The Singapore Eye Care Workforce Model was created as a continuous time compartment model with explicit workforce stocks using the systems modeling methodology of system dynamics [6–8]. The model consists of interacting sets of differential and algebraic equations developed from a broad range of relevant empirical data. The systems modeling methodology is well suited to address the dynamic complexity that characterizes health workforce planning [9, 10]. Senese et al. [11] developed a system dynamics model to projects the evolution of the supply of medical specialists. Ishikawa et al. [9] used system dynamics methodology and model to forecast future needs for clinical physicians and OB/GYN specialist and estimated the likely shortfall. Barber et al. [12] created a demand/need simulation model for 43 medical specialists using system dynamics.
The Singapore Eye Care Model was developed to evaluate at the national level demand for eye care services and the implication of service demand for the future workforce and training requirements in the public sector. First, a conceptual computer model that simulated the current behavior pattern of key variables was developed. Next, the conceptual model was presented to the modeling team, which consisted of ophthalmologists, senior nurses, healthcare planners and managers, and health educators from SNEC, to verify its structure and assumptions regarding causal relationships. Following verification, the model was parameterized using data. When data were not available, estimates from experts were used. Finally, the model was simulated, and base-case and alternative scenario projections were made. The insights gained were presented and shared with the modeling team and the strategic planning committee of SNEC including its medical director and chief operating officer, senior ophthalmologists, senior nurses, and researchers.
Generally, health workforce projections employ supply-based methods [13–15] or demand-based methods [15–18]. The sources cited provide more information on the different approaches [19, 20].
Compared with the supply-based and demand-based forecasting approaches, our comprehensive/integrated approach combines the supply-based and demand-based methods to project the eye health workforce needs.
Singapore Eye Care Workforce Model
The model was constructed as three linked modules: the prevalence of eye disease module, the demand module, and the ophthalmologist requirement and supply module.
Prevalence of eye disease module
The prevalence of eye disease module applies the prevalence of eye diseases from the Singapore Epidemiology of Eye Diseases (SEED) study [21–23] for resident Singaporeans 40 years and older to the population model of resident Singaporeans (Figure 2). The prevalence of eye diseases was disaggregated by age (age 0–age 100 and older), ethnicity (Chinese, Malays, Indians, and others), and educational attainment (no formal education, primary school, secondary, and tertiary). The eye conditions included herein are cataracts, diabetic retinopathy (DR), glaucoma, age-related macular degeneration (AMD), myopia, refractive errorc, epiretinal membrane (ERM), retinal vein occlusion (RVO), and other conditions.d The resident population module illustrates an aging process of Singapore’s resident population and the age distribution of the resident population disaggregated by 1-year age cohorts by gender, ethnicity, and educational attainment. The resident population module shows births, deaths, immigration, and emigration as the four determinants of population change over time. It is calibrated using publicly available national statistical data [24] and is described in detail elsewhere [25–27].
To project the number of Singaporeans and permanent residents over 40 with eye conditions, the prevalence estimates from the SEED study was applied to the projected population of residents over 40 years of age till 2040. The projection is disaggregated by age, ethnicity, educational attainment, and eye conditions. The projection for DR takes the expected future increase in diabetes into account [28]. Due to a lack in data, it was not possible to project the prevalence of eye diseases among the younger population; however, with the exception of myopia, the prevalence of eye disease among the young is likely to be much lower than that among the population over 40 years.
Demand module
The demand module (Figure 3) uses output from the prevalence of eye disease module to project demand for eye services. For this module, we are interested in the demand for public sector specialist eye care services. While the majority of patients at public sector eye care centers are Singaporean and permanent residents over the age of 40, younger people and foreigners also use these centers. Moreover, Singaporeans and permanent residents over 40 will also seek care in the private sector.
We have taken the current number of demand (visits and waiting list) in the public sector (disaggregated by disease according to administrative case mix data from SNEC) as a starting point. Based on the assumption that the change in number of all new patients seeking care will be proportional to the change in the prevalence of conditions among residents, we can project the number of new patients entering the system over the time frame of the simulation. Although foreigners and younger people represent only a comparatively small part of all patients at public sector eye centers, there is a degree of uncertainty connected with this assumption; hence, a sensitivity analysis was performed.
We define the relationship between the number of new patients entering care and the number of Singaporean and permanent residents of age 40+ with untreated eye diseases as (disease-specific) uptake factor. This uptake factor therefore accounts for the visits by foreigners and young people as well. It was estimated by calibration. The uptake factor multiplied by the 40+-year-old resident population in Singapore with eye conditions not receiving eye care services therefore estimates the number of new patients seeking care.
The stock of patients in care increases via new patients seeking care and decreases via death and patient in care attrition. Thus, new patients flow into the age cohorts of patients in care, while the stock of surviving patients in care flows into the subsequent age cohort with the exception of the final age cohort (age 100 and older). Those who have completed treatment flow out to the completed care population stock. The non-surviving patients in each age cohort are removed via deaths—reflecting age-specific mortality. New patients represent individuals seeking care for the first time, whereas attrition of patients in care represents those who have completed treatment in the specialist centers (potentially to seek further care in the community). The completion of treatment is applicable only to cataracts, myopia, and refractive error, with estimated treatment duration at the public specialist eye care centers of 3, 1, and 2 years, respectively. All other eye conditions are assumed to require lifelong care in the specialist eye centers. Mortality rates of patients in care were determined by age-specific mortality from life tables. Attrition of patients in care is calculated as patients in care divided by average duration in care. The completed care population increases via attrition of patients in care and decreases via death. Attrition of patients flow into the population of completed eye care treatment, while the surviving individuals flow into the subsequent cohort with the exception of the final age cohort—age 100 and older. The non-surviving individuals in each age cohort are removed via deaths, reflecting the age-specific mortality.
The demand was calculated from the number of patients in care and average visits per year. The completed care population stock consisted of individuals who have completed eye care treatment for cataracts, myopia, and refractive error.
Ophthalmologist requirement and supply module
The ophthalmologist requirement and supply module (Figure 4) is a continuous time compartment model that tracks the demand and the changing number of ophthalmologists employed over time in the public sector, as well as the training pipeline of ophthalmologists. The change in the number of ophthalmologists is a result of new hires and attrition, which is a blended value of retirements, deaths, and resignations. The ophthalmologist requirement module produces three main outputs: the required ophthalmologists, training pipeline of ophthalmologists, and ophthalmologists working in the public sector. The model accounts for sources of recruitments to ophthalmology residency, the training pipeline, decisions for hiring, and the demand-supply gap of ophthalmologists.
As represented in the module diagram, the stock of medical students increases via admissions and decreases via dropout and graduation. Graduating medical students flow out of the medical student stock through three flows: becoming house officers, entering ophthalmology residency, and entering other residency. The source of students entering medical school was considered outside the model boundary. In other words, the source of students suitable for starting medical school was not constrained, and so, it was not necessary to represent schooling prior to medical school.
Thus, the stock of house officers increases as new medical school graduates become house officers and decreases via attrition (becoming general practitioners, entering other residency programs, or taking other jobs), entering the ophthalmology residency program, or becoming medical officers after years of service as house officers.
Likewise, house officers becoming medical officers will eventually decide to remain as medical officers, leave the system for other opportunities, or enter the ophthalmology residency program. Thus, the stock of medical officers increases as new medical officers are hired and decreases via attrition and admission to ophthalmology residency. The transition from house officer to medical officer is determined by the difference between demand for medical officers and current medical officers. Accordingly, medical officer hiring is dependent on desired medical officer hiring. Desired medical officer hiring is defined herein as the medical officers’ gap (difference between desired medical officers and medical officers employed) and expected attrition of medical officers.
The stock of ophthalmology residents (representing the training pipeline) increases as new residents are admitted and decreases via completing the residency program. Upon completion, residents exit the residency stock via hiring to become ophthalmologists or take up other jobs (i.e., become ophthalmologists in the private sector, migrate or take other jobs). The ophthalmology residency intake is represented in the module as a policy variable determined yearly by policy makers. The stock of ophthalmologists integrates new hires (ophthalmology graduate hiring) and attrition (deaths, retirement, quit for other opportunities). Ophthalmologist hiring is determined by desired ophthalmologist hiring, which is defined as the sum of ophthalmologist gap and the expected attrition of ophthalmologist.
On the demand side, the model uses demand for eye care services to project required ophthalmologists. The future ophthalmologist requirement is determined herein by total demand and the estimated workload per ophthalmologist. The workload per ophthalmologist (patient-visits-to-ophthalmologist ratio) is calculated using data from 2003 to 2014.
Data sources
Demographic data used as inputs for the population module were obtained from the Singapore Department of Statistics (SDS) [24]. Time series data of the resident Singapore population from the SDS were used to calibrate the simulation result of the population module. Age-specific prevalence estimates from the SEED study [21–23] were used. The Ministry of Health (MOH) provided administrative patient visit data disaggregated by patient type (i.e., subsidized and non-subsidized) for the six public hospitals and SNEC in Singapore. SNEC provided administrative patient visit case mix data, disaggregated by age, eye disease, and ethnicity, as well as data from 2003 to 2013 on the numbers of each type of healthcare worker employed by SNEC, and data on ophthalmologists’ work schedule used to estimate the proportion of time spent on clinical work, research, teaching, and administration duties. Data on the number of ophthalmologists in Singapore were obtained from Singapore Medical Council annual reports from 2003 to 2014 [29]. Registration records of ophthalmologists were used to identify their current workplaces. The various data sources and model input parameters are listed in Table 1.
Model validation
For the model validation, two critical tests (behavior and structure validation test) were selected to demonstrate its fit and quality. The behavior test shows simulated behavior compared to available time series data of selected variables, demand, and number of ophthalmologists employed (refer to Additional file 1). The results indicate that the simulated model compares well with the time series data suggesting that on the face value, the model performs credibly for the visual fit test.
For the structure test, the model was presented to the stakeholders, to verify its structure and assumptions regarding causal relationships. Hence, the model is firmly grounded in current available evidence on the interactions between prevalence of eye conditions, utilization of eye care services, and the capacity of eye healthcare system.
Scenarios
The following scenarios were developed to cover the range of potential future directions that were expressed by stakeholders:
Business-as-usual (BAU): The BAU scenario assumes no change to key variables that may be affected by policy change, i.e., uptake factor of eye services, current model of care, subsidies, and workload of eye care workforce remain unchanged from 2013 values up to 2040. Under this scenario, the uptake factor, which is calibrated, is 4.5% for individuals with no education, 7% for those with primary education, 7.6% for those with secondary education, and individuals with tertiary education is 15%. Also, it is assumed that under the new Primary Eyecare Clinic (PEC) initiative only 5% of all patients with DR, glaucoma, myopia, and refractive error are decanted from SOCs to PECs to be cared for by non-specialists. This hypothetical scenario is unlikely in the current context in which uptake factor is expected to change as the population becomes more aware of services and new models of care are introduced, including new technology, subsidies, and new care pathways. However, it is included to serve as a reference point for evaluating the alternative scenarios.
Current policy: This policy scenario is identical to the BAU scenario with the exception that the uptake factor among individuals with eye condition not receiving eye care is assumed to change. This is due to an expected increase in eye disease screening (which will significantly increase the number of people with diagnosed eye condition and consequently the use of services), awareness and availability of eye care clinics in the community, and new models of care including new technology which makes eye care more accessible and available. Thus, it is assumed that care seeking among individuals with untreated eye condition increases from 4.5% to 13% by 2040 for those with no education, while that for individuals with primary, secondary, and tertiary education are 20%, 21%, and 46%, respectively.
New model of care: The new model of care scenario is like the current policy scenario except that, under the new PEC initiative, 20% of all patients with DR, and glaucoma, as well as 90% of patients seeking care with myopia and refractive error, are decanted from SOCs to PECs to be cared for by non-specialists [30, 31]. The role of non-specialists (e.g., optometrists) running clinics is currently very limited (there is no bachelor education in optometry available in Singapore). Experiences in other countries such as the U.K. and Australia show, however, the potential of larger transitions.
Moderated workload: The moderated workload scenario is indistinguishable to the new model of care scenario with the exception of a 15% reduction in the clinical workload of ophthalmologists due to efforts to pursue non-clinical goals (such as research and education), improve work-life balance, and improve patient care in line with the focus on care delivery in an academic medical center setting.
Sensitivity analysis
Sensitivity analysis was performed using Markov chain Monte Carlo (MCMC) [32] on the base-case and other scenarios to observe how a change in the most important parameter affects output of interest. The uptake factor parameter was identified to be the most important parameter. Using MCMC, accepted points (after the optimal burn-in period) from the MCMC calibration were used as input to the sensitivity runs so as to explore the response of variables of interest in the model subject to the posterior probabilities from the calibration. The model was run 24 000 times. Next, the minimum and maximum values at 95% confidence level for each run were used to show the credible interval.
