Estimating Human Immunodeficiency Virus (HIV) Prevention Effects in Low-incidence Settings

Background: Randomized controlled trials (RCTs) for determining efficacy of preexposure prophylaxis (PrEP) in preventing human immunodeficiency virus (HIV) infection have not been conducted among US women because their lower HIV incidence requires impractically large studies. Results from higher-incidence settings, like Sub-Saharan Africa, may not apply to US women owing to differences in age, sexual behavior, coinfections, and adherence. Methods: We propose a novel strategy for evaluating PrEP efficacy in the United States using data from both settings to obtain four parameters: (1) intention-to-treat (ITT) and (2) per-protocol effects in the higher-incidence setting, (3) per-protocol effect generalized to the lower-incidence setting, and (4) back-calculated ITT effect using adherence data from the lower-incidence setting. To illustrate, we simulated two RCTs comparing PrEP against placebo: one in 4000 African women and another in 500 US women. We estimated all parameters using g-computation and report risk ratios averaged over 2000 simulations, alongside the 2.5th and 97.5th percentiles of the simulation results. Results: Twelve months after randomization, the African ITT and per-protocol risk ratios were 0.65 (0.47, 0.88) and 0.20 (0.08, 0.34), respectively. The US ITT and per-protocol risk ratios were 0.42 (0.20, 0.62) and 0.17 (0.03, 0.38), respectively. These results matched well the simulated true effects. Conclusions: Our simple demonstration informs the design of future studies seeking to estimate the effectiveness of a treatment (like PrEP) in lower-incidence settings where a traditional RCT would not be feasible. See video abstract at, http://links.lww.com/EDE/B506

On the absence of ferromagnetism in typical 2D ferromagnets

We consider the Ising systems in $d$ dimensions with nearest-neighbor ferromagnetic interactions and long-range repulsive (antiferromagnetic) interactions which decay with a power, $s$, of the distance. The physical context of such models is discussed; primarily this is $d=2$ and $s=3$ where, at long distances, genuine magnetic interactions between genuine magnetic dipoles are of this form. We prove that when the power of decay lies above $d$ and does not exceed $d+1$, then for all temperatures, the spontaneous magnetization is zero. In contrast, we also show that for powers exceeding $d+1$ (with $d\ge2$) magnetic order can occur.Comment: 15 pages, CMP style fil

Striped periodic minimizers of a two-dimensional model for martensitic phase transitions

In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic shape-memory alloys at the interface between a region occupied by the parent (austenite) phase and a region occupied by the product (martensite) phase, which can occur in two variants (twins). The model, first proposed by Kohn and Mueller, is defined by the following functional: $${\cal E}(u)=\beta||u(0,\cdot)||^2_{H^{1/2}([0,h])}+ \int_{0}^{L} dx \int_0^h dy \big(|u_x|^2 + \epsilon |u_{yy}| \big)$$ where $u:[0,L]\times[0,h]\to R$ is periodic in $y$ and $u_y=\pm 1$ almost everywhere. Conti proved that if $\beta\gtrsim\epsilon L/h^2$ then the minimal specific energy scales like $\sim \min\{(\epsilon\beta/L)^{1/2}, (\epsilon/L)^{2/3}\}$, as $(\epsilon/L)\to 0$. In the regime $(\epsilon\beta/L)^{1/2}\ll (\epsilon/L)^{2/3}$, we improve Conti's results, by computing exactly the minimal energy and by proving that minimizers are periodic one-dimensional sawtooth functions.Comment: 29 pages, 3 figure