On Higher Derivatives of Expectations

It is understood that derivatives of an expectation $E [\phi(S(T)) | S(0) = x]$ with respect to $x$ can be expressed as $E [\phi(S(T)) \pi | S(0) = x]$, where $S(T)$ is a stochastic variable at time $T$ and $\pi$ is a stochastic weighting function (weight) independent of the form of $\phi$. Derivatives of expectations of this form are encountered in various fields of knowledge. We establish two results for weights of higher order derivatives under the dynamics given by (\ref{dynamics}). Specifically, we derive and solve a recursive relationship for generating weights. This results in a tractable formula for weights of any order.price sensitivities, greeks, malliavin calculus

An assessment of the reported impact of the COVID-19 pandemic on leprosy services using an online survey of practitioners in leprosy referral centres.

BACKGROUND: The coronavirus disease 2019 (COVID-19) pandemic has led to governments implementing a variety of public health measures to control transmission and has affected health services. Leprosy is a communicable neglected tropical disease caused by Mycobacterium leprae and is an important health problem in low- and middle-income countries. The natural history of leprosy means that affected individuals need long-term follow-up. The measures recommended to reduce transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) can create barriers to health services. We evaluated the impact of the COVID-19 epidemic response on leprosy services and disease management. METHODS: We conducted a cross-sectional online survey with healthcare professionals in leprosy referral centres. RESULTS: Eighty percent of leprosy diagnostic services were reduced. All respondents reported that multidrug therapy (MDT) was available but two reported a reduced stock. Clinicians used alternative strategies such as telephone consultations to maintain contact with patients. However, patients were not able to travel to the referral centres. DISCUSSION: This study highlights the effects of the initial phase of the SARS-CoV-2 pandemic on leprosy services in a range of leprosy-endemic countries. Many services remained open, providing leprosy diagnosis, MDT and leprosy reaction medications. Centres developed innovative measures to counter the negative impacts of the COVID-19 pandemic

Epigenome-wide association of DNA methylation markers in peripheral blood from Indian Asians and Europeans with incident type 2 diabetes:A nested case-control study

BACKGROUND: Indian Asians, who make up a quarter of the world’s population, are at high risk of developing type 2 diabetes. We investigated whether DNA methylation is associated with future type 2 diabetes incidence in Indian Asians and whether differences in methylation patterns between Indian Asians and Europeans are associated with, and could be used to predict, differences in the magnitude of risk of developing type 2 diabetes. METHODS: We did a nested case-control study of DNA methylation in Indian Asians and Europeans with incident type 2 diabetes who were identified from the 8-year follow-up of 25 372 participants in the London Life Sciences Prospective Population (LOLIPOP) study. Patients were recruited between May 1, 2002, and Sept 12, 2008. We did epigenome-wide association analysis using samples from Indian Asians with incident type 2 diabetes and age-matched and sex-matched Indian Asian controls, followed by replication testing of top-ranking signals in Europeans. For both discovery and replication, DNA methylation was measured in the baseline blood sample, which was collected before the onset of type 2 diabetes. Epigenome-wide significance was set at p<1 × 10(−7). We compared methylation levels between Indian Asian and European controls without type 2 diabetes at baseline to estimate the potential contribution of DNA methylation to increased risk of future type 2 diabetes incidence among Indian Asians. FINDINGS: 1608 (11·9%) of 13 535 Indian Asians and 306 (4·3%) of 7066 Europeans developed type 2 diabetes over a mean of 8·5 years (SD 1·8) of follow-up. The age-adjusted and sex-adjusted incidence of type 2 diabetes was 3·1 times (95% CI 2·8–3·6; p<0·0001) higher among Indian Asians than among Europeans, and remained 2·5 times (2·1–2·9; p<0·0001) higher after adjustment for adiposity, physical activity, family history of type 2 diabetes, and baseline glycaemic measures. The mean absolute difference in methylation level between type 2 diabetes cases and controls ranged from 0·5% (SD 0·1) to 1·1% (0·2). Methylation markers at five loci were associated with future type 2 diabetes incidence; the relative risk per 1% increase in methylation was 1·09 (95% CI 1·07–1·11; p=1·3 × 10(−17)) for ABCG1, 0·94 (0·92–0·95; p=4·2 × 10(−11)) for PHOSPHO1, 0·94 (0·92–0·96; p=1·4 × 10(−9)) for SOCS3, 1·07 (1·04–1·09; p=2·1 × 10(−10)) for SREBF1, and 0·92 (0·90–0·94; p=1·2 × 10(−17)) for TXNIP. A methylation score combining results for the five loci was associated with future type 2 diabetes incidence (relative risk quartile 4 vs quartile 1 3·51, 95% CI 2·79–4·42; p=1·3 × 10(−26)), and was independent of established risk factors. Methylation score was higher among Indian Asians than Europeans (p=1 × 10(−34)). INTERPRETATION: DNA methylation might provide new insights into the pathways underlying type 2 diabetes and offer new opportunities for risk stratification and prevention of type 2 diabetes among Indian Asians. FUNDING: The European Union, the UK National Institute for Health Research, the Wellcome Trust, the UK Medical Research Council, Action on Hearing Loss, the UK Biotechnology and Biological Sciences Research Council, the Oak Foundation, the Economic and Social Research Council, Helmholtz Zentrum Munchen, the German Research Center for Environmental Health, the German Federal Ministry of Education and Research, the German Center for Diabetes Research, the Munich Center for Health Sciences, the Ministry of Science and Research of the State of North Rhine-Westphalia, and the German Federal Ministry of Health

Epigenome-wide association of DNA methylation markers in peripheral blood from Indian Asians and Europeans with incident type 2 diabetes: a nested case-control study

BACKGROUND: Indian Asians, who make up a quarter of the world’s population, are at high risk of developing type 2 diabetes. We investigated whether DNA methylation is associated with future type 2 diabetes incidence in Indian Asians and whether differences in methylation patterns between Indian Asians and Europeans are associated with, and could be used to predict, differences in the magnitude of risk of developing type 2 diabetes. METHODS: We did a nested case-control study of DNA methylation in Indian Asians and Europeans with incident type 2 diabetes who were identified from the 8-year follow-up of 25 372 participants in the London Life Sciences Prospective Population (LOLIPOP) study. Patients were recruited between May 1, 2002, and Sept 12, 2008. We did epigenome-wide association analysis using samples from Indian Asians with incident type 2 diabetes and age-matched and sex-matched Indian Asian controls, followed by replication testing of top-ranking signals in Europeans. For both discovery and replication, DNA methylation was measured in the baseline blood sample, which was collected before the onset of type 2 diabetes. Epigenome-wide significance was set at p<1 × 10(−7). We compared methylation levels between Indian Asian and European controls without type 2 diabetes at baseline to estimate the potential contribution of DNA methylation to increased risk of future type 2 diabetes incidence among Indian Asians. FINDINGS: 1608 (11·9%) of 13 535 Indian Asians and 306 (4·3%) of 7066 Europeans developed type 2 diabetes over a mean of 8·5 years (SD 1·8) of follow-up. The age-adjusted and sex-adjusted incidence of type 2 diabetes was 3·1 times (95% CI 2·8–3·6; p<0·0001) higher among Indian Asians than among Europeans, and remained 2·5 times (2·1–2·9; p<0·0001) higher after adjustment for adiposity, physical activity, family history of type 2 diabetes, and baseline glycaemic measures. The mean absolute difference in methylation level between type 2 diabetes cases and controls ranged from 0·5% (SD 0·1) to 1·1% (0·2). Methylation markers at five loci were associated with future type 2 diabetes incidence; the relative risk per 1% increase in methylation was 1·09 (95% CI 1·07–1·11; p=1·3 × 10(−17)) for ABCG1, 0·94 (0·92–0·95; p=4·2 × 10(−11)) for PHOSPHO1, 0·94 (0·92–0·96; p=1·4 × 10(−9)) for SOCS3, 1·07 (1·04–1·09; p=2·1 × 10(−10)) for SREBF1, and 0·92 (0·90–0·94; p=1·2 × 10(−17)) for TXNIP. A methylation score combining results for the five loci was associated with future type 2 diabetes incidence (relative risk quartile 4 vs quartile 1 3·51, 95% CI 2·79–4·42; p=1·3 × 10(−26)), and was independent of established risk factors. Methylation score was higher among Indian Asians than Europeans (p=1 × 10(−34)). INTERPRETATION: DNA methylation might provide new insights into the pathways underlying type 2 diabetes and offer new opportunities for risk stratification and prevention of type 2 diabetes among Indian Asians. FUNDING: The European Union, the UK National Institute for Health Research, the Wellcome Trust, the UK Medical Research Council, Action on Hearing Loss, the UK Biotechnology and Biological Sciences Research Council, the Oak Foundation, the Economic and Social Research Council, Helmholtz Zentrum Munchen, the German Research Center for Environmental Health, the German Federal Ministry of Education and Research, the German Center for Diabetes Research, the Munich Center for Health Sciences, the Ministry of Science and Research of the State of North Rhine-Westphalia, and the German Federal Ministry of Health