Extreme value and Haar series estimates of point process boundaries

We present a new method for estimating the edge of a two-dimensional bounded set, given a finite random set of points drawn from the interior. The estimator is based both on Haar series and extreme values of the point process. We give conditions for various kind of convergence and we obtain remarkably different possible limit distributions. We propose a method of reducing the negative bias, illustrated by a simulation

Complexity Estimates for Two Uncoupling Algorithms

Uncoupling algorithms transform a linear differential system of first order into one or several scalar differential equations. We examine two approaches to uncoupling: the cyclic-vector method (CVM) and the Danilevski-Barkatou-Z\"urcher algorithm (DBZ). We give tight size bounds on the scalar equations produced by CVM, and design a fast variant of CVM whose complexity is quasi-optimal with respect to the output size. We exhibit a strong structural link between CVM and DBZ enabling to show that, in the generic case, DBZ has polynomial complexity and that it produces a single equation, strongly related to the output of CVM. We prove that algorithm CVM is faster than DBZ by almost two orders of magnitude, and provide experimental results that validate the theoretical complexity analyses.Comment: To appear in Proceedings of ISSAC'13 (21/01/2013

Evaluation of geospatial methods to generate subnational HIV prevalence estimates for local level planning.

OBJECTIVE: There is evidence of substantial subnational variation in the HIV epidemic. However, robust spatial HIV data are often only available at high levels of geographic aggregation and not at the finer resolution needed for decision making. Therefore, spatial analysis methods that leverage available data to provide local estimates of HIV prevalence may be useful. Such methods exist but have not been formally compared when applied to HIV. DESIGN/METHODS: Six candidate methods - including those used by the Joint United Nations Programme on HIV/AIDS to generate maps and a Bayesian geostatistical approach applied to other diseases - were used to generate maps and subnational estimates of HIV prevalence across three countries using cluster level data from household surveys. Two approaches were used to assess the accuracy of predictions: internal validation, whereby a proportion of input data is held back (test dataset) to challenge predictions; and comparison with location-specific data from household surveys in earlier years. RESULTS: Each of the methods can generate usefully accurate predictions of prevalence at unsampled locations, with the magnitude of the error in predictions similar across approaches. However, the Bayesian geostatistical approach consistently gave marginally the strongest statistical performance across countries and validation procedures. CONCLUSIONS: Available methods may be able to furnish estimates of HIV prevalence at finer spatial scales than the data currently allow. The subnational variation revealed can be integrated into planning to ensure responsiveness to the spatial features of the epidemic. The Bayesian geostatistical approach is a promising strategy for integrating HIV data to generate robust local estimates

Concurrent partnerships in Cape Town, South Africa : race and sex differences in prevalence and duration of overlap

Introduction: Concurrent partnerships (CPs) have been suggested as a risk factor for transmitting HIV, but their impact on the epidemic depends upon how prevalent they are in populations, the average number of CPs an individual has and the length of time they overlap. However, estimates of prevalence of CPs in Southern Africa vary widely, and the duration of overlap in these relationships is poorly documented. We aim to characterize concurrency in a more accurate and complete manner, using data from three disadvantaged communities of Cape Town, South Africa. Methods: We conducted a sexual behaviour survey (n = 878) from June 2011 to February 2012 in Cape Town, using Audio Computer-Assisted Self-Interviewing to collect sexual relationship histories on partners in the past year. Using the beginning and end dates for the partnerships, we calculated the point prevalence, the cumulative prevalence and the incidence rate of CPs, as well as the duration of overlap for relationships begun in the previous year. Linear and binomial regression models were used to quantify race (black vs. coloured) and sex differences in the duration of overlap and relative risk of having CPs in the past year. Results: The overall point prevalence of CPs six months before the survey was 8.4%: 13.4% for black men, 1.9% for coloured men, 7.8% black women and 5.6% for coloured women. The median duration of overlap in CPs was 7.5 weeks. Women had less risk of CPs in the previous year than men (RR 0.43; 95% CI: 0.32-0.57) and black participants were more at risk than coloured participants (RR 1.86; 95% CI: 1.17-2.97). Conclusions: Our results indicate that in this population the prevalence of CPs is relatively high and is characterized by overlaps of long duration, implying there may be opportunities for HIV to be transmitted to concurrent partners

Embracing different approaches to estimating HIV incidence, prevalence and mortality.

BACKGROUND: Joint United Nations Programme on HIV/AIDS (UNAIDS) and Murray et al. have both produced sets of estimates for worldwide HIV incidence, prevalence and mortality. Understanding differences in these estimates can strengthen the interpretation of each. METHODS: We describe differences in the two sets of estimates. Where possible, we have drawn on additional published data to which estimates can be compared. FINDINGS: UNAIDS estimates that there were 6 million more people living with HIV (PLHIV) in 2013 (35 million) compared with the Murray et al. estimates (29 million). Murray et al. estimate that new infections and AIDS deaths have declined more gradually than does UNAIDS. Just under one third of the difference in PLHIV is in Africa, where Murray et al. have relied more on estimates of adult mortality trends than on data on survival times. Another third of the difference is in North America, Europe, Central Asia and Australasia. Here Murray et al. estimates of new infections are substantially lower than the number of new HIV/AIDS diagnoses reported by countries, whereas published UNAIDS estimate tend to be greater. The remaining differences are in Latin America and Asia where the data upon which the UNAIDS methods currently rely are more sparse, whereas the mortality data leveraged by Murray et al. may be stronger. In this region, however, anomalies appear to exist between the both sets of estimates and other data. INTERPRETATION: Both estimates indicate that approximately 30 million PLHIV and that antiretroviral therapy has driven large reductions in mortality. Both estimates are useful but show instructive discrepancies with additional data sources. We find little evidence to suggest that either set of estimates can be considered systematically more accurate. Further work should seek to build estimates on as wide a base of data as possible

Coital frequency and condom use in monogamous and concurrent sexual relationships in Cape Town, South Africa

Introduction: A decreased frequency of unprotected sex during episodes of concurrent relationships may dramatically reduce the role of concurrency in accelerating the spread of HIV. Such a decrease could be the result of coital dilution - the reduction in per-partner coital frequency from additional partners - and/or increased condom use during concurrency. To study the effect of concurrency on the frequency of unprotected sex, we examined sexual behaviour data from three communities with high HIV prevalence around Cape Town, South Africa. Methods: We conducted a cross-sectional survey from June 2011 to February 2012 using audio computer-assisted self-interviewing to reconstruct one-year sexual histories, with a focus on coital frequency and condom use. Participants were randomly sampled from a previous TB and HIV prevalence survey. Mixed effects logistic and Poisson regression models were fitted to data from 527 sexually active adults reporting on 1210 relationship episodes to evaluate the effect of concurrency status on consistent condom use and coital frequency. Results: The median of the per-partner weekly average coital frequency was 2 (IQR: 1 - 3), and consistent condom use was reported for 36% of the relationship episodes. Neither per-partner coital frequency nor consistent condom use changed significantly during episodes of concurrency (aIRR = 1.05; 95% confidence interval (CI): 0.99-1.24 and aOR = 1.01; 95% CI: 0.38-2.68, respectively). Being male, coloured, having a tertiary education, and having a relationship between 2 weeks and 9 months were associated with higher coital frequencies. Being coloured, and having a relationship lasting for more than 9 months, was associated with inconsistent condom use. Conclusions: We found no evidence for coital dilution or for increased condom use during concurrent relationship episodes in three communities around Cape Town with high HIV prevalence. Given the low levels of self- reported consistent condom use, our findings suggest that if the frequency of unprotected sex with each of the sexual partners is sustained during concurrent relationships, HIV-positive individuals with concurrent partners may disproportionately contribute to onward HIV transmission

Estimating Incidence from Prevalence in Generalised HIV Epidemics: Methods and Validation

Timothy Hallett and colleagues develop and test two user-friendly methods to estimate HIV incidence based on changes in cross-sectional prevalence, using either mortality rates or survival after infection

Non-hispanic whites have higher risk for pulmonary impairment from pulmonary tuberculosis

<p>Abstract</p> <p>Background</p> <p>Disparities in outcomes associated with race and ethnicity are well documented for many diseases and patient populations. Tuberculosis (TB) disproportionately affects economically disadvantaged, racial and ethnic minority populations. Pulmonary impairment after tuberculosis (PIAT) contributes heavily to the societal burden of TB. Individual impacts associated with PIAT may vary by race/ethnicity or socioeconomic status.</p> <p>Methods</p> <p>We analyzed the pulmonary function of 320 prospectively identified patients with pulmonary tuberculosis who had completed at least 20 weeks standard anti-TB regimes by directly observed therapy. We compared frequency and severity of spirometry-defined PIAT in groups stratified by demographics, pulmonary risk factors, and race/ethnicity, and examined clinical correlates to pulmonary function deficits.</p> <p>Results</p> <p>Pulmonary impairment after tuberculosis was identified in 71% of non-Hispanic Whites, 58% of non-Hispanic Blacks, 49% of Asians and 32% of Hispanics (<it>p </it>< 0.001). Predictors for PIAT varied between race/ethnicity. PIAT was evenly distributed across all levels of socioeconomic status suggesting that PIAT and socioeconomic status are not related. PIAT and its severity were significantly associated with abnormal chest x-ray, <it>p </it>< 0.0001. There was no association between race/ethnicity and time to beginning TB treatment, <it>p </it>= 0.978.</p> <p>Conclusions</p> <p>Despite controlling for cigarette smoking, socioeconomic status and time to beginning TB treatment, non-Hispanic White race/ethnicity remained an independent predictor for disproportionately frequent and severe pulmonary impairment after tuberculosis relative to other race/ethnic groups. Since race/ethnicity was self reported and that race is not a biological construct: these findings must be interpreted with caution. However, because race/ethnicity is a proxy for several other unmeasured host, pathogen or environment factors that may contribute to disparate health outcomes, these results are meant to suggest hypotheses for further research.</p