Reinfection by untreated partners of people treated for Chlamydia trachomatis and Neisseria gonorrhoeae: mathematical modelling study

OBJECTIVES Reinfection after treatment for Chlamydia trachomatis or Neisseria gonorrhoeae reduces the effect of control interventions. We explored the impact of delays in treatment of current partners on the expected probability of reinfection of index cases using a mathematical model. METHODS We used previously reported parameter distributions to calculate the probability that index cases would be reinfected by their untreated partners. We then assumed different delays between index case and partner treatment to calculate the probabilities of reinfection. RESULTS In the absence of partner treatment, the medians of the expected reinfection probabilities are 19.4% (IQR 9.2-31.6%) for C trachomatis and 12.5% (IQR 5.6-22.2%) for N gonorrhoeae. If all current partners receive treatment 3 days after the index case, the expected reinfection probabilities are 4.2% (IQR 2.1-6.9%) for C trachomatis and 5.5% (IQR 2.6-9.5%) for N gonorrhoeae. CONCLUSIONS Quicker partner referral and treatment can substantially reduce reinfection rates for C trachomatis and N gonorrhoeae by untreated partners. The formula we used to calculate reinfection rates can be used to inform the design of randomised controlled trials of novel partner notification technologies like accelerated partner therapy.

Direct and indirect effects of screening for Chlamydia trachomatis on the prevention of pelvic inflammatory disease: a mathematical modeling study

BACKGROUND Pelvic inflammatory disease (PID) results from the ascending spread of microorganisms, including Chlamydia trachomatis, to the upper genital tract. Screening could improve outcomes by identifying and treating chlamydial infections before they progress to PID (direct effect) or by reducing chlamydia transmission (indirect effect). METHODS We developed a compartmental model that represents a hypothetical heterosexual population and explicitly incorporates progression from chlamydia to clinical PID. Chlamydia screening was introduced, with coverage increasing each year for 10 years. We estimated the separate contributions of the direct and indirect effects of screening on PID cases prevented per 100,000 women. We explored the influence of varying the time point at which clinical PID could occur and of increasing the risk of PID after repeated chlamydial infections. RESULTS The probability of PID at baseline was 3.1% by age 25 years. After 5 years, the intervention scenario had prevented 187 PID cases per 100,000 women and after 10 years 956 PID cases per 100,000 women. At the start of screening, most PID cases were prevented by the direct effect. The indirect effect produced a small net increase in PID cases, which was outweighed by the effect of reduced chlamydia transmission after 2.2 years. The later that progression to PID occurs, the greater the contribution of the direct effect. Increasing the risk of PID with repeated chlamydial infection increases the number of PID cases prevented by screening. CONCLUSIONS This study shows the separate roles of direct and indirect PID prevention and potential harms, which cannot be demonstrated in observational studies.

Cost-effectiveness of different strategies to monitor adults on antiretroviral treatment: a combined analysis of three mathematical models

Background: WHO's 2013 revisions to its Consolidated Guidelines on antiretroviral drugs recommend routine viral load monitoring, rather than clinical or immunological monitoring, as the preferred monitoring approach on the basis of clinical evidence. However, HIV programmes in resource-limited settings require guidance on the most cost-effective use of resources in view of other competing priorities such as expansion of antiretroviral therapy coverage. We assessed the cost-effectiveness of alternative patient monitoring strategies. Methods: We evaluated a range of monitoring strategies, including clinical, CD4 cell count, and viral load monitoring, alone and together, at different frequencies and with different criteria for switching to second-line therapies. We used three independently constructed and validated models simultaneously. We estimated costs on the basis of resource use projected in the models and associated unit costs; we quantified impact as disability-adjusted life years (DALYs) averted. We compared alternatives using incremental cost-effectiveness analysis. Findings: All models show that clinical monitoring delivers significant benefit compared with a hypothetical baseline scenario with no monitoring or switching. Regular CD4 cell count monitoring confers a benefit over clinical monitoring alone, at an incremental cost that makes it affordable in more settings than viral load monitoring, which is currently more expensive. Viral load monitoring without CD4 cell count every 6—12 months provides the greatest reductions in morbidity and mortality, but incurs a high cost per DALY averted, resulting in lost opportunities to generate health gains if implemented instead of increasing antiretroviral therapy coverage or expanding antiretroviral therapy eligibility. Interpretation: The priority for HIV programmes should be to expand antiretroviral therapy coverage, firstly at CD4 cell count lower than 350 cells per μL, and then at a CD4 cell count lower than 500 cells per μL, using lower-cost clinical or CD4 monitoring. At current costs, viral load monitoring should be considered only after high antiretroviral therapy coverage has been achieved. Point-of-care technologies and other factors reducing costs might make viral load monitoring more affordable in future. Funding: Bill & Melinda Gates Foundation, WHO.

Blended Learning: Integrating an e-Learning Component for Competency Validation

Introduction: Emergency care providers are required to demonstrate competency in the management of life-threatening situation. The care provider’s ability to manage an emergency situation depends upon his/her knowledge and skills in basic CPR; and the use of emergency equipment and supplies. The education department at our healthcare facility is responsible for CPR/Emergency Management competency validation of over 2500 employees annually. Historically each employee was scheduled to attend 4 hours of class every year to review the content, complete the post-test and demonstrate skills. It was resource-intensive, time consuming, stressful and often difficult to schedule the 24/7 employees for the sessions. [See PDF for complete abstract]

Self-Assessment in a Competency-Based Curriculum: Preliminary Findings

Introduction: The introduction of the ACGME core competency framework brought challenges of developing appropriate evaluation tools (i.e. self assessment) to provide evidence of competency. Baylor College of Medicine has 43 competency goals organized within the 6 ACGME domains, each domain having 4-10 goals. [See PDF for complete abstract]

A cardiovascular mathematical model of graded head-up tilt

A lumped parameter model of the cardiovascular system has been developed and optimized using experimental data obtained from 13 healthy subjects during graded head-up tilt (HUT) from the supine position to [Formula: see text]. The model includes descriptions of the left and right heart, direct ventricular interaction through the septum and pericardium, the systemic and pulmonary circulations, nonlinear pressure volume relationship of the lower body compartment, arterial and cardiopulmonary baroreceptors, as well as autoregulatory mechanisms. A number of important features, including the separate effects of arterial and cardiopulmonary baroreflexes, and autoregulation in the lower body, as well as diastolic ventricular interaction through the pericardium have been included and tested for their significance. Furthermore, the individual effect of parameter associated with heart failure, including LV and RV contractility, baseline systemic vascular resistance, pulmonary vascular resistance, total blood volume, LV diastolic stiffness and reflex gain on HUT response have also been investigated. Our fitted model compares favorably with our experimental measurements and published literature at a range of tilt angles, in terms of both global and regional hemodynamic variables. Compared to the normal condition, a simulated congestive heart failure condition produced a blunted response to HUT with regards to the percentage changes in cardiac output, stroke volume, end diastolic volume and effector response (i.e., heart contractility, venous unstressed volume, systemic vascular resistance and heart rate) with progressive tilting.

Uniqueness of the Embedding Continuous Convolution Semigroup of a Gaussian Probability Measure on the Affine Group and an Application in Mathematical Finance

Let {μ(i)t}t≥0 ( i=1,2 ) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that μ(1)1=μ(2)1 . Assume furthermore that {μ(1)t}t≥0 is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then μ(1)t=μ(2)t for all t≥0 . We end up with a possible application in mathematical finance.

Beyond questionnaires – Exploring adult education teachers' mathematical beliefs with pictures and interviews

Because of the impact that mathematical beliefs have on an individual’s behaviour, they are generally well researched. However, little mathematical belief research has taken place in the field of adult education. This paper presents preliminary results from a study conducted in this field in Switzerland. It is based on Ernest’s (1989) description of mathematics as an instrumental, Platonist or problem solving construct. The analysis uses pictures drawn by the participants and interviews conducted with them as data. Using a categorising scheme developed by Rolka and Halverscheid (2011), the author argues that adults’ mathematical beliefs are complex and especially personal aspects are difficult to capture with said scheme. Particularly the analysis of visual data requires a more refined method of analysis.

Delay effects in the response of low-grade gliomas to radiotherapy: a mathematical model and its therapeutical implications

Low-grade gliomas (LGGs) are a group of primary brain tumours usually encountered in young patient populations. These tumours represent a difficult challenge because many patients survive a decade or more and may be at a higher risk for treatment-related complications. Specifically, radiation therapy is known to have a relevant effect on survival but in many cases it can be deferred to avoid side effects while maintaining its beneficial effect. However, a subset of LGGs manifests more aggressive clinical behaviour and requires earlier intervention. Moreover, the effectiveness of radiotherapy depends on the tumour characteristics. Recently Pallud et al. (2012. Neuro-Oncology, 14: , 1-10) studied patients with LGGs treated with radiation therapy as a first-line therapy and obtained the counterintuitive result that tumours with a fast response to the therapy had a worse prognosis than those responding late. In this paper, we construct a mathematical model describing the basic facts of glioma progression and response to radiotherapy. The model provides also an explanation to the observations of Pallud et al. Using the model, we propose radiation fractionation schemes that might be therapeutically useful by helping to evaluate tumour malignancy while at the same time reducing the toxicity associated to the treatment.

Pushing forward in embodied cognition: May we mouse the mathematical mind?

Freely available software has popularized “mousetracking” to study cognitive processing; this involves the on-line recording of cursor positions while participants move a computer mouse to indicate their choice. Movement trajectories of the cursor can then be reconstructed off-line to assess the efficiency of responding in time and across space. Here we focus on the process of selecting among alternative numerical responses. Several studies have recently measured the mathematical mind with cursor movements while people decided about number magnitude or parity, computed sums or differences, or simply located numbers on a number line. After some general methodological considerations about mouse tracking we discuss several conceptual concerns that become particularly evident when “mousing” the mathematical mind.

Sample size considerations using mathematical models: an example with Chlamydia trachomatis infection and its sequelae pelvic inflammatory disease.

BACKGROUND The success of an intervention to prevent the complications of an infection is influenced by the natural history of the infection. Assumptions about the temporal relationship between infection and the development of sequelae can affect the predicted effect size of an intervention and the sample size calculation. This study investigates how a mathematical model can be used to inform sample size calculations for a randomised controlled trial (RCT) using the example of Chlamydia trachomatis infection and pelvic inflammatory disease (PID). METHODS We used a compartmental model to imitate the structure of a published RCT. We considered three different processes for the timing of PID development, in relation to the initial C. trachomatis infection: immediate, constant throughout, or at the end of the infectious period. For each process we assumed that, of all women infected, the same fraction would develop PID in the absence of an intervention. We examined two sets of assumptions used to calculate the sample size in a published RCT that investigated the effect of chlamydia screening on PID incidence. We also investigated the influence of the natural history parameters of chlamydia on the required sample size. RESULTS The assumed event rates and effect sizes used for the sample size calculation implicitly determined the temporal relationship between chlamydia infection and PID in the model. Even small changes in the assumed PID incidence and relative risk (RR) led to considerable differences in the hypothesised mechanism of PID development. The RR and the sample size needed per group also depend on the natural history parameters of chlamydia. CONCLUSIONS Mathematical modelling helps to understand the temporal relationship between an infection and its sequelae and can show how uncertainties about natural history parameters affect sample size calculations when planning a RCT.

The need for second-line antiretroviral therapy in adults in sub-Saharan Africa up to 2030: a mathematical modelling study.

BACKGROUND The number of patients in need of second-line antiretroviral drugs is increasing in sub-Saharan Africa. We aimed to project the need of second-line antiretroviral therapy in adults in sub-Saharan Africa up to 2030. METHODS We developed a simulation model for HIV and applied it to each sub-Saharan African country. We used the WHO country intelligence database to estimate the number of adult patients receiving antiretroviral therapy from 2005 to 2014. We fitted the number of adult patients receiving antiretroviral therapy to observed estimates, and predicted first-line and second-line needs between 2015 and 2030. We present results for sub-Saharan Africa, and eight selected countries. We present 18 scenarios, combining the availability of viral load monitoring, speed of antiretroviral scale-up, and rates of retention and switching to second-line. HIV transmission was not included. FINDINGS Depending on the scenario, 8·7-25·6 million people are expected to receive antiretroviral therapy in 2020, of whom 0·5-3·0 million will be receiving second-line antiretroviral therapy. The proportion of patients on treatment receiving second-line therapy was highest (15·6%) in the scenario with perfect retention and immediate switching, no further scale-up, and universal routine viral load monitoring. In 2030, the estimated range of patients receiving antiretroviral therapy will remain constant, but the number of patients receiving second-line antiretroviral therapy will increase to 0·8-4·6 million (6·6-19·6%). The need for second-line antiretroviral therapy was two to three times higher if routine viral load monitoring was implemented throughout the region, compared with a scenario of no further viral load monitoring scale-up. For each monitoring strategy, the future proportion of patients receiving second-line antiretroviral therapy differed only minimally between countries. INTERPRETATION Donors and countries in sub-Saharan Africa should prepare for a substantial increase in the need for second-line drugs during the next few years as access to viral load monitoring improves. An urgent need exists to decrease the costs of second-line drugs. FUNDING World Health Organization, Swiss National Science Foundation, National Institutes of Health.