Modelling the health impact and cost-effectiveness of lymphatic filariasis eradication under varying levels of mass drug administration scale-up and geographic coverage

Background A global programme to eliminate lymphatic filariasis (GPELF) is underway, yet two key programmatic features are currently still lacking: (1) the extension of efforts to all lymphatic filariasis (LF) endemic countries, and (2) the expansion of geographic coverage of mass drug administration (MDA) within countries. For varying levels of scale-up of MDA, we assessed the health benefits and the incremental cost-effectiveness ratios (ICERs) associated with LF eradication, projected the potential savings due to decreased morbidity management needs, and estimated potential household productivity gains as a result of reduced LF-related morbidity. Methods We extended an LF transmission model to track hydrocele and lymphoedema incidence in order to obtain estimates of the disability adjusted life years (DALYs) averted due to scaling up MDA over a period of 50 years. We then estimated the ICERs and the cost-effectiveness acceptability curves associated with different rates of MDA scale-up. Health systems savings were estimated by considering the averted morbidity, treatment-seeking behaviour and morbidity management costs. Gains in worker productivity were estimated by multiplying estimated working days lost as a result of morbidity with country-specific per-worker agricultural wages. Results Our projections indicate that a massive scaling-up of MDA could lead to 4.38 million incremental DALYs averted over a 50-year time horizon compared to a scenario which mirrors current efforts against LF. In comparison to maintaining the current rate of progress against LF, massive scaling-up of MDA—pursuing LF eradication as soon as possible—was most likely to be cost-effective above a willingness to pay threshold of US$71.5/DALY averted. Intensified MDA scale-up was also associated with lower ICERs. Furthermore, this could result in health systems savings up to US$483 million. Extending coverage to all endemic areas could generate additional economic benefits through gains in worker productivity between US$3.4 and US$14.4 billion. Conclusions In addition to ethical and political motivations for scaling-up MDA rapidly, this analysis provides economic support for increasing the intensity of MDA programmes.

The lymphatic filariasis (LF) elimination and eradication scenarios are based on an analysis of the currently ongoing elimination programme. The composition of the scenarios have previously been described in detail. 1 Briefly, the scenarios were based on the mass drug administration (MDA) of filaricidal drugs: albendazole (ABZ) either in combination with diethylcarbamazine citrate (DEC) or, in areas where coendemicity of Onchocerca volvulus is a concern, with ivermectin (IVM).
To account for heterogeneity in transmission intensity within countries, we assigned proportions of each at-risk population to transmission archetypes of approximately 0% (i.e., the proportion of implementation units (IUs) that were false positive), 5%, 10%, 15% and 20% microfilaremia prevalence. The data reflect the situation in African countries, i.e., the proportion of endemic implementation units that fall within >0-5% prevalence, >5-10%, >10-15%, or >15%. The archetypes used in the analysis reflect an upper boundary to the underlying data, save for the highest level, where a 20% prevalence was taken as a representation of very high transmission levels. The average proportion of IUs that fell within these categories was extrapolated to all other countries for which these data were not available. Uncertainty in this estimate was included by treating these averages as a probability in a multinomial distribution. 1 We used the estimated number of treatments required for each year, in each LF-endemic country and each scenario from Kastner et al. 1 These estimates were based upon the number of annual treatment rounds of MDA necessary, taking into consideration the underlying microfilaria prevalence quartiles in each country, whether transmission is due to Anopheles spp. or Culex spp., the drug regimen used, and the number of effective MDA rounds that had already occurred prior to 2013. These estimates are conservative in the sense that they allowed 97.5% of our simulations to achieve elimination. We thus assumed that public health officials implemented MDA programmes of these durations in order to assure a high probability of achieving elimination. We then used these estimated durations to predict the number of treatments required per year for each of the elimination and eradication scenarios, as well as to develop estimates of the financial and economic costs associated with implementing the scenarios (Kastner et al., submitted).

Transmission model
We used two versions of the deterministic model, EpiFil 2 , to simulate adult filarial worm, microfilaria and infective stage larvae (L3) transmission and dynamics when the mosquito vectors were either Anopheles or Culex spp. The model versions we used largely followed the structure presented by Gambhir & Michael,3 which includes the possibility of female worms remaining unmated in humans at low densities, and provides different microfilariae uptake functions (facilitation and limitation) for Anopheles spp. and Culex spp. vectors. We assumed that transmission by other mosquito genera (e.g., Aedes, Mansonia) is approximated well enough by these model versions.
The transmission model was thus the same as used and described in our related analysis. 1 The model consists of the following partial differential equations used to describe changes in state parameters: The state parameters represent the mean adult worm burden in humans, W; the mean microfilariae density in humans, M; and the mean level of immunity to infection, I. The initial conditions were W(0,t) = M(0,t) = I(0,t) = 0, while W(a,0), M(a,0) and I(a,0) were the equilibrium levels in the absence of interventions, obtained numerically by simulating the model for a sufficiently long period. L*, the mean L3 density in the mosquito population, is given by: The functions h(a) and π(a) represent the age-dependent availability to mosquitoes (represented as a linear increase from 0 to 1 over the first 10 years of life and a value of 1 for further years) and an approximation of the human age distribution (π(a) = 0·035 e -0·026 a ), respectively, as in Norman et al. 2 .
The population-averaged uptake of infective stage filarial larvae by mosquitoes, f(M), is defined as: with f(M) C describing the function used for Culex spp. 2 and f(M) A for Anopheles spp. 3 . The worm mating function 3, 4 is given by:

Disease model
To assess the resulting health impact of the different scenarios, the progression of disease, adapted from the ordinary differential equations of Chan et al., 5 was added to the model of LF transmission.
These equations suggest that progression to hydrocele and lymphoedema result directly from damage to the lymphatic system. This damage is assumed to accrue over time as a direct consequence of harbouring adult worms. In our model (equation 8) the prevalence of lymphatic damage thus increases over time and with age as a function of the mean adult worm burden in the community. In the absence of adult worms, we assume that the prevalence of lymphatic damage may slowly diminish, as will the prevalence of hydroceles, but not lymphoedema. Different grades of lymphoedema or hydrocele, or other aspects of disability related to LF, are not accounted for:  (10) where D represents the mean proportion of humans with lymphatic damage; the mean proportion of humans with lymphoedema is given by L; and the mean proportion of males in areas where W.
bancrofti is the causative agent with hydrocele by H. The rate parameters and range of prior values used are described in Supplementary Table 1.

Parameter estimation
We used the same posterior parameter estimates for the parameters of the transmission model (i.e, those appearing in equations 1-7) that resulted in stable prevalence levels associated with the transmission archetypes (ca. 5%, 10%, 15%, and 20% prevalence), as well as the expected durations of MDA programmes in the different transmission settings. 1 The effects of filaricidal treatment were included through a once-yearly instantaneous killing of a proportion of adult worms, μ w , and microfilariae, μ mf , within the proportion of humans (85% of the total population) covered by the programs. Additionally, the fecundity of adult worms, , was reduced to zero for six to nine months following a round of MDA within treated humans. 6 The exact values of these killing parameters were randomly sampled from their ranges to allow for a degree of uncertainty in the efficacy of MDA programmes.
The parameters related to the disease model (those in equations 8-10) were estimated for each of the four levels of prevalence associated with our archetypes using the same importance-resampling method as previously described, and similar to that which has been used to fit EpiFil to transmission patterns in specific geographic settings. 1,7,8 For the purpose of obtaining disease parameter estimates, we fixed the transmission related parameters at the medians of their previously estimated values, while for the disease-related parameters we drew 10,000 random samples from their uninformative prior ranges. A relation between the prevalence of chronic disease states due to LF (hydrocele and lymphoedema) and microfilaria prevalence in given localities has been investigated and these data are presented by Michael et al. 9 and replotted (Fig S1a). The median and interquartile ranges of the data points per our transmission archetypes are depicted in Fig. S1b.
We ran 10,000 simulations and calculated the goodness of fit of each simulation to the data on chronic disease prevalence. Because we required estimates of the prevalence of hydrocele and lymphoedema, rather than a combined prevalence of chronic disease, the total prevalence was decomposed to male and female prevalence following the global estimate of Michael et al. 10 , so that Pr cd,male = Pr cd,total *1·75 and Pr cd,female = Pr cd,total *0·25, where Pr cd,male is equal to Pr l+h and Pr cd,female is equal to Pr l .
We therefore make the simplifying assumptions that males and females acquire lymphoedema at equivalent rates, and that co-occurrence of lymphoedema and hydrocele in males is rare. The goodness of fit to a point prevalence level was assessed through a binomial likelihood: , where N is the human population size (assumed to be 1,000), p s the target prevalence levels of disease associated with the transmission archetype, and x s is the simulated number of afflicted humans for the simulation run with parameter set, i. Male and female populations are indicated by s. We then randomly sampled, with replacement, 500 parameter sets from the original 10,000 sets proportional to their likelihood,  to obtain an approximation of their posterior distribution. 7 The prevalence of chronic LF-induced disease outcomes from sets of 500 simulations using the resampled parameter sets are depicted in Fig. S1c.  The median and interquartile ranges of the data points binned per prevalence levels associated with transmission archetypes. Right: Probability densities of chronic disease outcomes from sets of 500 simulations using resampled parameter sets.

Assessing the disability adjusted life years averted by the eradication scenarios
Based on the results of the transmission and disease model, and accounting for the different transmission archetypes and the number of MDA rounds that countries had already completed, the mean prevalence of lymphoedema and hydrocele for each age class over a period of 50 years was computed and recorded as matrices P l (t,a) and P h (t,a). In areas where Brugian filariasis predominates, we assumed that males are not affected by hydrocele 11 and (due to paucity of data to improve on this assumption) that lymphoedema progressed as in Bancroftian filariasis. This was implemented for 20% of the Philippines and 60% of Indonesia, based on the ratio of prevalences between types, 11 rounded up or down.
To translate prevalence to incidence per age class, we used country-specific demographic parameters  (2) where the matrices are multiplied using the Hadamard product (i.e., element-wise), subscript i indicates the deciles within a country which differ only in their history of MDA, j indicates the four transmission intensity levels, and k each of the 500 iterations of the model. We then summed the cases over the deciles, I f,j,k (t,a) and I m,j,k (t,a), and obtained the number of new cases per 5-y-period and 5-yage-group, as: where the future discounting rate, dr, was set to 1·03.

Assessing costs of implementing the global elimination and eradication scenarios
The costs of the scenarios modelled were estimated from the perspective of each LF-endemic country's health system. USAID's NTD Master Plan Costing Tool in the African Region from eight AFRO countries were reviewed to assess essential activities and resources needed to undertake the GPELF activities at a country level. Essential activities, resources, and their associated costs were then confirmed by the LF elimination team in Uganda. All costs are reported in 2012 U.S. dollars and discounted at 3%. Using Ugandan costs as a reference, the prospective costs for non-tradable goods and services in all other LF-endemic countries were imputed by adjusting with country-specific purchasing power parity (PPP) conversion factors. 13 All laboratory supplies and capital items were valued at their recommended retails prices. Salaries, as well as prices that were unable to be determined elsewhere,

Supplementary
were taken from the WHO-CHOICE databank. 14