Global access to surgical care: a modelling study

Program in Global Surgery and Social Change (B C Alkire MD, N P Raykar MD, M G Shrime MD, J N Riesel MD, J G Meara MD, Prof P E Farmer MD), Department of Global Health and Social Medicine (C T Nutt BA), Harvard Medical School, Boston, USA; Department of Otolaryngology-Head and Neck Surgery (B C Alkire), Offi ce of Global Surgery and Health (M G Shrime), Massachusetts Eye and Ear Infi rmary, Boston, USA; Department of Surgery, Beth Israel Deaconess Medical Center, Boston, USA (N P Raykar MD); Department of Surgery, Stanford University, Palo Alto, USA (T G Weiser MD); Rudy Children’s Hospital, University of California, San Diego, CA, USA (Prof S W Bickler MD); Department of Surgery, University of California, San Diego, CA, USA (J Rose MD); Center for Surgery and Public Health, Brigham and Women’s Hospital, Boston, USA; Department of Surgery, Medical College of Wisconsin, Wauwatosa, USA (S L M Greenberg MD); Department of Surgery, University of Washington, Seattle, USA (M Kotagal MD); Department of Surgery, Massachusetts General Hospital, Boston, USA (J N Riesel MD); Department of Surgery, Stanford University, Palo Alto, USA (M Esquivel MD, T Uribe-Leitz MD); Ariadne Labs, Boston, USA (G Molina MD); Department of Surgery, Massachusetts General Hospital, Boston, USA (G Molina MD); Department of Surgery, BARC Hospital, Global access to surgical care: a modelling study


Introduction
The vision of the Lancet Commission on Global Surgery 1 of universal access to safe, aff ordable surgical care when needed supports the notion that access to surgical care and access to health care are synonymous. Although healthcare delivery is a complex enterprise with many interconnected parts, there are four essential components: the staff who do the work, the equipment with which they work, the space they work in, and the systems that help the staff and the equipment work together in a shared space. 2 However, evidence and anecdote suggest that the availability of the so-called staff , stuff , space, and systems of surgical care delivery is limited in many, if not most, low-resource settings. [3][4][5] For example, an assessment of operating theatre density showed that 90% of the population of sub-Saharan Africa has access to roughly one operating theatre per 100 000 people. 4 The few theatres that do exist have limited capacity to provide safe surgical care. For instance, up to 70% lack pulse oximetry, an anaesthetic monitoring standard. 4 Even when adequate surgical capacity and robust safety mechanisms exist, patients in both high-income and low-income settings often confront other barriers to access. 6,7 A fully equipped operating theatre serves little purpose for patients who cannot reach the hospital in a timely fashion, or for whom a surgical team is unavailable. Finally, patients who do receive appropriate surgical care often risk impoverishment secondary to out-of-pocket payments. 8 Previous estimates have suggested that at least 2 billion people lack access to surgical care based on the density of operating theatres alone. 4 We use the more inclusive Commission defi nition of access, which includes capacity, safety, timeliness, and aff ordability, and use a mathematical modelling approach to answer the following question: "How many people worldwide lack access to safe, aff ordable, and timely surgical care?"

Model construction
We defi ned access to surgery in a country using four dimensions: timeliness, surgical capacity with respect to workforce and infrastructure, safety, and aff ordability. Applying these dimensions, we estimated the number of patients worldwide without access to surgical services. Our study population did not include patients who needed surgical services, but identifi ed the population who would not have access to surgical services if needed at any given time. Modelling was done at the country level, and all countries for which the World Bank provides data and for which the necessary data were available were included.
First, we estimated the proportion of the population with access to surgery at the country level. For each country, we used a chance tree to model the probability that an individual had access to surgery (fi gure 1) with the binary outcome of access (1) or no access (0). Each chance node represents the probability of an access dimension being available to an individual patient conditional on the availability of the preceding dimensions. In view of data for each of these dimensions not being directly available, we used proxies. For baseline results, timeliness was approximated by the proportion of serious injuries transported by an ambulance, 9 surgical capacity by the number of surgical procedures under taken in a country as a proportion of the number of surgeries needed to meet demand, 3,10 safety by the proportion of operating theatres with pulse oximetry, 4 and aff ordability by the proportion of

Research in context
Evidence before this study During preparation for this study, we searched Medline and Google Scholar to identify studies that had attempted to estimate the global population without access to surgery. We were able to identify one study that used an arbitrary cutoff of operating theatres per person (the primary measure) to derive an estimate of the population without access to surgery. We found no other global estimates in the scientifi c literature. Furthermore, the Lancet Commission on Global Surgery only recently defi ned access as inclusive of timeliness, capacity, safety, and aff ordability. For these reasons, we did not do a systematic review. We would note that others have provided indirect assessments of our primary outcome. Funk and colleagues estimated operating theatres per person by country; from these estimates, they identifi ed countries with less than two operating theatres per 100 000 people and then added the population of these countries to estimate the global population without access to surgery, arriving at 2·2 billion. Weiser and colleagues indirectly assessed equity in access to care by estimating surgical procedure rates by country and noted that, although countries that expend less than US$100 gross domestic product per person make up 35% of the global population, only 3·5% of the total volume of surgery takes place in these countries.

Added value of this study
At least 4·8 billion people in the world do not have timely access to safe, aff ordable surgical care. This estimate is substantially higher than the 2·2 billion estimate commonly referenced in the global surgery literature. When considered with recent estimates that suggest that up to 30% of the global burden of disease is surgical, the estimates of this study suggest that there is an urgent need to address the undersupply of surgical services. The Lancet Commission on Global Surgery has made recommendations for a way forward, including the appropriate allocation of fi nancial resources to build surgical capacity and strengthen health systems, building a robust surgical workforce, ensuring that surgery is delivered in a safe manner, and providing for fi nancial protection against impoverishment through universal health coverage. Our estimates suggest there is a long way to go, but if the global health community wishes to address ongoing inequities and the growing burden of disease, improving access to surgical care cannot be ignored.

Implications of all the available evidence
The world's population without access to surgical care is much greater than previously reported, since previous estimates relied on a rather narrow defi nition of access. In a world focusing on universal health coverage, the vision of the Lancet Commission on Global Surgery is universal access to safe, aff ordable surgical and anaesthesia care when needed. When all components of this vision are assessed, at least 4·8 billion people do not have access to surgical care. The burden of this inequity falls most heavily on the world's rural poor. Expanding access to surgery and anaesthesia care will require a coordinated investment in surgical scale-up that grows the workforce, builds infrastructure, removes cultural and geographical barriers, and provides fi nancial protection.  patients undergoing surgery who are protected from catastrophic expenditure from out-of-pocket payments. 8 The appendix provides more detail about each proxy.
Because the outcome value assigned to no access is zero in our chance tree, the expected value of the chance tree for each country is the joint probability of all four dimensions being available to an individual. The probability of access to surgery in a country, i, can therefore be given by: where p(A)=probability of access to surgery, p(T)=probability of timely surgical care, p(C)=probability that surgical capacity is available, p(S)=probability that surgery can be delivered in a safe manner, and p(Af)=probability that surgery is aff ordable (patient does not experience catastrophic expenditure). The ∩ symbol indicates joint probability, and the | symbol indicates conditional probability. For example, p(A∩B) is the joint probability of both event A and B occurring, while p(A|B) is the probability of event A occurring given than event B has occurred. The population without access to surgery in a country is given by: where NA i =total number of individuals without access to surgery in a country and TP i =total population in a country. The global population without access to surgical care, or NA, is therefore represented by the summation of the country-specifi c estimates described above: Because access probably diff ers between urban and rural populations, we did a secondary analysis in which all four access dimensions are applied to the rural population, but only the probability of catastrophic expenditure and safe surgery was applied to the urban population. The selective application of proxies to the urban population was based on the assumption that timely access and capacity are more likely to be available in a city. Ultimately, assuming that 100% of the urban population can receive surgery quickly, although clearly false, facilitates the creation of a lower-bound estimate for access. Therefore: where p(A) i,r = probability of access within the rural population and p(A) i,u = probability of access within the urban population. We term this the selective model, and the total global population without access to surgery is given in this model by: where TP i,r =total rural population and TP i,u =total urban population for each country i. Notably, given that our data Online for appendix originated from countrywide estimates, the selective tree likely underestimates access in rural settings and defi nitely overestimates access in urban settings. However, we believe it serves as a reasonable lower-bound estimate for the population without access to surgery. 180 countries, representing 6·97 billion people, or 98% of the global population, had data for each proxy readily available. To estimate the global population without access to care, we assumed missingness at random and employed a multiple imputation approach described in the appendix to capture the additional uncertainty of missing data.

Sensitivity analysis
Our baseline results include two sets of assumptions: that the full chance tree is applied to the entire population (full tree), and that all four dimensions are applied to the rural population and only aff ordability and safety are applied to the urban population (selective tree). To test the robustness of our results, we did several one-way sensitivity analyses. First, baseline assumptions were retested against the exclusion of each dimension of access separately. For example, the fi rst scenario includes capacity, safety, and aff ordability with timeliness excluded; the second includes timeliness, safety, and aff ordability with capacity excluded, and so on.
Second, baseline assumptions were tested against diff erent proxies for capacity and aff ordability. For capacity, our baseline results used an adjustment factor (appendix), to model p(C|T). In a one-way sensitivity analysis, we assumed that p(C|T)=p(C) as an upperbound, and p(C|T)=min(2*p(C),1·0) as a lower-bound estimate for the population without access to surgical services. We also used results from a model that regresses each country's surgical procedure rate 2 against life-expectancy to establish the optimum procedure rate in the context of life-expectancy, or in other words, the country that achieves the maximum life-expectancy with the minimum-necessary procedure rate (Sweden, in this case). 11 The index country's current surgical procedure rate was taken to be the needed procedure rate (NPR) for all countries. Similar methods were used for under-5 survival (Germany) and maternal survival (Singapore). We also used the defi nition by Funk and colleagues 3 in which countries with less than two operating rooms per 100 000 population were deemed to have no access, with the simplistic yet  conservative assumption that those with more than two operating rooms per 100 000 had 100% access to surgical capacity. For aff ordability, we reran our baseline assumptions with Shrime's model 8 and assumed that out-of-pocket expenditure was a function of only direct medical costs and did not include non-medical costs. Finally, second-order Monte Carlo simulation, with 50 000 draws from the variables (parameterised in appendix) was used to account for parameter uncertainty from our baseline assumptions. Statistical analysis was done in Excel 2010. Monte Carlo simulation was done with the RiskAmp plugin, and multiple imputation with chained equations was done with the Real Statistics software package for Excel.

Results
Data were readily available to assess surgical access for 180 countries, representing 6·97 billion people (98% of the global population). After accounting for missing data using multiple imputation, our model assessed 196 countries, representing 7·1 billion people. Applying our baseline assumptions, the full tree model estimated that 5·3 billion (95% posterior credible interval [PCI] 5·0-5·5) do not have access to surgical services; the selective tree estimated 4·8 billion (4·6-5·0) (table 1, fi gure 2). The proportion of the population without access to surgical services varied widely when stratifi ed by World Bank income classifi cation, with the selective tree estimating that 97·7% (95·6-99·5) and 92·3% (89·3-94·5) of the populations in low-income countries and lower-middle-income countries lack access (table 1), compared with 14·9% (11·4-16·3) of the population in high-income countries. We noted a similar pattern when countries were stratifi ed by the Institute for Health Metrics and Evaluation's global burden of disease regions: 12 the selective model estimates that greater than 95% of the population in south Asia and central, eastern, and western sub-Saharan Africa do not have access to care, whereas less than 5% of the population in Australasia, high-income North America, and western Europe lack access to surgery (table 2, fi gures 3 and 4).
We tested several diff erent scenarios to assess the robustness of our results. The baseline assumptions were fi rst tested against the exclusion of each access dimension (table 3). When capacity, timeliness, or safety is excluded, our estimates of the global population without access to surgery remained higher than 4 billion in both the full and selective trees. The aff ordability dimension had the greatest impact on our estimates, as it is the only dimension that when excluded, results in estimates of less than 4 billion people without surgical access. Specifi cally, the selective tree estimates that 3·6 billion do not have access to surgical services when aff ordability is excluded from the model (table 3). We also tested variations of the proxies for timeliness, capacity, and aff ordability (table 4). For each variation, again with the exception of aff ordability, the estimates remained well above 4 billion. Figure 2 shows the results of the probabilistic sensitivity analysis, which informs the 95% posterior credible intervals.
We recognise that these results might seem implausible at fi rst; our estimates are more than double those previously reported by Funk and colleagues 4 and suggest that less than 1% of individuals in low-income countries and less than 5% of individuals in lower-middle-income countries have access to surgical care. 4 However, our defi nition of access is inclusive of more than simply surgical capacity: it also includes aff ordability, safety, and timeliness of care. Within this context, these results compare reasonably with other estimates that apply a more limited defi nition of access. Funk and colleagues suggested that at least 2·2 billion individuals are without access on the basis of operating theatre density alone. 4 The World Bank estimates that more than 3 billion people live on less than US$2·50 per day and are, hence, poorly positioned to aff ord surgical care. Consistent with the distribution of poverty, we fi nd that individuals without access to surgery are overwhelmingly represented in low-income and middle-income countries (fi gures 3 and 4).
To providers who practice regularly in these parts of the world, these estimates validate a common but untold experience. 13 Assessments of surgical infrastructure in low-resources settings describe a stark reality: steady electricity was present in only 81 (35%) of 231 district  Full tree Selective tree hospitals in 12 sub-Saharan African countries; 14 running water was consistently available in just two of the ten hospitals surveyed in a county in Sierra Leone; 15 oxygen sources were only available in 24 (40%) of 60 surgical hospitals surveyed across east Africa; 16 and only seven (64%) of 11 surveyed county hospitals in Liberia had an in-house blood bank, and those that did had a mean of four units per hospital. 17 In Liberia, even before the Ebola crisis, there were fewer than three native surgeons working in the entire country. 18 Our results and these data imply that access to safe, aff ordable, and timely surgical care is absent for much of the world. Nonetheless, for each access dimension, we argue that, if anything, our model is conservative and risks understating the magnitude of the crisis. Our estimates of the probability of receiving timely surgical care, for example, rely on the WHO's estimates of the proportion of road traffi c injuries transported to a hospital by ambulance. 9 They overestimate timely access in several important ways. First, these estimates, which refl ect the likelihood of the presence of a prehospital system, consist of broad country-level assessments, and ignore geospatial realities. For example, the proportion of patients with serious injuries transported by ambulance in India is estimated to range from 11% to 50%. Since our model applies the upper bound of the interval, it ascribes timely access to half of the rural population even though the scarcity of rural surgical providers means most of these patients live hours away from the nearest surgeon, which would preclude timely access even in the presence of excellent prehospital transportation. 19 Second, although the WHO data are a reasonable proxy for timeliness in patient transport during emergencies, they do not capture delays associated with chronic conditions (ie, the inability of a surgical facility to off er planned surgical care given overwhelming acute volume), nor do they directly account for the delay in the decision to seek care. 1 Additionally, the practical delays related to receiving care on reaching the hospital from seemingly trivial issues like patients navigating the hospital environment, or poor triage processes, for example, are not insignifi cant. 13,16 Third, this proxy does not account for known inequities in access in high-income countries, which would require more granularity than can be aff orded with aggregate country-level data. Assessed at the local level, for example, the USA often performs poorly with prehospital delays. This phenomenon is best shown by the so-called trauma deserts of Chicago, in which gun-shot victims who lived more than 5 miles from a trauma centre had signifi cant increased odds of mortality. 7 Delays in surgical care for chronic disorders are also found in high-income countries as shown by the fact that late-stage presentation of cancer in the USA is associated with ethnic origin and insurance status. 20 For instance, in Boston, black women have a breast cancer mortality rate that is more than twice that of white women. 21 Next we assessed surgical capacity in each country by constructing a ratio of present surgical procedure rate to the necessary surgical procedure rate to meet demand, and this can also result in an overestimate of access. The ability to perform surgical procedures requires a functioning operating theatre, supplies, and staff , and therefore procedure rates are a reliable indicator of gross surgical capacity. However, although surgical volume can reveal defi cits in capacity, it says little about case mix or where surgical capacity exists. The thousand cleft-lip repairs done in the tertiary centre in the city can provide a false impression of the access to laparotomy or caesarean delivery in the rural setting. In 2013, for example, rural Sierra Leone had a surgeon-to-population ratio almost four times lower than that of the urban areas. 19 Therefore, low surgical rates are a specifi c but insensitive indicator of access; if surgery is not being done, it follows that surgical care is not being delivered; however, high surgical rates cannot speak to the distribution of surgical access.
Additionally, the inherent uncertainty in the models used to estimate surgical capacity deserves special mention. The estimate of necessary procedure rates created by Rose and colleagues, 10 although based on prevalence data for most disorders included in global burden of disease studies, does not capture all diseases and is consequently a conservative estimate of need. If the true necessary procedure rate, inclusive of all disease disorders, is actually higher than the one proposed by Rose and colleagues, our model would overestimate access at all procedure levels. If country-specifi c surgical procedure rates are under estimated in the model developed by Weiser and colleagues, 22 our estimates will underestimate access; however, we believe that in view of its methods, on the whole, our estimates of capacity lead to net overestimates of access.
Next, our model's sole use of the presence of pulse oximetry as a proxy for safety can overestimate access as pulse oximetry, by itself, is a necessary but insuffi cient criterion for safe surgery. 23,24 As described, low-resource environments face severe defi cits in trained workforce, equipment, supplies, and basic physical infrastructure, in many cases precluding provision of what could be regarded as safe surgery (even if a pulse oximeter was present). Consequently, the use of pulse oximetry penetrance as the main requisite for safe surgery amounts to a conservative estimate of the lower bound without access. More encompassing indicators of safety such as the perioperative mortality rate might provide a more accurate assessment of the upper bound without access to safe surgical care. However the paucity of these data collected worldwide precludes their use in our present model. 1 Finally, our aff ordability proxy, based on Shrime and colleagues' model for catastrophic expenditure, 8 estimates aff ordability at a conservative boundary by only accounting for patients who would be impoverished should they need surgery. For our baseline estimates, we chose to use Shrime and colleagues' estimates for catastrophic expenditure that are inclusive of direct medical costs and indirect medical costs (eg, cost of transportation to a health facility and lost wages) because we believed it was only sensible that all costs experienced by the patient be included to reasonably assess the risk of impoverishment. 25,26 Ultimately, in a just world, aff ordability should hardly be defi ned as simply an expense that does not impoverish. As such, billions of people are at risk of losing fi nancial security due to payments for surgical care even if they do not force them below the poverty line. 27,28 As mentioned previously, aff ordability not only aff ects those who receive care, but also infl uences the decision to seek it. Grimes and colleagues 6 noted that, from cataracts to maternal health, direct and indirect costs prevent patients from using the health system. Therefore, aff ordability and timeliness are closely related, and our model is unable to account for patients who avoid the health-care system entirely.
Our study has many important limitations, most of which are addressed in the discussion of each access dimension. More broadly, we recognise that any model is restricted by the quality of inputs, and in view of the absence of empirical data in many low-income and middle-income countries; much of the data used in this

Aff ordability
Direct medical costs only 4·82 (68%) 3·99 (56%) Table 4: Sensitivity analysis of variation on proxies, by population (billions) and proportion without access study are the result of a model. To account for this, we tested our assumptions against a number of one-way sensitivity analyses and incorporated uncertainty in our parameters with probabilistic sensitivity analysis. Data were missing for 2% of the global population, and therefore we used statistical techniques to impute the parameters for this segment of the population. Although every attempt was made to capture this additional uncertainty in our 95% PCIs, we still need to acknowledge the missing data as a major limitation. Further, we recognise that our estimates are sensitive to the defi nition of access that is applied. Specifi cally, exclusion of the aff ordability parameter has a signifi cant eff ect on our estimates, such that when removed from our selective model, our estimate of the global population without access to surgery falls to 3·6 billion. Although this is still greater than the previously reported 2·2 billion, it falls short of the 4·8 billion reported in our baseline results. Nonetheless, we fi nd it unreasonable to ignore aff ordability in assessing access to care which often hinges on the ability to pay. The remaining sensitivity analyses suggest, however, that our results are robust and resilient to a number of diff erent assumptions (tables 3 and 4).
The world's population without access to surgical care is signifi cantly greater than previously reported, as prior estimates relied on a relatively narrow defi nition of access. In a world focusing on universal health coverage, the vision of the Lancet Commission on Global Surgery is universal access to safe and aff ordable surgical and anaesthesia care when needed. When all components of this vision are examined, at least 4·8 billion people do not have access to surgical care. The burden of this inequity falls most heavily on the world's rural poor people. Expanding access to surgery and anaesthesia care will require coordinated investment in surgical scale-up that grows the workforce, builds infrastructure, removes cultural and geographic barriers, and provides fi nancial protection.

Contributors
All coauthors have made substantial intellectual contributions in terms of conception, drafting, and critical appraisal of this manuscript.

Declaration of interests
We declare no competing interests.