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In hindsight, even a cursory look may have revealed substantial growth of the 2014 Ebola infection and death cases in West Africa before drastic interventions showed an effect in late 2014. Yet a timely assessment as to whether an intervention has a sufficient impact to stabilize and eventually end an outbreak is equally important as early detection and accurate prediction of the magnitude of the outbreak several months before it spins out of control. To this aim, we consider an intervention effect in the GARCE branching process model, proposed by Hueter, that was successful to early detect the magnitude of the outbreak when data became available in early 2014. This model provides a novel and simple approach to branching processes that allows for time-varying random environments and instances of peak growth and near extinction-type rates as seen in Ebola viruses, tuberculosis infections, and infectious diseases. We present results on the survival and extinction behaviours, characterization of the phase transition between the subcritical and supercritical phases, and a sufficient condition for escape from supercriticality upon a level shift intervention. Intervention analysis of the Ebola outbreak data are presented and findings on the outbreak’s estimated phase and intervention effect are discussed.

BACKGROUND: Survival rates for women with a diagnosis of breast cancer continue to improve. However, some women may experience physical, psychological and emotional effects post diagnosis, throughout treatment and beyond. Support groups can provide opportunities for people to share their experiences and learn from others. As the number of online support groups increases, more and more women with breast cancer will likely access them. OBJECTIVES: To assess effects of online support groups on the emotional distress, uncertainty, anxiety, depression and quality of life (QoL) of women with breast cancer. SEARCH METHODS: We searched for trials in the Cochrane Breast Cancer Specialised Register, the Cochrane Central Register of Controlled Trials (CENTRAL; 2016, Issue 4), MEDLINE, Embase and PsycINFO on 2 May 2016, and we handsearched journals and reference lists. We also searched the World Health Organization's International Clinical Trials Registry Platform (WHO ICTRP) search portal and clinicaltrials.gov on 2 May 2016. SELECTION CRITERIA: We included randomised controlled trials (RCTs) assessing effects of online support groups on women with a diagnosis of breast cancer and women who have completed breast cancer treatment. We included studies comparing online support groups with a usual care group, and studies comparing two or more types of online support groups (without a usual care group). DATA COLLECTION AND ANALYSIS: Two review authors independently extracted data and assessed risk of bias. We presented outcome data using mean differences (MDs) and standardised mean differences (SMDs) along with 95% confidence intervals (CIs), and we used the fixed‐effect model when appropriate. We assessed the quality of the body of evidence using the GRADE approach. MAIN RESULTS: We included six studies (492 women) that assessed online support groups for women with breast cancer. Online support groups in these six trials lasted from six to 30 weeks. Women participated in these groups between 1.5 and 2.5 hours per week, and investigators conducted all studies in the USA. Participants were predominantly white and well educated and were moderate to high earners. Four studies compared an online support group versus a control group, and the other two compared a 'moderated' versus a 'peer‐led' online support group, and a 'standard' versus an 'enhanced' online support group, respectively. None of the included studies measured 'emotional distress' or uncertainty. One study (78 women) for which data for analysis were missing reported no positive effects of online support on 'distress' and 'cancer‐specific distress' versus support provided by a control group. Two studies measured anxiety: One study (72 women) found no difference in anxiety at the end of the intervention between the online support group and the control group (MD ‐0.40, 95% CI ‐6.42 to 5.62; low‐quality evidence), and the second study (184 women) reported a reduction in anxiety levels at the end of the intervention when comparing the 'standard' support group (run by participants without prompting from health professionals) versus an 'enhanced' online support group (in which participants were specifically asked by the researcher to respond to one another's need for support). Five studies (414 women) measured depression. Three studies compared depression in the online support group with depression in the control group. Pooled data from two studies (120 women) showed a small to moderate reduction in depression in the online support group compared with control groups at the end of the intervention (SMD ‐0.37, 95% CI ‐0.75 to 0.00; very low‐quality evidence). The third study, a pilot study (30 women), provided no data for analysis but reported no difference in depression between participants in support and control groups at the end of the intervention. Of the remaining two studies that measured depression, one study (60 women) provided no extractable data for comparison but reported no difference in depressive symptoms between a 'moderated' and a 'peer‐led' support group; the other study (184 women) reported greater reduction in depression in the 'standard' support group than in the 'enhanced' online support group. Three studies measured quality of life. One pilot study (30 women) provided limited data for analysis but reported no change in quality of life at the end of the intervention. Only two studies (140 women) provided data for pooling and showed no positive effects on quality of life at four months post intervention compared with controls (SMD ‐0.11, 95% CI ‐0.47 to 0.24; very low‐quality evidence). At 12 months post intervention, one study (78 women) reported that the intervention group did not attain better quality of life scores than the control group (MD ‐10.89, 95% CI ‐20.41 to ‐1.37; low‐quality evidence). We found no data for subgroup analyses on stage of disease, treatment modality and types and doses of interventions. No studies measured adverse effects. AUTHORS' CONCLUSIONS: This review did not find the evidence required to show whether participation in online support groups was beneficial for women with breast cancer, because identified trials were small and of low or very low quality. Large, rigorous trials with ethnically and economically diverse participants are needed to provide robust evidence regarding the psychosocial outcomes selected for this review.

Background: Little is known about the incidence of prosthesis-patient mismatch (PPM) and its impact on outcomes after transcatheter aortic valve replacement (TAVR).Objectives: The objective...

Branching processes in random environments have been widely studied and applied to population growth systems to model the spread of epidemics, infectious diseases, cancerous tumor growth, and social network traffic. However, Ebola virus, tuberculosis infections, and avian flu grow or change at rates that vary with time—at peak rates during pandemic time periods, while at low rates when near extinction. The branching processes in generalized autoregressive conditional environments we propose provide a novel approach to branching processes that allows for such time-varying random environments and instances of peak growth and near extinction-type rates. Offspring distributions we consider to illustrate the model include the generalized Poisson, binomial, and negative binomial integer-valued GARCH models. We establish conditions on the environmental process that guarantee stationarity and ergodicity of the mean offspring number and environmental processes and provide equations from which their variances, autocorrelation, and cross-correlation functions can be deduced. Furthermore, we present results on fundamental questions of importance to these processes—the survival-extinction dichotomy, growth behavior, necessary and sufficient conditions for noncertain extinction, characterization of the phase transition between the subcritical and supercritical regimes, and survival behavior in each phase and at criticality.

Background— The effect of preoperative mitral regurgitation (MR) on clinical outcomes of patients undergoing transcatheter aortic valve replacement (TAVR) is controversial. This study sought to examine the impact of moderate and severe MR on outcomes after TAVR and surgical aortic valve replacement (SAVR). Methods and Results— Data were drawn from the randomized Placement of Aortic Transcatheter Valve (PARTNER) Trial cohort A patients with severe, symptomatic aortic stenosis undergoing either TAVR (n=331) or SAVR (n=299). Both TAVR and SAVR patients were dichotomized according to the degree of preoperative MR (moderate/severe versus none/mild). At baseline, moderate or severe MR was reported in 65 TAVR patients (19.6%) and 63 SAVR patients (21.2%). At 30 days, among survivors who had isolated SAVR/TAVR, moderate/severe MR had improved in 25 SAVR patients (69.4%) and 30 TAVR patients (57.7%), was unchanged in 10 SAVR patients (27.8%) and 19 TAVR patients (36.5%), and worsened in 1 SAVR patient (2.8%) and 4 TAVR patients (5.8%; all P =NS). Mortality at 2 years was higher in SAVR patients with moderate or severe MR than in those with mild or less MR (49.8% versus 28.1%; adjusted hazard ratio, 1.73; 95% confidence interval, 1.01–2.96; P =0.04). In contrast, MR severity at baseline did not affect mortality in TAVR patients (37.0% versus 32.7%, moderate/severe versus none/mild; hazard ratio, 1.14; 95% confidence interval, 0.72–1.78; P =0.58; P for interaction=0.05). Conclusions— Both TAVR and SAVR were associated with a significant early improvement in MR in survivors. However, moderate or severe MR at baseline was associated with increased 2-year mortality after SAVR but not after TAVR. TAVR may be a reasonable option in selected patients with combined aortic and mitral valve disease. Clinical Trial Registration— URL: http://www.clinicaltrials.gov . Unique identifier: NCT00530894.

Background— The Placement of Aortic Transcatheter Valves (PARTNER) trial demonstrated similar survival after transcatheter and surgical aortic valve replacement (TAVR and SAVR, respectively) in high-risk patients with symptomatic, severe aortic stenosis. The aim of this study was to evaluate the effect of left ventricular (LV) dysfunction on clinical outcomes after TAVR and SAVR and the impact of aortic valve replacement technique on LV function. Methods and Results— The PARTNER trial randomized high-risk patients with severe aortic stenosis to TAVR or SAVR. Patients were stratified by the presence of LV ejection fraction (LVEF) P P P Conclusions— In high-risk patients with severe aortic stenosis and LV dysfunction, mortality rates and LV functional recovery were comparable between valve replacement techniques. TAVR is a feasible alternative for patients with symptomatic severe aortic stenosis and LV dysfunction who are at high risk for SAVR. Clinical Trial Registration— URL: http://www.clinicaltrials.gov . Unique identifier: NCT00530894.

Background— The prognosis and treatment of patients with low-flow (LF) severe aortic stenosis are controversial. Methods and Results— The Placement of Aortic Transcatheter Valves (PARTNER) trial randomized patients with severe aortic stenosis to medical management versus transcatheter aortic valve replacement (TAVR; inoperable cohort) and surgical aortic valve replacement versus TAVR (high-risk cohort). Among 971 patients with evaluable echocardiograms (92%), LF (stroke volume index ≤35 mL/m 2 ) was observed in 530 (55%); LF and low ejection fraction (P =0.006). In the inoperable cohort, patients with LF had higher mortality than those with normal flow, but both groups improved with TAVR (46% versus 76% with LF and 38% versus 53% with normal flow; P P =0.02). LF was an independent predictor of mortality in all patient cohorts (hazard ratio, ≈1.5), whereas ejection fraction and gradient were not. Conclusions— LF is common in severe aortic stenosis and independently predicts mortality. Survival is improved with TAVR compared with medical management and similar with TAVR and surgical aortic valve replacement. A measure of flow (stroke volume index) should be included in the evaluation and therapeutic decision making of patients with severe aortic stenosis. Clinical Trial Registration— URL: http://www.clinicaltrial.gov . Unique identifier: NCT0053089.4.

We examine the asymptotic behavior of the number of vertices of the convex hull spanned by n consecutive pairs from a time series model. We consider data from three models, the moving average (MA) process with regularly varying noise, the stochastic volatility (SV) process with regularly varying noise and the GARCH process. The latter two processes are commonly used for modeling returns of financial assets. If \(N_n\) denotes the number of vertices of the convex hull of n consecutive pairs of observations, we show that for a SV model, \(N_n \stackrel {P}{\rightarrow } 4 \) as \(n \rightarrow \infty\), whereas for a GARCH model, \(N_n \geq 5\) with positive probability. This provides another measure that distinguishes the behavior of the extremes for SV and GARCH models. Geometrically the extreme GARCH pairs fall in butterfly-like shapes away from the axes, while the SV pairs suitably scaled drift towards the coordinate axes with increasing n. MA pairs show a similar flavor as the SV pairs except that their convex hull vertices produce segments of extreme pairs that no longer align themselves exclusively along the axes, but are also distributed along other directions, determined solely by the MA coefficients. We show that the non-degenerate limiting distribution of \( N_n \) as \(n \rightarrow \infty \) depends on the model parameters and limiting law of the ratio of the maximal and minimal observations.

Acute kidney injury (AKI) is associated with a poor prognosis after transcatheter aortic valve replacement (TAVR). A paucity of data exists regarding the incidence and effect of AKI after TAVR using the new recommended Valve Academic Research Consortium criteria. At Columbia University Medical Center, 218 TAVR procedures (64.2% transfemoral, 35.8% transapical) were performed from 2008 to July 2011. The creatinine level was evaluated daily until discharge. Using the Valve Academic Research Consortium definitions, the 30-day and 1-year outcomes were compared between patients with significant AKI (AKI stage 2 or 3) and those without significant AKI (AKI stage 0 or 1). Significant AKI occurred in 18 patients (8.3%). Of these 18 patients, 10 (55.6%) had AKI stage 3 and 9 (50%) required dialysis. AKI was associated with a lower baseline mean transvalvular gradient (37.6 ± 11.4 vs 45.6 ± 14.8 mm Hg for no AKI, p = 0.03). After TAVR, the AKI group had a greater hemoglobin decrease (3.6 ± 2.0 vs 2.4 ± 1.3 g/dl, p = 0.01), greater white blood cell elevation at 72 hours (21.09 ± 12.99 vs 13.18 ± 4.82 × 103/μl, p = 0.001), a more severe platelet decrease (118 ± 40 vs 75 ± 43 × 103/μl, p

This paper considers the estimation problem in linear regression when endogeneity is present, that is, when explanatory variables are correlated with the random error, and also addresses the question of a priori testing for potential endogeneity. We provide a survey of the latent instrumental variables (LIV) approach proposed by Ebbes (2004) and Ebbes et al. (2004, 2005, 2009) and examine its performance compared to the methods of ordinary least squares (OLS) and IV regression. The distinctive feature of Ebbes’ approach is that no observed instruments are required. Instead ‘optimal’ instruments are estimated from data and allow for endogeneity testing. Importantly, this Hausman-LIV test is a simple tool that can be used to test for potential endogeneity in regression analysis and indicate when LIV regression is more appropriate and should be performed instead of OLS regression. The LIV models considered comprise the standard one where the latent variable is discrete with at least two fixed categories and two interesting extensions, multilevel models where a nonparametric Bayes algorithm completely determines the LIV’s distribution from data. This paper suggests that while Ebbes’ new method is a distinct contribution, its formulation is problematic in certain important respects. Specifically the various publications of Ebbes and collaborators employ three distinct and inequivalent statistical concepts exchangeably, treating all as one and the same. We clarify this and then discuss estimation of returns of education in income based on data from three studies that Ebbes (2004) revisited, where ‘education’ is potentially endogenous due to omitted ‘ability.’ While the OLS estimate exhibits a slight upwards bias of 7%, 8%, and 6%, respectively, relative to the LIV estimate for the three studies, IV estimation leads to an enormous bias of 93%, 40%, and -24% when there is no consensus about the direction of the bias. This provides one instance among many well known applications where IVs introduced more substantial biases to the estimated causal effects than OLS, even though IVs were pioneered to overcome the endogeneity problem. In a second example we scrutinize the results of Ferguson et al. (2015) on the estimated effect of campaign expenditures on the proportions of Democratic and Republican votes in US House and Senate elections between 1980 and 2014, where ‘campaign money’ is potentially endogenous in view of omitted variables such as ‘a candidate’s popularity.’ A nonparametric Bayesian spatial LIV regression model was adopted to incorporate identified spatial autocorrelation and account for endogeneity. The relative bias of the spatial regression estimate as compared to the spatial LIV estimate ranges between -17% to 18% for the House and between -25% to 7% for the Senate.

Objectives This study sought to identify incidence, predictors, and impact of vascular complications (VC) after transfemoral (TF) transcatheter aortic valve replacement (TAVR). Background VC after TF-TAVR are frequent and may be associated with unfavorable prognosis. Methods From the randomized controlled PARTNER (Placement of AoRTic TraNscathetER Valve) trial, a total of 419 patients (177 from cohort B [inoperable] and 242 from cohort A [operable high-risk]) were randomly assigned to TF-TAVR and actually received the designated treatment. First-generation Edwards-Sapien valves and delivery systems were used, via a 22- or 24-F sheath. The 30-day rates of major and minor VC (modified Valve Academic Research Consortium definitions), predictors, and effect on 1-year mortality were assessed. Results Sixty-four patients (15.3%) had major VC and 50 patients (11.9%) had minor VC within 30 days of the procedure. Among patients with major VC, vascular dissection (62.8%), perforation (31.3%), and access-site hematoma (22.9%) were the most frequent modes of presentation. Major VC, but not minor VC, were associated with significantly higher 30-day rates of major bleeding, transfusions, and renal failure requiring dialysis, and with a significantly higher rate of 30-day and 1-year mortality. The only identifiable independent predictor of major VC was female gender (hazard ratio [HR]: 2.31 [95% confidence interval (CI): 1.08 to 4.98], p = 0.03). Major VC (HR: 2.31 [95% CI: 1.20 to 4.43], p = 0.012), and renal disease at baseline (HR: 2.26 [95% CI: 1.34 to 3.81], p = 0.002) were identified as independent predictors of 1-year mortality. Conclusions Major VC were frequent after TF-TAVR in the PARTNER trial using first-generation devices and were associated with high mortality. However, the incidence and impact of major VC on 1-year mortality decreased with lower-risk populations.

An exact expression is determined for the asymptotic constant c 2 in the limit theorem by P. Groeneboom (1988), which states that the number of vertices of the convex hull of a uniform sample of n random points from a circular disk satisfies a central limit theorem, as n → ∞, with asymptotic variance 2πc 2 n 1/3.

An exact expression is determined for the asymptotic constant c2 in the limit theorem by P. Groeneboom (1988), which states that the number of vertices of the convex hull of a uniform sample of n random points from a circular disk satisfies a central limit theorem, as n → ∞, with asymptotic variance 2πc2n1/3.

Consider the anisotropic symmetric contact process on a homogeneous tree T 2d of degree 2d⩾2 with a single initially infected site at the root vertex of the tree. We show that, for all values of the infection vector λ, each integer n⩾1, and each vertex x∈ T 2d at distance n from the root vertex, the probability P (x is ever infected )=u x (λ) satisfies ux(λ)⩽[βc(λ)]n−1 for some function βc that we will specify. This geometric decay property governs the growth and dispersal behaviour of the process and lies at the core of the method of Hueter (preprint, arXiv: math.PR/0109047), which applies the thermodynamic formalism and the theory of Gibbs states by Bowen (Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Mathematics, Vol. 470, Springer, Berlin, 1975) to the contact process on trees. We leave open the question as to when (if at all) λc is the maximal infection rate among the components of λ.

Little is known about the incidence of prosthesis-patient mismatch (PPM) and its impact on outcomes after transcatheter aortic valve replacement (TAVR).The objectives of this study were: 1) to compare the incidence of PPM in the TAVR and surgical aortic valve replacement (SAVR) randomized control trial (RCT) arms of the PARTNER (Placement of AoRTic TraNscathetER Valves) I Trial cohort A; and 2) to assess the impact of PPM on regression of left ventricular (LV) hypertrophy and mortality in these 2 arms and in the TAVR nonrandomized continued access (NRCA) registry cohort.The PARTNER Trial cohort A randomized patients 1:1 to TAVR or bioprosthetic SAVR. Postoperative PPM was defined as absent if the indexed effective orifice area (EOA) was0.85 cm(2)/m(2), moderate if the indexed EOA was ≥0.65 but ≤0.85 cm(2)/m(2), or severe if the indexed EOA was0.65 cm(2)/m(2). LV mass regression and mortality were analyzed using the SAVR-RCT (n = 270), TAVR-RCT (n = 304), and TAVR-NRCA (n = 1,637) cohorts.The incidence of PPM was 60.0% (severe: 28.1%) in the SAVR-RCT cohort versus 46.4% (severe: 19.7%) in the TAVR-RCT cohort (p0.001) and 43.8% (severe: 13.6%) in the TAVR-NRCA cohort. In patients with an aortic annulus diameter20 mm, severe PPM developed in 33.7% undergoing SAVR compared with 19.0% undergoing TAVR (p = 0.002). PPM was an independent predictor of less LV mass regression at 1 year in the SAVR-RCT (p = 0.017) and TAVR-NRCA (p = 0.012) cohorts but not in the TAVR-RCT cohort (p = 0.35). Severe PPM was an independent predictor of 2-year mortality in the SAVR-RCT cohort (hazard ratio [HR]: 1.78; p = 0.041) but not in the TAVR-RCT cohort (HR: 0.58; p = 0.11). In the TAVR-NRCA cohort, severe PPM was not a predictor of 1-year mortality in all patients (HR: 1.05; p = 0.60) but did independently predict mortality in the subset of patients with no post-procedural aortic regurgitation (HR: 1.88; p = 0.02).In patients with severe aortic stenosis and high surgical risk, PPM is more frequent and more often severe after SAVR than TAVR. Patients with PPM after SAVR have worse survival and less LV mass regression than those without PPM. Severe PPM also has a significant impact on survival after TAVR in the subset of patients with no post-procedural aortic regurgitation. TAVR may be preferable to SAVR in patients with a small aortic annulus who are susceptible to PPM to avoid its adverse impact on LV mass regression and survival. (The PARTNER Trial: Placement of AoRTic TraNscathetER Valve Trial; NCT00530894).

Hyetographs are essential to many hydrological designs. Many studies have shown that hyetographs are specific to storm types and durations. Recent work presented evidence that dimensionless hyetographs are scale invariant. We show that the simple scaling property of rainfall guarantees that the normalized rainfall rates of different storm durations are identically distributed and propose a nonstationary Gauss-Markov model based on the annual maximum events that arise from the dominant storm type. We derive the unique estimators for the parameters of the Gauss-Markov model under two constraints that: (a) the typical peak rainfall rate is preserved, and (b) the most likely hyetograph is obtained. One attractive feature of this model is that it allows translating hyetographs between storms of different durations. Two examples illustrate our model.

Symmetric branching random walk on a homogeneous tree exhibits a weak survival phase: For parameter values in a certain interval, the population survives forever with positive probability, but, with probability one, eventually vacates every finite subset of the tree. In this phase, particle trails must converge to the geometric boundaryΩ of the tree. The random subset Λ of the boundary consisting of all ends of the tree in which the population survives, called the limit set of the process, is shown to have Hausdorff dimension no larger than one half the Hausdorff dimension of the entire geometric boundary. Moreover, there is strict inequality at the phase separation point between weak and strong survival except when the branching random walk is isotropic. It is further shown that in all cases there is a distinguished probability measure μ supported by Ω such that the Hausdorff dimension of Λ∩Ωμ, where Ωμ is the set of μ-generic points of Ω, converges to one half the Hausdorff dimension of Ωμ at the phase separation point. Exact formulas are obtained for the Hausdorff dimensions of Λ and Λ∩Ωμ, and it is shown that the log Hausdorff dimension of Λ has critical exponent 1/2 at the phase separation point.

In (S. Bahar, Chaos Solitons Fractals, 5 (1995), pp. 1001-1006; 7 (1996), pp. 41-47), pictures were presented of the forward orbit {zn}n in the plane, where zn satisfies zn+1 = znAn+1 for certain affine transformations An. These orbits (a) appear to lie on closed curves, and (b) assume forms reminiscent of strange attractors. We answer the questions raised in these references and prove that indeed in the aperiodic case the invariant orbits of this "iterated function system" lie on closed curves and that in some sense the maps act "chaotically" on the set of closed curves. A key role is being played by almost periodic functions. Furthermore, we provide an expression for the top Lyapunov exponent, that is, a sum in the periodic case and an integral in the aperiodic case. Our results have important implications in applications of computer visualization and imaging and shed some light on nonlinear dynamical systems.

Suppose that {(Xt, Yt): t>}0 is a family of two independent Gaussian random variables with means m1(t) and m2(t) and variances σ21(t) and σ22(t). If at every time t>0 the first and second moment of the minimum processXt∧Yt are known, are the parameters governing these four moment functions uniquely determined ? We answer this question in the negative for a large class of Gaussian families including the “Brownian” case. Except for some degenerate situation where one variance function dominates the other, in which case the recovery of the parameters is fully successful, the second moment of the minimum process does not provide any additional clues on identifying the parameters.

Let X 1, X 2,… be i.i.d. random points in ℝ2 with distribution ν, and let N n denote the number of points spanning the convex hull of X 1, X 2,…,X n . We obtain lim inf n→∞ E (N n )n -1/3 ≥ γ1 and E (N n ) ≤ γ2 n 1/3(logn)2/3 for some positive constants γ1, γ2 and sufficiently large n under the assumption that ν is a certain self-similar measure on the unit disk. Our main tool consists in a geometric application of the renewal theorem. Exactly the same approach can be adopted to prove the analogous result in ℝ d .

We explore the ‘Hausdorff dimension at infinity’ for self-affine carpets defined on the square lattice. This notion of dimension (due to Barlow and Taylor), which is the correct notion from a probabilistic perspective, differs for these sets from more ‘naive’ indices of fractal dimension.

Let A1, A2,…,Ak be a finite set of contractive, affine, invertible self-mappings of R2. A compact subset Λ of R2 is said to be self-affine with affinitiesA1, A2,…,Ak ifIt is known [8] that for any such set of contractive affine mappings there is a unique (compact) SA set with these affinities. When the affine mappings A1, A2,…,Ak are similarity transformations, the set Λ is said to be self-similar. Self-similar sets are well understood, at least when the images Ai(Λ) have ‘small’ overlap: there is a simple and explicit formula for the Hausdorff and box dimensions [12, 10]; these are always equal; and the δ-dimensional Hausdorff measure of such a set (where δ is the Hausdorff dimension) is always positive and finite.

Background Multicenter clinical trials use echocardiographic core laboratories to ensure expertise and consistency in the assessment of imaging eligibility criteria, as well as safety and efficacy end points. The aim of this study was to report the real-world implementation of guidelines for best practices in echocardiographic core laboratories, including their feasibility and quality results, in a large, international multicenter trial. Methods Processes and procedures were developed to optimize the acquisition and analysis of echocardiograms for the Placement of Aortic Transcatheter Valves (PARTNER) I trial of percutaneous aortic valve replacement for aortic stenosis. Comparison of baseline findings in the operative and nonoperative cohorts and reproducibility analyses were performed. Results Echocardiography was performed in 1,055 patients (mean age, 83 years; 54% men) The average peak and mean aortic valve gradients were 73 ± 24 and 43 ± 15 mm Hg, and the average aortic valve area was 0.64 ± 0.20 cm 2 . The average ejection fraction was 52 ± 13% by visual estimation and 53 ± 14% by biplane planimetry. The mean left ventricular mass index was 151 ± 42 g/m 2 . The inoperable cohort had lower left ventricular mass and mass indexes and tended to have more severe mitral regurgitation. Core lab reproducibility was excellent, with intraclass correlation coefficients ranging from 0.92 to 0.99 and κ statistics from 0.58 to 0.85 for key variables. The image acquisition quality improvement process brought measurability to >85%, which was maintained for the duration of the study. Conclusions This real-world echocardiographic core lab experience in the PARTNER I trial demonstrates that a high standard of measurability and reproducibility can result from extensive quality assurance efforts in both image acquisition and analysis. These results and the echocardiographic data reported here provide a reference for future studies of aortic stenosis patients and should encourage the wider use of echocardiography in clinical research.

This study sought to identify incidence, predictors, and impact of vascular complications (VC) after transfemoral (TF) transcatheter aortic valve replacement (TAVR).VC after TF-TAVR are frequent and may be associated with unfavorable prognosis.From the randomized controlled PARTNER (Placement of AoRTic TraNscathetER Valve) trial, a total of 419 patients (177 from cohort B [inoperable] and 242 from cohort A [operable high-risk]) were randomly assigned to TF-TAVR and actually received the designated treatment. First-generation Edwards-Sapien valves and delivery systems were used, via a 22- or 24-F sheath. The 30-day rates of major and minor VC (modified Valve Academic Research Consortium definitions), predictors, and effect on 1-year mortality were assessed.Sixty-four patients (15.3%) had major VC and 50 patients (11.9%) had minor VC within 30 days of the procedure. Among patients with major VC, vascular dissection (62.8%), perforation (31.3%), and access-site hematoma (22.9%) were the most frequent modes of presentation. Major VC, but not minor VC, were associated with significantly higher 30-day rates of major bleeding, transfusions, and renal failure requiring dialysis, and with a significantly higher rate of 30-day and 1-year mortality. The only identifiable independent predictor of major VC was female gender (hazard ratio [HR]: 2.31 [95% confidence interval (CI): 1.08 to 4.98], p = 0.03). Major VC (HR: 2.31 [95% CI: 1.20 to 4.43], p = 0.012), and renal disease at baseline (HR: 2.26 [95% CI: 1.34 to 3.81], p = 0.002) were identified as independent predictors of 1-year mortality.Major VC were frequent after TF-TAVR in the PARTNER trial using first-generation devices and were associated with high mortality. However, the incidence and impact of major VC on 1-year mortality decreased with lower-risk populations.

Consider the convex hull of n independent, identically distributed points in the plane. Functionals of interest are the number of vertices Nn , the perimeter Ln and the area An of the convex hull. We study the asymptotic behaviour of these three quantities when the points are standard normally distributed. In particular, we derive the variances of Nn, Ln and An for large n and prove a central limit theorem for each of these random variables. We enlarge on a method developed by Groeneboom (1988) for uniformly distributed points supported on a bounded planar region. The process of vertices of the convex hull is of central importance. Poisson approximation and martingale techniques are used.

The Placement of Aortic Transcatheter Valves (PARTNER) trial Cohort A demonstrated similar survival after transcatheter and surgical aortic valve replacement (TAVR and SAVR, respectively) in high-risk operable patients with symptomatic, severe aortic stenosis (AS). The impact of valve replacement