Forecasting: theory and practice

Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases

Global, regional, and national incidence, prevalence, and mortality of HIV, 1980–2017, and forecasts to 2030, for 195 countries and territories: a systematic analysis for the Global Burden of Diseases, Injuries, and Risk Factors Study 2017

Background Understanding the patterns of HIV/AIDS epidemics is crucial to tracking and monitoring the progress of prevention and control efforts in countries. We provide a comprehensive assessment of the levels and trends of HIV/AIDS incidence, prevalence, mortality, and coverage of antiretroviral therapy (ART) for 1980–2017 and forecast these estimates to 2030 for 195 countries and territories. Methods We determined a modelling strategy for each country on the basis of the availability and quality of data. For countries and territories with data from population-based seroprevalence surveys or antenatal care clinics, we estimated prevalence and incidence using an open-source version of the Estimation and Projection Package—a natural history model originally developed by the UNAIDS Reference Group on Estimates, Modelling, and Projections. For countries with cause-specific vital registration data, we corrected data for garbage coding (ie, deaths coded to an intermediate, immediate, or poorly defined cause) and HIV misclassification. We developed a process of cohort incidence bias adjustment to use information on survival and deaths recorded in vital registration to back-calculate HIV incidence. For countries without any representative data on HIV, we produced incidence estimates by pulling information from observed bias in the geographical region. We used a re-coded version of the Spectrum model (a cohort component model that uses rates of disease progression and HIV mortality on and off ART) to produce age-sex-specific incidence, prevalence, and mortality, and treatment coverage results for all countries, and forecast these measures to 2030 using Spectrum with inputs that were extended on the basis of past trends in treatment scale-up and new infections. Findings Global HIV mortality peaked in 2006 with 1·95 million deaths (95% uncertainty interval 1·87–2·04) and has since decreased to 0·95 million deaths (0·91–1·01) in 2017. New cases of HIV globally peaked in 1999 (3·16 million, 2·79–3·67) and since then have gradually decreased to 1·94 million (1·63–2·29) in 2017. These trends, along with ART scale-up, have globally resulted in increased prevalence, with 36·8 million (34·8–39·2) people living with HIV in 2017. Prevalence of HIV was highest in southern sub-Saharan Africa in 2017, and countries in the region had ART coverage ranging from 65·7% in Lesotho to 85·7% in eSwatini. Our forecasts showed that 54 countries will meet the UNAIDS target of 81% ART coverage by 2020 and 12 countries are on track to meet 90% ART coverage by 2030. Forecasted results estimate that few countries will meet the UNAIDS 2020 and 2030 mortality and incidence targets. Interpretation Despite progress in reducing HIV-related mortality over the past decade, slow decreases in incidence, combined with the current context of stagnated funding for related interventions, mean that many countries are not on track to reach the 2020 and 2030 global targets for reduction in incidence and mortality. With a growing population of people living with HIV, it will continue to be a major threat to public health for years to come. The pace of progress needs to be hastened by continuing to expand access to ART and increasing investments in proven HIV prevention initiatives that can be scaled up to have population-level impact

Past, present, and future of global health financing : a review of development assistance, government, out-of-pocket, and other private spending on health for 195 countries, 1995-2050

Background Comprehensive and comparable estimates of health spending in each country are a key input for health policy and planning, and are necessary to support the achievement of national and international health goals. Previous studies have tracked past and projected future health spending until 2040 and shown that, with economic development, countries tend to spend more on health per capita, with a decreasing share of spending from development assistance and out-of-pocket sources. We aimed to characterise the past, present, and predicted future of global health spending, with an emphasis on equity in spending across countries. Methods We estimated domestic health spending for 195 countries and territories from 1995 to 2016, split into three categories-government, out-of-pocket, and prepaid private health spending-and estimated development assistance for health (DAH) from 1990 to 2018. We estimated future scenarios of health spending using an ensemble of linear mixed-effects models with time series specifications to project domestic health spending from 2017 through 2050 and DAH from 2019 through 2050. Data were extracted from a broad set of sources tracking health spending and revenue, and were standardised and converted to inflation-adjusted 2018 US dollars. Incomplete or low-quality data were modelled and uncertainty was estimated, leading to a complete data series of total, government, prepaid private, and out-of-pocket health spending, and DAH. Estimates are reported in 2018 US dollars, 2018 purchasing-power parity-adjusted dollars, and as a percentage of gross domestic product. We used demographic decomposition methods to assess a set of factors associated with changes in government health spending between 1995 and 2016 and to examine evidence to support the theory of the health financing transition. We projected two alternative future scenarios based on higher government health spending to assess the potential ability of governments to generate more resources for health. Findings Between 1995 and 2016, health spending grew at a rate of 4.00% (95% uncertainty interval 3.89-4.12) annually, although it grew slower in per capita terms (2.72% [2.61-2.84]) and increased by less than $1 per capita over this period in 22 of 195 countries. The highest annual growth rates in per capita health spending were observed in upper-middle-income countries (5.55$ 8.0 trillion (7.8-8.1) in 2016 (comprising 8.6% [8.4-8.7] of the global economy and $10.3 trillion [10.1-10.6] in purchasing-power parity-adjusted dollars), with a per capita spending of US$ 5252 (5184-5319) in high-income countries, $491 (461-524) in upper-middle-income countries,$ 81 (74-89) in lower-middle-income countries, and $40 (38-43) in low-income countries. In 2016, 0.4$ 9.5 billion, 24.3% of total DAH), although spending on other infectious diseases (excluding tuberculosis and malaria) grew fastest from 2010 to 2018 (6.27% per year). The leading sources of DAH were the USA and private philanthropy (excluding corporate donations and the Bill & Melinda Gates Foundation). For the first time, we included estimates of China's contribution to DAH ($644.7 million in 2018). Globally, health spending is projected to increase to$ 15.0 trillion (14.0-16.0) by 2050 (reaching 9.4% [7.6-11.3] of the global economy and $ 21.3 trillion [19.8-23.1] in purchasing-power parity-adjusted dollars), but at a lower growth rate of 1.84% (1.68-2.02) annually, and with continuing disparities in spending between countries. In 2050, we estimate that 0.6% (0.6-0.7) of health spending will occur in currently low-income countries, despite these countries comprising an estimated 15.7% of the global population by 2050. The ratio between per capita health spending in high-income and low-income countries was 130.2 (122.9-136.9) in 2016 and is projected to remain at similar levels in 2050 (125.9 [113.7-138.1]). The decomposition analysis identified governments' increased prioritisation of the health sector and economic development as the strongest factors associated with increases in government health spending globally. Future government health spending scenarios suggest that, with greater prioritisation of the health sector and increased government spending, health spending per capita could more than double, with greater impacts in countries that currently have the lowest levels of government health spending. Interpretation Financing for global health has increased steadily over the past two decades and is projected to continue increasing in the future, although at a slower pace of growth and with persistent disparities in per-capita health spending between countries. Out-of-pocket spending is projected to remain substantial outside of high-income countries. Many low-income countries are expected to remain dependent on development assistance, although with greater government spending, larger investments in health are feasible. In the absence of sustained new investments in health, increasing efficiency in health spending is essential to meet global health targets.Peer reviewe

Past, present, and future of global health financing: a review of development assistance, government, out-of-pocket, and other private spending on health for 195 countries, 1995–2050

Background: Comprehensive and comparable estimates of health spending in each country are a key input for health policy and planning, and are necessary to support the achievement of national and international health goals. Previous studies have tracked past and projected future health spending until 2040 and shown that, with economic development, countries tend to spend more on health per capita, with a decreasing share of spending from development assistance and out-of-pocket sources. We aimed to characterise the past, present, and predicted future of global health spending, with an emphasis on equity in spending across countries. Methods: We estimated domestic health spending for 195 countries and territories from 1995 to 2016, split into three categories—government, out-of-pocket, and prepaid private health spending—and estimated development assistance for health (DAH) from 1990 to 2018. We estimated future scenarios of health spending using an ensemble of linear mixed-effects models with time series specifications to project domestic health spending from 2017 through 2050 and DAH from 2019 through 2050. Data were extracted from a broad set of sources tracking health spending and revenue, and were standardised and converted to inflation-adjusted 2018 US dollars. Incomplete or low-quality data were modelled and uncertainty was estimated, leading to a complete data series of total, government, prepaid private, and out-of-pocket health spending, and DAH. Estimates are reported in 2018 US dollars, 2018 purchasing-power parity-adjusted dollars, and as a percentage of gross domestic product. We used demographic decomposition methods to assess a set of factors associated with changes in government health spending between 1995 and 2016 and to examine evidence to support the theory of the health financing transition. We projected two alternative future scenarios based on higher government health spending to assess the potential ability of governments to generate more resources for health. Findings: Between 1995 and 2016, health spending grew at a rate of 4·00% (95% uncertainty interval 3·89–4·12) annually, although it grew slower in per capita terms (2·72% [2·61–2·84]) and increased by less than $1 per capita over this period in 22 of 195 countries. The highest annual growth rates in per capita health spending were observed in upper-middle-income countries (5·55 in lower-middle-income countries (3·71$8·0 trillion (7·8–8·1) in 2016 (comprising 8·6% [8·4–8·7] of the global economy and $10·3 trillion [10·1–10·6] in purchasing-power parity-adjusted dollars), with a per capita spending of US$5252 (5184–5319) in high-income countries, $491 (461–524) in upper-middle-income countries,$81 (74–89) in lower-middle-income countries, and $40 (38–43) in low-income countries. In 2016, 0·4 countries, despite these countries comprising 10·0 DAH targeted HIV/AIDS ($9·5 billion, 24·3% of total DAH), although spending on other infectious diseases (excluding tuberculosis and malaria) grew fastest from 2010 to 2018 (6·27% per year). The leading sources of DAH were the USA and private philanthropy (excluding corporate donations and the Bill & Melinda Gates Foundation). For the first time, we included estimates of China’s contribution to DAH ($644·7 million in 2018). Globally, health spending is projected to increase to$15·0 trillion (14·0–16·0) by 2050 (reaching 9·4% [7·6–11·3] of the global economy and $21·3 trillion [19·8–23·1] in purchasing-power parity-adjusted dollars), but at a lower growth rate of 1·84% (1·68–2·02) annually, and with continuing disparities in spending between countries. In 2050, we estimate that 0·6% (0·6–0·7) of health spending will occur in currently low-income countries, despite these countries comprising an estimated 15·7% of the global population by 2050. The ratio between per capita health spending in high-income and low-income countries was 130·2 (122·9–136·9) in 2016 and is projected to remain at similar levels in 2050 (125·9 [113·7–138·1]). The decomposition analysis identified governments’ increased prioritisation of the health sector and economic development as the strongest factors associated with increases in government health spending globally. Future government health spending scenarios suggest that, with greater prioritisation of the health sector and increased government spending, health spending per capita could more than double, with greater impacts in countries that currently have the lowest levels of government health spending Interpretation: Financing for global health has increased steadily over the past two decades and is projected to continue increasing in the future, although at a slower pace of growth and with persistent disparities in per-capita health spending between countries. Out-of-pocket spending is projected to remain substantial outside of high-income countries. Many low-income countries are expected to remain dependent on development assistance, although with greater government spending, larger investments in health are feasible. In the absence of sustained new investments in health, increasing efficiency in health spending is essential to meet global health targets. Funding: Bill & Melinda Gates Foundatio

The global distribution of lymphatic filariasis, 2000–18: a geospatial analysis

Background Lymphatic filariasis is a neglected tropical disease that can cause permanent disability through disruption of the lymphatic system. This disease is caused by parasitic filarial worms that are transmitted by mosquitos. Mass drug administration (MDA) of antihelmintics is recommended by WHO to eliminate lymphatic filariasis as a public health problem. This study aims to produce the first geospatial estimates of the global prevalence of lymphatic filariasis infection over time, to quantify progress towards elimination, and to identify geographical variation in distribution of infection. Methods A global dataset of georeferenced surveyed locations was used to model annual 2000–18 lymphatic filariasis prevalence for 73 current or previously endemic countries. We applied Bayesian model-based geostatistics and time series methods to generate spatially continuous estimates of global all-age 2000–18 prevalence of lymphatic filariasis infection mapped at a resolution of 5 km2 and aggregated to estimate total number of individuals infected. Findings We used 14 927 datapoints to fit the geospatial models. An estimated 199 million total individuals (95% uncertainty interval 174–234 million) worldwide were infected with lymphatic filariasis in 2000, with totals for WHO regions ranging from 3·1 million (1·6–5·7 million) in the region of the Americas to 107 million (91–134 million) in the South-East Asia region. By 2018, an estimated 51 million individuals (43–63 million) were infected. Broad declines in prevalence are observed globally, but focal areas in Africa and southeast Asia remain less likely to have attained infection prevalence thresholds proposed to achieve local elimination. Interpretation Although the prevalence of lymphatic filariasis infection has declined since 2000, MDA is still necessary across large populations in Africa and Asia. Our mapped estimates can be used to identify areas where the probability of meeting infection thresholds is low, and when coupled with large uncertainty in the predictions, indicate additional data collection or intervention might be warranted before MDA programmes cease

Localization and broadband follow-up of the gravitational-wave transient GW150914

A gravitational-wave (GW) transient was identified in data recorded by the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO) detectors on 2015 September 14. The event, initially designated G184098 and later given the name GW150914, is described in detail elsewhere. By prior arrangement, preliminary estimates of the time, significance, and sky location of the event were shared with 63 teams of observers covering radio, optical, near-infrared, X-ray, and gamma-ray wavelengths with ground- and space-based facilities. In this Letter we describe the low-latency analysis of the GW data and present the sky localization of the first observed compact binary merger. We summarize the follow-up observations reported by 25 teams via private Gamma-ray Coordinates Network circulars, giving an overview of the participating facilities, the GW sky localization coverage, the timeline, and depth of the observations. As this event turned out to be a binary black hole merger, there is little expectation of a detectable electromagnetic (EM) signature. Nevertheless, this first broadband campaign to search for a counterpart of an Advanced LIGO source represents a milestone and highlights the broad capabilities of the transient astronomy community and the observing strategies that have been developed to pursue neutron star binary merger events. Detailed investigations of the EM data and results of the EM follow-up campaign are being disseminated in papers by the individual teams