Recursive marginal quantization of higher-order schemes

© 2018 Informa UK Limited, trading as Taylor & Francis Group. Quantization techniques have been applied in many challenging finance applications, including pricing claims with path dependence and early exercise features, stochastic optimal control, filtering problems and efficient calibration of large derivative books. Recursive marginal quantization (RMQ) of the Euler scheme has recently been proposed as an efficient numerical method for evaluating functionals of solutions of stochastic differential equations. This method involves recursively quantizing the conditional marginals of the discrete-time Euler approximation of the underlying process. By generalizing this approach, we show that it is possible to perform RMQ for two higher-order schemes: the Milstein scheme and a simplified weak order 2.0 scheme. We further extend the applicability of RMQ by showing how absorption and reflection at the zero boundary may be incorporated, when necessary. To illustrate the improved accuracy of the higher-order schemes, various computations are performed using geometric Brownian motion and the constant elasticity of variance model. For both models, we provide evidence of improved weak order convergence and computational efficiency. By pricing European, Bermudan and barrier options, further evidence of improved accuracy of the higher-order schemes is demonstrated

BED Estimates of HIV Incidence: Resolving the Differences, Making Things Simpler

Objective: Develop a simple method for optimal estimation of HIV incidence using the BED capture enzyme immunoassay. Design: Use existing BED data to estimate mean recency duration, false recency rates and HIV incidence with reference to a fixed time period, T. Methods: Compare BED and cohort estimates of incidence referring to identical time frames. Generalize this approach to suggest a method for estimating HIV incidence from any cross-sectional survey. Results: Follow-up and BED analyses of the same, initially HIV negative, cases followed over the same set time period T, produce estimates of the same HIV incidence, permitting the estimation of the BED mean recency period for cases who have been HIV positive for less than T. Follow-up of HIV positive cases over T, similarly, provides estimates of the false-recent rate appropriate for T. Knowledge of these two parameters for a given population allows the estimation of HIV incidence during T by applying the BED method to samples from cross-sectional surveys. An algorithm is derived for providing these estimates, adjusted for the false-recent rate. The resulting estimator is identical to one derived independently using a more formal mathematical analysis. Adjustments improve the accuracy of HIV incidence estimates. Negative incidence estimates result from the use of inappropriate estimates of the false-recent rate and/or from sampling error, not from any error in the adjustment procedure

HIV Incidence in Rural South Africa: Comparison of Estimates from Longitudinal Surveillance and Cross-Sectional cBED Assay Testing

The original publication is available at http:/www.plosone.orgBackground: The BED IgG-Capture Enzyme Immunoassay (cBED assay), a test of recent HIV infection, has been used to estimate HIV incidence in cross-sectional HIV surveys. However, there has been concern that the assay overestimates HIV incidence to an unknown extent because it falsely classifies some individuals with non-recent HIV infections as recently infected. We used data from a longitudinal HIV surveillance in rural South Africa to measure the fraction of people with nonrecent HIV infection who are falsely classified as recently HIV-infected by the cBED assay (the long-term false-positive ratio (FPR)) and compared cBED assay-based HIV incidence estimates to longitudinally measured HIV incidence. Methodology/Principal Findings: We measured the long-term FPR in individuals with two positive HIV tests (in the HIV surveillance, 2003-2006) more than 306 days apart (sample size n = 1,065). We implemented four different formulae to calculate HIV incidence using cBED assay testing (n = 11,755) and obtained confidence intervals (CIs) by directly calculating the central 95th percentile of incidence values. We observed 4,869 individuals over 7,685 person-years for longitudinal HIV incidence estimation. The long-term FPR was 0.0169 (95% CI 0.0100-0.0266). Using this FPR, the cross-sectional cBED-based HIV incidence estimates (per 100 people per year) varied between 3.03 (95% CI 2.44-3.63) and 3.19 (95% CI 2.57-3.82), depending on the incidence formula. Using a long-term FPR of 0.0560 based on previous studies, HIV incidence estimates varied between 0.65 (95% CI 0.00-1.32) and 0.71 (95% CI 0.00-1.43). The longitudinally measured HIV incidence was 3.09 per 100 people per year (95% CI 2.69-3.52), after adjustment to the sex-age distribution of the sample used in cBED assay-based estimation. Conclusions/Significance: In a rural community in South Africa with high HIV prevalence, the long-term FPR of the cBED assay is substantially lower than previous estimates. The cBED assay performs well in HIV incidence estimation if the locally measured long-term FPR is used, but significantly underestimates incidence when a FPR estimate based on previous studies in other settings is used. © 2008 Bärnighausen et al.Publishers' Versio

Biomarker-Based HIV Incidence in a Community Sample of Men Who Have Sex with Men in Paris, France

BACKGROUND: Population-based estimates of HIV incidence in France have revealed that men who have sex with men (MSM) are the most affected population and contribute to nearly half of new infections each year. We sought to estimate HIV incidence among sexually active MSM in Paris gay community social venues. METHODOLOGY/ PRINCIPAL FINDINGS: A cross-sectional survey was conducted in 2009 in a sample of commercial venues such as bars, saunas and backrooms. We collected a behavioural questionnaire and blood sample. Specimens were tested for HIV infection and positive specimens then tested for recent infection by the enzyme immunoassay for recent HIV-1 infection (EIA-RI). We assessed the presence of antiretroviral therapy among infected individuals to rule out treated patients in the algorithm that determined recent infection. Biomarker-based cross-sectional incidence estimates were calculated. We enrolled 886 MSM participants among which 157 (18%) tested HIV positive. In positive individuals who knew they were infected, 75% of EIA-RI positive results were due to ART. Of 157 HIV positive specimens, 15 were deemed to be recently infected. The overall HIV incidence was estimated at 3.8% person-years (py) [95%CI: 1.5-6.2]. Although differences were not significant, incidence was estimated to be 3.5% py [0.1-6.1] in men having had a negative HIV test in previous year and 4.8% py [0.1-10.6] in men having had their last HIV test more than one year before the survey, or never tested. Incidence was estimated at 4.1% py [0-8.3] in men under 35 years and 2.5% py [0-5.4] in older men. CONCLUSIONS/ SIGNIFICANCE: This is the first community-based survey to estimate HIV incidence among MSM in France. It includes ART detection and reveals a high level of HIV transmission in sexually active individuals, despite a high uptake of HIV testing. These data call for effective prevention programs targeting MSM engaged in high-risk behaviours

HIV Incidence Remains High in KwaZulu-Natal, South Africa: Evidence from Three Districts

Background: HIV prevalence and incidence among sexually active women in peri-urban areas of Ladysmith, Edendale, and Pinetown, KwaZulu-Natal, South Africa, were assessed between October 2007 and February 2010 in preparation for vaginal microbicide trials. Methodology/Principal Findings: Sexually active women 18-35 years, not known to be HIV-positive or pregnant were tested cross-sectionally to determine HIV and pregnancy prevalence (798 in Ladysmith, 1,084 in Edendale, and 891 in Pinetown). Out of these, approximately 300 confirmed non-pregnant, HIV-negative women were subsequently enrolled at each clinical research center (CRC) in a 12-month cohort study with quarterly study visits. Women in the cohort studies were required to use a condom plus a hormonal contraceptive method. HIV prevalence rates in the baseline cross-sectional surveys were high: 42% in Ladysmith, 46% in Edendale and 41% in Pinetown. Around 90% of study participants at each CRC reported one sex partner in the last 3 months, but only 14-30% stated that they were sure that none of their sex partners were HIV-positive. HIV incidence rates based on seroconversions over 12 months were 14.8/100 person-years (PY) (95% CI 9.7, 19.8) in Ladysmith, 6.3/100 PY (95% CI 3.2, 9.4) in Edendale, and 7.2/100 PY (95% CI 3.7, 10.7) in Pinetown. The 12-month pregnancy incidence rates (in the context of high reported contraceptive use) were: 5.7/100 PY (95% CI 2.6, 8.7) in Ladysmith, 3.1/100 PY (95% CI 0.9, 5.2) in Edendale and 6.3/100 PY (95% CI 3.0, 9.6) in Pinetown. Conclusions/Significance: HIV prevalence and incidence remain high in peri-urban areas of KwaZulu-Nata

Performance of Risk-Based Criteria for Targeting Acute HIV Screening in San Francisco

Federal guidelines now recommend supplemental HIV RNA testing for persons at high risk for acute HIV infection. However, many rapid HIV testing sites do not include HIV RNA or p24 antigen testing due to concerns about cost, the need for results follow-up, and the impact of expanded venipuncture on clinic flow. We developed criteria to identify patients in a municipal STD clinic in San Francisco who are asymptomatic but may still be likely to have acute infection.Data were from patients tested with serial HIV antibody and HIV RNA tests to identify acute HIV infection. BED-CEIA results were used to classify non-acute cases as recent or longstanding. Demographics and self-reported risk behaviors were collected at time of testing. Multivariate models were developed and preliminarily evaluated using predictors associated with recent infection in bivariate analyses as a proxy for acute HIV infection. Multivariate models demonstrating ≥70% sensitivity for recent infection while testing ≤60% of patients in this development dataset were then validated by determining their performance in identifying acute infections.From 2004-2007, 137 of 12,622 testers had recent and 36 had acute infections. A model limiting acute HIV screening to MSM plus any one of a series of other predictors resulted in a sensitivity of 83.3% and only 47.6% of patients requiring testing. A single-factor model testing only patients reporting any receptive anal intercourse resulted in 88.9% sensitivity with only 55.2% of patients requiring testing.In similar high risk HIV testing sites, acute screening using "supplemental" HIV p24 antigen or RNA tests can be rationally targeted to testers who report particular HIV risk behaviors. By improving the efficiency of acute HIV testing, such criteria could facilitate expanded acute case identification

Dual Testing Algorithm of BED-CEIA and AxSYM Avidity Index Assays Performs Best in Identifying Recent HIV Infection in a Sample of Rwandan Sex Workers

To assess the performance of BED-CEIA (BED) and AxSYM Avidity Index (Ax-AI) assays in estimating HIV incidence among female sex workers (FSW) in Kigali, Rwanda. Eight hundred FSW of unknown HIV status were HIV tested; HIV-positive women had BED and Ax-AI testing at baseline and ≥12 months later to estimate assay false-recent rates (FRR). STARHS-based HIV incidence was estimated using the McWalter/Welte formula, and adjusted with locally derived FRR and CD4 results. HIV incidence and local assay window periods were estimated from a prospective cohort of FSW. At baseline, 190 HIV-positive women were BED and Ax-AI tested; 23 were classified as recent infection (RI). Assay FRR with 95% confidence intervals were: 3.6% (1.2-8.1) (BED); 10.6% (6.1-17.0) (Ax-AI); and 2.1% (0.4-6.1) (BED/Ax-AI combined). After FRR-adjustment, incidence estimates by BED, Ax-AI, and BED/Ax-AI were: 5.5/100 person-years (95% CI 2.2-8.7); 7.7 (3.2-12.3); and 4.4 (1.4-7.3). After CD4-adjustment, BED, Ax-AI, and BED/Ax-AI incidence estimates were: 5.6 (2.6-8.6); 9.7 (5.0-14.4); and 4.7 (2.0-7.5). HIV incidence rates in the first and second 6 months of the cohort were 4.6 (1.6-7.7) and 2.2 (0.1-4.4). Adjusted incidence estimates by BED/Ax-AI combined were similar to incidence in the first 6 months of the cohort. Furthermore, false-recent rate on the combined BED/Ax-AI algorithm was low and substantially lower than for either assay alone. Improved assay specificity with time since seroconversion suggests that specificity would be higher in population-based testing where more individuals have long-term infectio

Diagnostic performance of line-immunoassay based algorithms for incident HIV-1 infection

Background: Serologic testing algorithms for recent HIV seroconversion (STARHS) provide important information for HIV surveillance. We have previously demonstrated that a patient's antibody reaction pattern in a confirmatory line immunoassay (INNO-LIA™ HIV I/II Score) provides information on the duration of infection, which is unaffected by clinical, immunological and viral variables. In this report we have set out to determine the diagnostic performance of Inno-Lia algorithms for identifying incident infections in patients with known duration of infection and evaluated the algorithms in annual cohorts of HIV notifications. Methods: Diagnostic sensitivity was determined in 527 treatment-naive patients infected for up to 12 months. Specificity was determined in 740 patients infected for longer than 12 months. Plasma was tested by Inno-Lia and classified as either incident (< = 12 m) or older infection by 26 different algorithms. Incident infection rates (IIR) were calculated based on diagnostic sensitivity and specificity of each algorithm and the rule that the total of incident results is the sum of true-incident and false-incident results, which can be calculated by means of the pre-determined sensitivity and specificity. Results: The 10 best algorithms had a mean raw sensitivity of 59.4% and a mean specificity of 95.1%. Adjustment for overrepresentation of patients in the first quarter year of infection further reduced the sensitivity. In the preferred model, the mean adjusted sensitivity was 37.4%. Application of the 10 best algorithms to four annual cohorts of HIV-1 notifications totalling 2'595 patients yielded a mean IIR of 0.35 in 2005/6 (baseline) and of 0.45, 0.42 and 0.35 in 2008, 2009 and 2010, respectively. The increase between baseline and 2008 and the ensuing decreases were highly significant. Other adjustment models yielded different absolute IIR, although the relative changes between the cohorts were identical for all models Conclusions: The method can be used for comparing IIR in annual cohorts of HIV notifications. The use of several different algorithms in combination, each with its own sensitivity and specificity to detect incident infection, is advisable as this reduces the impact of individual imperfections stemming primarily from relatively low sensitivities and sampling bias

HIV and Other Sexually Transmitted Infections among Men Who Have Sex with Men Recruited by RDS in Buenos Aires, Argentina: High HIV and HPV Infection

The aim of this study was to estimate the prevalence of HIV and other STIs, among MSM from Buenos Aires (2007-2009).Responding Driven Sampling was used for recruitment of MSM. Participants completed a structured web-based survey and provided biological samples.A total of 496 MSM were studied for HIV, HBV, HCV, and T. pallidum infections. Chlamydia and HPV diagnoses were only performed in 98 and 109 participants, respectively. Prevalence of HIV was 17.3%, HBV 22.9%, HCV 7.5%, T. pallidum 20.5%, HPV 83.5%, and C. trachomatis 1.7%. In the year prior to the evaluation, 71% of the participants had had sex with men and/or trans and women (MMW) while 29% had not had sex with women (MM). Comparing MM to MMW, prevalence of HIV (30.7% vs. 11.9%, p<0.001), HBV (36.4% vs. 17.8%, p<0.001), T. pallidum (32.1% vs. 15.7%, p<0.001), and HPV (88.3% vs. 70.4%, p = 0.039) were significantly higher among MM, whereas no significant differences were found for HCV and C. trachomatis. The MM group had also significantly higher HIV incidence (5.60 vs. 4.28 per 100 persons-year, p = 0.032). HPV genotypes 16, 6, and 11 were the most frequently found; 40.7% of the MSM had more than one genotype and one high risk genotype was detected in 43.6% of participants.Both MM and MMW are at high risk of infection for HIV and other STIs. Rates of HIV, HBV, T. pallidum and HPV infections are higher in the MM group