles-related deaths. These factors include the proportion of ^aNHGDPPC to GDPPC, discount rate, PTDM and conflict and fragility conditions. The existence of a range of values of these factors necessitated the accounting for uncertainty [Reference Levin and McEwan28, Reference McEwan29], a methodology emphasised in health economic models [Reference Cartwright30, Reference Taylor31].