Generalised risk-sensitive control with full and partial state observation

This paper generalises the risk-sensitive cost functional by introducing noise dependent penalties on the state and control variables. The optimal control problems for the full and partial state observation are considered. Using a change of probability measure approach, explicit closed-form solutions are found in both cases. This has resulted in a new risk-sensitive regulator and filter, which are generalisations of the well-known classical results

Age and frailty are independently associated with increased COVID-19 mortality and increased care needs in survivors: results of an international multi-centre study

Introduction Increased mortality has been demonstrated in older adults with coronavirus disease 2019 (COVID-19), but the effect of frailty has been unclear. Methods This multi-centre cohort study involved patients aged 18 years and older hospitalised with COVID-19, using routinely collected data. We used Cox regression analysis to assess the impact of age, frailty and delirium on the risk of inpatient mortality, adjusting for sex, illness severity, inflammation and co-morbidities. We used ordinal logistic regression analysis to assess the impact of age, Clinical Frailty Scale (CFS) and delirium on risk of increased care requirements on discharge, adjusting for the same variables. Results Data from 5,711 patients from 55 hospitals in 12 countries were included (median age 74, interquartile range [IQR] 54–83; 55.2% male). The risk of death increased independently with increasing age (>80 versus 18–49: hazard ratio [HR] 3.57, confidence interval [CI] 2.54–5.02), frailty (CFS 8 versus 1–3: HR 3.03, CI 2.29–4.00) inflammation, renal disease, cardiovascular disease and cancer, but not delirium. Age, frailty (CFS 7 versus 1–3: odds ratio 7.00, CI 5.27–9.32), delirium, dementia and mental health diagnoses were all associated with increased risk of higher care needs on discharge. The likelihood of adverse outcomes increased across all grades of CFS from 4 to 9. Conclusion Age and frailty are independently associated with adverse outcomes in COVID-19. Risk of increased care needs was also increased in survivors of COVID-19 with frailty or older age

Global, regional, and national comparative risk assessment of 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks, 1990-2015: a systematic analysis for the Global Burden of Disease Study 2015

BACKGROUND: The Global Burden of Diseases, Injuries, and Risk Factors Study 2015 provides an up-to-date synthesis of the evidence for risk factor exposure and the attributable burden of disease. By providing national and subnational assessments spanning the past 25 years, this study can inform debates on the importance of addressing risks in context. METHODS: We used the comparative risk assessment framework developed for previous iterations of the Global Burden of Disease Study to estimate attributable deaths, disability-adjusted life-years (DALYs), and trends in exposure by age group, sex, year, and geography for 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks from 1990 to 2015. This study included 388 risk-outcome pairs that met World Cancer Research Fund-defined criteria for convincing or probable evidence. We extracted relative risk and exposure estimates from randomised controlled trials, cohorts, pooled cohorts, household surveys, census data, satellite data, and other sources. We used statistical models to pool data, adjust for bias, and incorporate covariates. We developed a metric that allows comparisons of exposure across risk factors-the summary exposure value. Using the counterfactual scenario of theoretical minimum risk level, we estimated the portion of deaths and DALYs that could be attributed to a given risk. We decomposed trends in attributable burden into contributions from population growth, population age structure, risk exposure, and risk-deleted cause-specific DALY rates. We characterised risk exposure in relation to a Socio-demographic Index (SDI). FINDINGS: Between 1990 and 2015, global exposure to unsafe sanitation, household air pollution, childhood underweight, childhood stunting, and smoking each decreased by more than 25%. Global exposure for several occupational risks, high body-mass index (BMI), and drug use increased by more than 25% over the same period. All risks jointly evaluated in 2015 accounted for 57·8% (95% CI 56·6-58·8) of global deaths and 41·2% (39·8-42·8) of DALYs. In 2015, the ten largest contributors to global DALYs among Level 3 risks were high systolic blood pressure (211·8 million [192·7 million to 231·1 million] global DALYs), smoking (148·6 million [134·2 million to 163·1 million]), high fasting plasma glucose (143·1 million [125·1 million to 163·5 million]), high BMI (120·1 million [83·8 million to 158·4 million]), childhood undernutrition (113·3 million [103·9 million to 123·4 million]), ambient particulate matter (103·1 million [90·8 million to 115·1 million]), high total cholesterol (88·7 million [74·6 million to 105·7 million]), household air pollution (85·6 million [66·7 million to 106·1 million]), alcohol use (85·0 million [77·2 million to 93·0 million]), and diets high in sodium (83·0 million [49·3 million to 127·5 million]). From 1990 to 2015, attributable DALYs declined for micronutrient deficiencies, childhood undernutrition, unsafe sanitation and water, and household air pollution; reductions in risk-deleted DALY rates rather than reductions in exposure drove these declines. Rising exposure contributed to notable increases in attributable DALYs from high BMI, high fasting plasma glucose, occupational carcinogens, and drug use. Environmental risks and childhood undernutrition declined steadily with SDI; low physical activity, high BMI, and high fasting plasma glucose increased with SDI. In 119 countries, metabolic risks, such as high BMI and fasting plasma glucose, contributed the most attributable DALYs in 2015. Regionally, smoking still ranked among the leading five risk factors for attributable DALYs in 109 countries; childhood underweight and unsafe sex remained primary drivers of early death and disability in much of sub-Saharan Africa. INTERPRETATION: Declines in some key environmental risks have contributed to declines in critical infectious diseases. Some risks appear to be invariant to SDI. Increasing risks, including high BMI, high fasting plasma glucose, drug use, and some occupational exposures, contribute to rising burden from some conditions, but also provide opportunities for intervention. Some highly preventable risks, such as smoking, remain major causes of attributable DALYs, even as exposure is declining. Public policy makers need to pay attention to the risks that are increasingly major contributors to global burden

A new risk-sensitive maximum principle

In this paper, a new maximum principle for the risk-sensitive control problem is established. One important feature of this result is that it applies to systems in which the diffusion term may depend on the control. Such control dependence gives rise to interesting phenomena not observed in the usual setting where control independence of the diffusion term is assumed. In particular, there is an additional second order adjoint equation and additional terms in the maximum condition that involve this second order process as well as the risk-sensitive parameter. Moreover, contrary to a conventional maximum principle, the first-order adjoint equation involved in our maximum principle is a nonlinear equation. An advantage of considering this new type of adjoint equation is that the risk-sensitive maximum principle derived is similar in form to its risk-neutral counterpart. The approach is based on the logarithmic transformation and the relationship between the adjoint variables and the value function. As an example, a linear-quadratic risk-sensitive problem is solved using the maximum principle derived. © 2005 IEEE