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.

Comparison of the capacity of enamel matrix derivative gel and enamel matrix derivative in liquid formulation to adsorb to bone grafting materials.

BACKGROUND The use of an enamel matrix derivative (EMD) has been shown to enhance periodontal regeneration (e.g., formation of root cementum, periodontal ligament, and alveolar bone). However, in certain clinical situations, the use of EMD alone may not be sufficient to prevent flap collapse or provide sufficient stability of the blood clot. Data from clinical and preclinical studies have demonstrated controversial results after application of EMD combined with different types of bone grafting materials in periodontal regenerative procedures. The aim of the present study is to investigate the adsorption properties of enamel matrix proteins to bone grafts after surface coating with either EMD (as a liquid formulation) or EMD (as a gel formulation). METHODS Three different types of grafting materials, including a natural bone mineral (NBM), demineralized freeze-dried bone allograft (DFDBA), or a calcium phosphate (CaP), were coated with either EMD liquid or EMD gel. Samples were analyzed by scanning electron microscopy or transmission electron microscopy (TEM) using an immunostaining assay with gold-conjugated anti-EMD antibody. Total protein adsorption to bone grafting material was quantified using an enzyme-linked immunosorbent assay (ELISA) kit for amelogenin. RESULTS The adsorption of amelogenin to the surface of grafting material varied substantially based on the carrier system used. EMD gel adsorbed less protein to the surface of grafting particles, which easily dissociated from the graft surface after phosphate-buffered saline rinsing. Analyses by TEM revealed that adsorption of amelogenin proteins were significantly farther from the grafting material surface, likely a result of the thick polyglycolic acid gel carrier. ELISA protein quantification assay demonstrated that the combination of EMD liquid + NBM and EMD liquid + DFDBA adsorbed higher amounts of amelogenin than all other treatment modalities. Furthermore, amelogenin proteins delivered by EMD liquid were able to penetrate the porous surface structure of NBM and DFDBA and adsorb to the interior of bone grafting particles. Grafting materials coated with EMD gel adsorbed more frequently to the exterior of grafting particles with little interior penetration. CONCLUSIONS The present study demonstrates a large variability of adsorbed amelogenin to the surface of bone grafting materials when enamel matrix proteins were delivered in either a liquid formulation or gel carrier. Furthermore, differences in amelogenin adsorption were observed among NBM, DFDBA, and biphasic CaP particles. Thus, the potential for a liquid carrier system for EMD, used to coat EMD, may be advantageous for better surface coating.

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.

A vaccine formulation combining rhoptry proteins NcROP40 and NcROP2 improves pup survival in a pregnant mouse model of neosporosis.

Currently there are no effective vaccines for the control of bovine neosporosis. During the last years several subunit vaccines based on immunodominant antigens and other proteins involved in adhesion, invasion and intracellular proliferation of Neospora caninum have been evaluated as targets for vaccine development in experimental mouse infection models. Among them, the rhoptry antigen NcROP2 and the immunodominant NcGRA7 protein have been assessed with varying results. Recent studies have shown that another rhoptry component, NcROP40, and NcNTPase, a putative dense granule antigen, exhibit higher expression levels in tachyzoites of virulent N. caninum isolates, suggesting that these could be potential vaccine candidates to limit the effects of infection. In the present work, the safety and efficacy of these recombinant antigens formulated in Quil-A adjuvant as monovalent vaccines or pair-wise combinations (rNcROP40+rNcROP2 and rNcGRA7+rNcNTPase) were evaluated in a pregnant mouse model of neosporosis. All the vaccine formulations elicited a specific immune response against their respective native proteins after immunization. Mice vaccinated with rNcROP40 and rNcROP2 alone or in combination produced the highest levels of IFN-γ and exhibited low parasite burdens and low IgG antibody levels after the challenge. In addition, most of the vaccine formulations were able to increase the median survival time in the offspring. However, pup survival only ensued in the groups vaccinated with rNcROP40+rNcROP2 (16.2%) and rNcROP2 (6.3%). Interestingly, vertical transmission was not observed in those survivor pups immunized with rNcROP40+rNcROP2, as shown by PCR analyses. These results show a partial protection against N. caninum infection after vaccination with rNcROP40+rNcROP2, suggesting a synergistic effect of the two recombinant rhoptry antigens.