FairChoices Methods

Table of Contents

1. Summary
2. Data Approach _^(Pending)
3. Impact Model _^(Pending)
4. Demography Model _^(Pending)
5. Cost Model
6. Limitations

Summary

FairChoices, at its analytical core, simply models a given country’s baseline population, disease burden, and health intervention coverage and then projects how that baseline would change given a hypothetical scale-up of health intervention investment in the country. The scale-up of health intervention investment is called an essential health benefit package (HBP).

This projection is expressed as a ratio of how many healthy-life-years you would gain in your population per dollar spent on the proposed HBP (i.e. incremental cost effectiveness ratio (ICER)). It allows users to project out different scenarios so that the end user (a policymaker) can ensure each dollar spent on health leads to the most possible benefit.

Impact Model

The FairChoices model uses a lifetime perspective on health. This is to capture benefits that last well beyond the implementation period from interventions like HPV vaccination of adolescents, kidney transplant, and obstetric fistula surgery. We do this using a model based on standard lifetable methodology, where input on demography and epidemiology is based on the World Population Prospects and the Global Burden of Diseases and Injuries study (GBD), input on the effects of the interventions is compiled from the medical literature, and input on baseline coverage is from Watkins et al. (2020).

Conceptually, we first assume that without implementing interventions, cause-, sex-, and age-specific mortality and morbidity will remain unchanged into the future. Then we calculate healthy life-expectancy for each cohort (i.e., the people born the same year) alive today and for the cohorts that will be born during the scale-up period. Assuming a scale-up period of 25 years and that mortality is 100% at age 100, we then need to consider 126 cohorts (C₀ through C₁₀₀ are the cohorts that are alive today, and C_-1 through C_-25 the cohorts that will be born the next 25 years). We can now present the mortality of these cohorts as follows:

Fig. 1: Table Baseline mortality.

M_x denotes the mortality from age x to age x+1. As seen, M₁₀₀ = 1 for all cohorts. denotes the cohort. A negative y is used if the cohort has not yet been born. C_-25 denotes the cohort that will be born in 25 years.

One table is constructed for each sex.

Corresponding tables are also constructed for disability (i.e., morbidity), based on the age- and sex-specific disability weights provided by GBD.

Fig. 2: Table Baseline disability.

Dx denotes the disability from age x to age x+1. Note that D₁₀₀ is not 1. C_y denotes the cohort. A negative y is used if the cohort has not yet been born. For example, C_-25 denotes the cohort that will be born in 25 years.

Once “Table Baseline mortality” and “Table Baseline disability” have been, we can introduce interventions. Interventions are specified to act on a condition (defined as one of the GBD causes of death or disability) and a sex- and age-specific population and have a duration where it is effective. For treatment of acute conditions, the duration is one year, whereas for interventions like vaccines and obstetric fistula surgery the duration is longer and may even be life-long.

Each intervention reduces mortality, disability, incidence, or prevalence of one or more conditions. The crude effect of the intervention, e_crude, is adjusted to account for the change in coverage during the scale-up period using the formula

where cov_baseline and cov_target are coverage at baseline and target.

We have that M_x can be divided into the cause-specific mortality from the targeted condition and what we may call “background mortality”, which is the risk of dying from any other cause, as follows,

Applying the intervention, we get

As seen, if e_adj=1, cause-specific mortality is reduced to zero in the targeted population. If a total of K interventions target the same condition, we get

where e_adj,k is the effect of the k’th intervention.

Note that this means that cause-specific mortality cannot be reduced to less than 0. We make similar calculations for interventions that reduce disability. Further, in our model, we scale up coverage of the intervention gradually over time. This means that the full effect will not be felt until the last year, so that the age-specific mortalities (and disabilities) in different cohorts (c_-25 through c_-100) will be affected differently. Hence, to make intervention-adjusted versions of Table Baseline mortality and Table Baseline disability, each cell is now both age- and cohort-specific.

Fig. 3: Table Adjusted mortality.

M_x,y denotes the mortality from age x to age x+1 in cohort y. As seen, M₁₀₀ = 1 for all cohorts. Cy denotes the cohort. A negative y is used if the cohort has not yet been born. C_-25 denotes the cohort that will be born in 25 years.

Fig. 4: Table Baseline disability.

D_x,y denotes the disability from age x to age x+1 in cohort y. Note that D₁₀₀ is not 1. C_y denotes the cohort. A negative y is used if the cohort has not yet been born. For example, C_-25 denotes the cohort that will be born in 25 years.

For an individual in cohort y, we can calculate healthy life-expectancy (HLE) based on the mortality rates and disability weights in Table Baseline mortality and Table Baseline disability (i.e., HLE_baseline,y) and on Table Adjusted mortality and Table Adjusted disability (i.e, HLE_adjusted,y). The healthy life-years (HLYs) gained is now simply

Total HLYs gained from scaling up one or more interventions then becomes the sum

where N_y is the number of individuals in cohort y.

Calculating statistical lives saved (SLS) for the individuals in cohort y can be done by taking the sum

where M_x and M_x,y are from Table Baseline mortality and Table Adjusted mortality. If we want to limit ourselves to counting SLS, for example, during the scale-up period, this is done by changing the start and end values of the index x.

Summing over y gives the total SLS,

Calculating lives saved under a certain age, X, we can first calculate the risk of dying before X for each cohort. At baseline, this risk is

Where max(y, 0) ensures that we do not consider pre-birth mortalities for cohorts C_-25 through C_-1 or the mortality of years past for cohorts C₁ through C₁₀₀. After scaling up the interventions, the risk becomes

Now, lives saved below X is the sum

Demography Model

In our study, we employ the cohort component projection method to model demographic changes, integrating the primary determinants of population dynamics: fertility, mortality, and migration. The initial population structure, segmented by sex and categorized by discrete age groups from 0 to 100 years, is based on the 2022 release of the World Population Prospects (WPP) by the United Nations Population Division.

We initiate our projections with a detailed population age structure, delineated by sex and organized into single-year age brackets, ranging from 0 to 100 years. For fertility, we utilize the age-specific fertility rates (ASFR) provided by the WPP. The number of births is calculated by multiplying the number of females in each reproductive age group (typically ages 15 to 49) by the corresponding ASFR, and integrating across all reproductive ages to include the entire fertility span:

However, due to the granularity of the data and the necessity for computational efficiency, we opt for a discrete approximation:

For mortality, we derive life tables from the WPP mortality rates. The survivorship of individuals in the population is calculated using life table survivor rates, S(a, t), which give the probability of surviving from age a to age a+1. This allows us to compute the population at each age and sex in the subsequent year:

Here, 𝑠 denotes the sex subscript, distinguishing between male (𝑚) and female (𝑓) populations. Finally, the population projection is refined by incorporating net migration, M_s(a,t), for each age and sex:

The total adjusted population for each age and sex in the subsequent year is thus the sum of the survivors from the preceding year and the net migrants. These equations collectively form the foundation of our demographic projections, providing a comprehensive account of population evolution based on rigorous statistical modeling of the fundamental demographic processes.

Cost Model

FairChoices employed the literature-based costing methodology from Watkins and colleagues in DCP3¹. This approach relies on annual unit cost estimates defined per population or per case treated for each specific intervention (C_i,lit). The unit costs are gathered from representative studies in individual countries and documented in evidence briefs. Recognizing the pivotal role of investing in health systems to facilitate the effective delivery of specific interventions, we added markups to each unit cost c and intervention i to capture additional health systems costs beyond the intervention specific cost.

C_i = C_i,lit + α._i,lit + β.(C_i,lit + α_.i,lit)

In alignment with the DCP3 methodology, our analysis utilized estimates from the Access, Bottlenecks, Costs, and Equity (ABCE) Project data offered by the Institute for Health Metrics and Evaluation. This data determined a markup α to accommodate facility-level “indirect” costs, covering utilities, maintenance, administration, laboratory, and pathology services. The α markup was calculated separately for outpatient and inpatient facilities, constituting 7.4% for outpatient facilities and 27% for inpatient facilities. A 17% markup β was computed to address “above-facility” health system costs, encompassing aspects such as supply chain, financing, governance and administration, and health information systems, per the DCP3 framework.

We extrapolated literature-based unit costs to all Low-Income Countries (LICs) and Middle-Income Countries (MICs), assuming a consistent proportion of traded goods across countries while allowing non-traded goods and services to vary in proportion to national income. The unit cost in the target country y with gross national income (GNI) per capita Sy is estimated as

C_i,y = (γ.C_i,x.S_y / S_x) + (1 − γ).C_i,x

for unit cost C_i in the originating country x with gross national income per capita S_y, and a traded proportion of total unit cost equal to γ.

The traded proportion γ for each unit cost data point was determined by examining individual studies to identify the specific portion of the unit cost attributable to traded goods. In cases lacking sufficient information to distinguish between traded and non-traded components, we applied an average traded proportion of approximately 0.3. This pragmatic approach offered a reasonable estimate when detailed information on traded proportions was unavailable.

We converted and adjusted all costs to 2020 US dollars using Watkins and colleagues’ methodology. Unit cost estimates were combined with assessments of populations in need, and population coverage estimates to calculate intervention costs at a population level, denoted as C_i,pop. In this context, w_i represents the proportion of the target population covered by intervention i, and p_i denotes the estimated number of individuals treated by intervention i, also referred to as the population in need.

C_i,pop = (_n/∑/_i=1) C_i.W_i.P_i

We maintained C_i, the unit cost, as a constant value in 2020 US dollars, and we employed year-specific estimates of P_i from the demographic model and year-specific values of W_i derived from our cost-effectiveness and pathway analyses. This methodology enabled us to generate a series of population-level costs for all interventions. These costs were then aggregated to compute the overall cost of the intervention “package.” The summation was conducted annually for the baseline scenario, representing no change in W_i, and for various intervention scenarios where W_i increased progressively each year.

Limitations

A significant limitation in our cost modeling approach is the lack of empirical data concerning economies (and diseconomies) of scope and scale in the context of Non-Communicable Disease (NCD) interventions. While health economists generally recognize the potential for economies of scope in interventions with similar delivery characteristics, empirical validation and quantification of such economies have proven challenging. Economies of scale are more readily demonstrated in national-level programs for communicable diseases, but very little is known about the cost of NCD programs nationally and how the unit costs change with variations in population coverage. Accordingly, our cost model assumed constant marginal costs concerning coverage, though marginal costs likely differ at very low and high coverage levels. Despite this limitation, our analysis focused on (10-20%) increases in coverage from 2023 to 2030, providing a more justifiable basis for assuming constant marginal costs.