Table 2.
Constrained analyses characteristics.
| Lead author (year) | Constrained analysis objective | Non-financial constraints | Constraints identification | Constraints parametrisation and data sources | Approach for modelling constraints | Constraints implementation, details | Scenarios description |
|---|---|---|---|---|---|---|---|
| Adisasmito et al. (2015) | Feasibility assessment - produce realistic intervention impact estimates given health system constraints | HR, bed space, equipment, pharmaceutical supplies | Literature | Literature and secondary data analysis (AsiaFluCap survey) | Transmission model-based estimation - Calculate resource requirements | Transmission model linked to resource calculator to estimate requirements during outbreak. Model calculates depletion rate of resources based on average requirements to treat one case, estimated through a mix of data from literature and routine sources. Needs are compared to capacity, estimated through a survey administered as part of AsiaFluCap project | Two scenarios with different hospitalization and mortality rates |
| Alistar et al. (2013) | Efficient resource allocation - maximising impact given health system constraints | Political constraint on decision-making | Assumption | Assumption | Transmission model-based estimation - Limit effects and calculate costs along the cascade | REACH is an Excel-based user-friendly model helping policy makers allocate resources across different HIV control interventions. It comprises transmission dynamics and optimisation function. Optimisation done under budget constraint only, but political/social/ethical constraints on allocation of resources can be specified in the user interface. Outputs sheet includes estimates of health care resources needed to support the allocations | – |
| Anderson et al. (2014, 2018) | Feasibility assessment and efficient resource allocation - produce realistic intervention impact estimates and maximise impact given health system constraints | Political constraint on decision-making, demand side barriers to access | Assumption | Assumption | Transmission model-based estimation - Limit effects and calculate costs along the cascade | Constraints determine the way funds are allocated to key populations (MSM, other men, FSW, other women), geographical areas and throughout 5-year funding cycles (fully flexible, frontloaded, constant or back-loaded). Intervention choice optimised under the different resulting budget constraints. Constraints to implementation also parametrised in the form of uptake limits to certain intervention components | For key populations and districts (paper 1), all possible intervention scenarios compared by constructing health production functions for a given cost. For spending cycle (paper 2), 5 scenarios: 2 with complete spending flexibility (one of which with intervention change at 10 years), choices optimised over 30-year period; 3 with front-loaded, equal and back-loaded funding cycles, respectively, and choices optimised over each 5-year cycle |
| Bärnighausen et al. (2016) | Feasibility assessment - produce realistic intervention impact estimates given health system constraints | HR | Assumption | Literature | Transmission model-based estimation - Limit effects and calculate resource requirements along the cascade | Given current HR supply, number of patients treated is computed assuming fixed ratios for each cadre to patient. Model projects the impact of reallocating scarce HR to varying patient distributions in the different HIV disease stages and can estimate potential shortages | 200 scenarios varying assumptions around HIV transmission probabilities, ART effect, retention and adherence. Two sets of constraints scenarios: one where allocation of HR is proportional to number of patients in TaSP and standard ART (treatment for advanced disease stages) pools, respectively; one where more HR allocated to pool with patients at more advanced disease stages |
| Barker et al. (2017) | Feasibility assessment - produce realistic intervention impact estimates given health system constraints | HR | Assumption | Secondary analysis of data from Tanzania and Mozambique on time spent by facility health workers delivering ART | Transmission model-based estimation - Calculate resource requirements | Model estimates total facility staff FTE needed for different ART differentiated care models, based on previous estimates of time spent delivering ART in Africa. An analysis of constraints is not presented because differentiated care models are expected to lead to cost and HR savings | – |
| Bottcher et al. (2015) | Feasibility assessment - produce realistic intervention impact estimates given health system constraints | Political constraint on decision-making, recurrent supplies | Assumption | Assumption | Transmission model-based estimation - Limit intervention effects | Model projects a global budget that increases by one unit with each additional healthy individual per unit of time and partially constrains recovery when available budget is insufficient for covering 'costs of healing' | – |
| Bozzani et al. (2018, 2020), Sumner et al. (2019) | Feasibility assessment and efficient resource allocation - produce realistic intervention impact estimates and maximise impact given health system constraints | HR, diagnostic equipment | Expert opinion | Secondary data collection from routine sources including district health information system (DHIS) and other Department of Health and Nursing Council records | Transmission model-based estimation - Limit effects and calculate resource requirements along the cascade | Unit costs and staff FTE to deliver different services are attached to model outputs to limit intervention effects once threshold of available resources is exceeded. Diagnostic constraint parametrised as maximum ratio of tests to TB notifications. Costs of 'relaxing' the constraints to achieve target coverage is calculated. | 3 scenarios (least limiting, medium and most limiting) considered for each constraint (budget, diagnostic and HR), respectively, based on projections of future resource availability |
| Chen et al. (2019) | Feasibility assessment - produce realistic intervention impact estimates given health system constraints | Resources that are necessary to contain an epidemic (not specified) | Assumption | Assumption | Transmission model-based estimation - Limit intervention effects | A value Rc, representing the level of resources in the system, is identified, whereby the epidemic can be effectively contained. If R < Rc the disease becomes widespread, recovery rate varies with time depending on average amount of resources that each infected individual receives | Scenarios explored with different levels of health system resourcing |
| Cruz-Aponte et al. (2011) | Feasibility assessment - produce realistic intervention impact estimates given health system constraints | Vaccine stockouts | Assumption | Assumption | Transmission model-based estimation - Limit intervention effects | Vaccine administration limited by daily maximum number. Vaccination campaign ends a) after some prescribed duration of time; or b) when stockpile is depleted. Results are compared with those from alternative model that ends campaign when target proportion of population is vaccinated. | Three scenarios varying the number of vaccines administered in a time period (56-, 28-, and 3-day campaign with different daily administration limits) |
| Curran et al. (2016) | Efficient resource allocation - maximising impact given health system constraints | HR, supplies and infrastructure | Group model building - System dynamics modelling techniques | Assumption | Transmission and system dynamics models linkage - Limit effects system-wide | The paper outlines possible ways of integrating transmission dynamics modelling with data generated from population surveys and sentinel surveillance and with system dynamics models to predict resource capacity during epidemic outbreaks and assist with resource allocation based on predicted pathogen spread | Multiple scenarios with varying disease transmission rates and health system capacity can be analysed |
| Dalgiç et al. (2017) | Efficient resource allocation - maximising impact given health system constraints | Vaccine stockouts | Assumption | Assumption | Constrained optimisation - Limit intervention effects | Optimise vaccine allocation in different age groups subject to constrained availability. Different objectives (minimise total costs, total infections, total deaths, total years of life lost) | Several vaccine coverage and delayed response time scenarios |
| Ferrer et al. (2014) | Feasibility assessment - produce realistic intervention impact estimates given health system constraints | HR | Assumption | Primary data collection at 5 ICUs on bed occupancy and staffing conditions | Transmission model-based estimation - Limit intervention effects | Model includes estimates of nurses' contact time with patients, which has an effect on pathogen spread. Daily rate of nurse absenteeism varied to adopt a fixed value between 10−40% and different coping mechanisms modelled | Systematic analysis of pathogen dissemination under different scenarios of pathogens circulating, level of nurses shortage and shortage management strategy |
| Hecht and Gandhi (2008) | Feasibility assessment - produce realistic intervention impact estimates given health system constraints | Political constraint on decision-making, demand side barriers to access | Literature and expert opinion | Assumptions based on expert consultation | Transmission model-based estimation - Limit intervention effects | Global demand for vaccine forecast by adding up demand estimates for individual country profiles | Four vaccine profile scenarios based on variations in efficacy, duration of protection and cost |
| Hontelez et al. (2016) | Efficient resource allocation - maximising impact given health system constraints | HR, infrastructure, demand-side barriers to access | Assumption | Assumptions made on effects of constraints on ART coverage. Costs of one-off investment needed to relax constraints calculated from routine AIDS spending reports | Transmission model-based estimation - Limit effects and calculate costs system-wide | Model calculates total investment needs, population health gains and cost-effectiveness of scaling-up new ART eligibility guidelines, including removal of health system constraints | Scenarios reflecting pessimistic, realistic and optimistic future health system developments, in which constraints apply to different extents |
| Krumkamp et al. (2011) | Efficient resource allocation - maximising impact given health system constraints | HR, pharmaceuticals supplies and other consumables | Assumption | Expert opinion and primary data collection (AsiaFluCap survey) | Transmission model-based estimation - Limit effects and calculate resource requirements along the cascade | Model constrains epidemic containment based on availability of resources and calculates resource depletion per hospital case. Resource usage data and impact of constraints estimated from a mix of survey data and expert opinion | Different epidemic control strategies modelled (antivirals stockpiling for critical cases, contact reductions) |
| Langley et al. (2014), Lin et al. (2011) | Efficient resource allocation - maximising impact given health system constraints | HR, diagnostic pathway bottlenecks, demand-side barriers to access | Group model building - Operational modelling techniques | Primary data collected from two diagnostic centres in Tanzania and calibrated using National TB programme reports | Transmission and operational models linkage - Limit intervention effects | Operational model outputs used to parametrise transmission model and vice versa. Operational component uses discrete-event simulation approach to model patient and sputum sample pathways | Different diagnostic algorithms modelled |
| Marks et al. (2017) | Feasibility assessment - produce realistic intervention impact estimates given health system constraints | Demand-side barriers to access | Assumption | Assumption | Transmission model-based estimation - Limit intervention effects | Eradication modelled under a range of plausible targeted treatment coverage estimates (65 %–95 %). Mass treatment compliance modelled as a random non-systematic process where every patient has the same, independent likelihood of receiving treatment | 3 transmission scenarios modelled (low, medium, high) based on literature and expert opinion |
| Martin et al. (2015a, b) | Feasibility assessment - produce realistic intervention impact estimates given health system constraints | Implementation' constraints, demand-side barriers to access | Group model building - System dynamics modelling techniques | Literature and expert opinion | Transmission and system dynamics models linkage - Limit intervention effects | Scenario analysis where the flow of patients along the HIV testing and care cascade is determined by different sets of assumptions regarding policy implementation. These were defined in consultation with experts and based on the literature, by developing a system dynamics model that assesses the impact and relationships of different policy components | 3 policy 'implementation' scenarios (low, high, perfect) and 3 testing policy scenarios (annual, five-year and no repeat offer of testing) combined to generate 9 unique combinations of policy conditions in addition to the base case |
| Martin et al. (2011) | Efficient resource allocation - maximising impact given health system constraints | Political constraint on decision-making | Assumption | Assumption | Constrained optimisation - Limit effects and calculate costs along the cascade | Optimal treatment strategy for HCV is examined under different economic and policy objectives: 1) minimise costs and QALY loss; 2) minimise prevalence; 3) minimise costs and QALY loss while achieving 20 % time prevalence reduction; 4) minimise costs while achieving 20 % time prevalence reduction | Analysis is repeated for a combination of annual budget constraints and two HCV baseline prevalences (30 % and 45 %) |
| McKay et al. (2018) | Feasibility assessment - produce realistic intervention impact estimates given health system constraints | HR | Assumption | Model parametrised with trial and implementation studies data and informed by published organizational and intervention sustainability models | Transmission model-based estimation - Limit effects and calculate resource requirements along the cascade | Model predicts the level of preventive services a health agency can provide given different combinations of i) staff positions; ii) turnover rates; iii) timing in training. | N/A |
| Peak et al. (2020) | Feasibility assessment - produce realistic intervention impact estimates given health system constraints | Barriers to effective contact tracing and quarantine interventions, including untrained monitoring of symptoms | Assumption | Assumption | Transmission model-based estimation - Limit intervention effects | R0 is estimated based on the implementation of quarantine and active monitoring in high- vs low-feasibility settings | Analysis compares a high- (90 % contacts traced and quarantined or monitored, reducing infectiousness by up to 90 %) and a low-feasibility setting (delays in locating contacts, imperfect quarantine) |
| Putthasri et al. (2009) | Efficient resource allocation - maximising impact given health system constraints | HR, supplies and infrastructure | Expert opinion | Expert opinion | Transmission model-based estimation - Calculate resource requirements | Actual and projected resources per case multiplied by the number of case-patients estimated by previous modelling exercises under different scenarios. Resource gaps estimated at the provincial level | 3 epidemic (human-to-human transmission) scenarios analysed, with specific numbers of index cases and contacts: 1) from case-patients to caregivers; 2) localised clusters; 3) transmission resulting in substantial number of cases |
| Rudge et al. (2012) | Feasibility assessment and efficient resource allocation - produce realistic intervention impact estimates and maximise impact given health system constraints | HR, bed space, equipment, pharmaceutical supplies | Multi-criteria decision analysis - Delphi consensus process with a panel of 24 experts integrated with literature review | Primary data collection at health facilities to enumerate available resources. Gaps estimated based on literature on resource needs | Transmission model-based estimation - Calculate resource requirements | Available quantities of resources estimated through a survey sent out to hospitals, district health offices and ministries of health. Additional model parameters describing clinical pathway of infected individuals, conditional upon availability of resources | Model runs: i) available resources; ii) unlimited resources (to calculate gaps and compare with availability data from survey) |
| Salomon et al. (2006) | Feasibility assessment - produce realistic intervention impact estimates given health system constraints | HR, infrastructure | Assumption | Assumption | Transmission model-based estimation - Limit intervention effects | Constraints not explicitly modelled, but scenarios are analysed where it is assumed that the intervention reduces constraints to case detection, thus improving case detection rates | Scenarios were modelled with varying assumptions about case detection coverage (including one where constraints are relaxed), cure rates and DOTS scale-up |
| Sébille and Valleron (1997) | Feasibility assessment - produce realistic intervention impact estimates given health system constraints | Pharmaceutical supplies, political constraint on decision-making | Assumption | Assumption | Transmission model-based estimation - Limit intervention effects | Scenarios with different risk of patient-to-staff transmission based on whether procurement of two essential antibiotics is simultaneous (both available), sequential (only one available at a given time, then the other) or a mix of the two | Software allows for different assumptions to be specified before running simulations (e.g. drug procurement policy, staff handwashing compliance) |
| Shattock et al. (2016) | Efficient resource allocation - maximising impact given health system constraints | Political constraint on decision-making | Assumption | Assumption | Transmission model-based estimation - Limit intervention effects | Time-varying optimization i.e. minimising objective function (cumulative HIV infections) associated with the budget allocation, such that: i) total programme spending equals a pre-defined budget (either constant, front-loaded etc.) at each time point; or ii) total spending across the optimisation period is equal to pre-defined budget, but total spending at each point is optimally determined | 4 optimization scenarios illustrating policy decisions where time considerations matter: 1) optimal 10-years allocation assuming baseline budget is annually available with no constraints to programme-specific allocation; 2) as in 1, but programme-specific funding cannot vary by more than 30% compared to baseline; 3) as in 1, but annual optimal allocation determined based on implementation and ethical constraints; 4) optimal 5-years allocation but cumulative new infections assessed after 5, 10 or 15 years, again within constraints |
| Shim et al. (2011) | Efficient resource allocation - maximising impact given health system constraints | Demand-side barriers to access | Assumption | Assumption | Transmission model-based estimation - Limit intervention effects | Decision to vaccinate characterised as a game, where monetary payoff for different age groups is modelled based on different individual strategies as well as on the average behaviour of the population | Two strategies modelled to calculate payoff to vaccinated and non-vaccinated: Nash and utilitarian |
| Stenberg et al. (2017) | Efficient resource allocation - maximising impact given health system constraints | HR, infrastructure, demand-side barriers to access | Assumption | Assumption | Transmission model-based estimation - Calculate intervention costs | Tracer interventions identified for each of the relevant SDGs, then gap estimated between current provision and universal coverage and country-specific programme costs multiplied by this gap. Costs estimated from the One Health Tool and from the literature. Progress towards 2030 targets adjusted by level of 'strength' of the health system (conflict, vulnerable, low-income, lower middle-income, upper middle-income) | Two financial space scenarios in each country, reflecting uncertainty around health systems' absorption capacity: i) ambitious, strengthening system towards global benchmarks and expanding coverage of full service package to 95%; ii) progress, not all SDG targets met by 2030 but improvements can be achieved by scaling up services delivered through the lower platforms |
| Stopard et al. (2019) | Efficient resource allocation - incidence minimizing | Political constraints on decision making (earmarking, externally imposed targets, minimising change to current program) | Assumption | Assumption | Transmission model-based estimation - Calculate intervention costs and impact | Constraints are modelled through initial conditions in each scenario representing minimum coverage by subgroups within the transmission model | Four scenarios of real-world constraints: 1) earmarking, where the first intervention funded would be PrEP for heterosexual women (excluding FSWs); 2) targets, where 90 % of PLHIV must receive UTT; 3) minimising change, baseline allocation represents an allocation at national level; and 4) all constriants simultaneously |
| Verma et al. (2020) | Feasibility assessment - produce realistic intervention impact estimates given health system constraints | Hospital beds, ICU beds and mechanical ventilation equipment | Assumption | Secondary data | Transmission model-based estimation - Limit effects and calculate resource requirements along the cascade | Available capacity estimated from public records, including for private sector. Capacity needs calculated based on requirements per case and turnover times from the literature. Capacity requirements during surge are based on model projections under different lockdown scenarios. Surge capacity compared to available capacity to estimate gap. | Different lockdown/social distancing scenarios |
| Zhang et al. (2020) | Efficient resource allocation - maximising impact given health system constraints | Vaccines availability | Assumption | Assumption | Constrained optimisation - Limit intervention effects | Optimise allocation of limited vaccines in order to minimise the number of infections | N/A |
AIDS: Acquired Immunodeficiency Syndrome; ART: Anti-Retroviral Therapy; FTE: Full-Time Equivalent; HCV: Hepatitis C Virrus; HR: Human Resources; ICU: Intensive Care Unit; QALY: Quality-Adjusted Life-Years; SDG: Sustainable Development Goals.