Weak and strong quantile representations for randomly truncated data with applications

Cataloged from PDF version of article.Suppose that we observe bivariate data (X,. q) only when Y, < Xi (left truncation). Denote with F the marginal d.f. of the X’s In this paper we derive a Bahadur-type representation for the quantile function of the pertaining product-limit estimator of F. As an application we obtain confidence intervals and bands for quantiles of F

Nonlinear regression with censored data

Suppose that the random vector (X, Y) satisfies the regression model Y = m(X) + sigma(X)epsilon, where m(.) = E(Y vertical bar.) belongs to some parametric class (m(theta)(.):theta is an element of Theta) of regression functions, sigma(2)(.) = var(Y vertical bar.) is unknown, and e is independent of X. The response Y is subject to random right censoring, and the covariate X is completely observed. A new estimation procedure for the true, unknown parameter vector theta(0) is proposed that extends the classical least squares procedure for nonlinear regression to the case where the response is subject to censoring. The consistency and asymptotic normality of the proposed estimator are established. The estimator is compared through simulations with an estimator proposed by Stute in 1999, and both methods are also applied to a fatigue life dataset of strain-controlled materials.Peer reviewe

Functional kernel estimators of conditional extreme quantiles

We address the estimation of "extreme" conditional quantiles i.e. when their order converges to one as the sample size increases. Conditions on the rate of convergence of their order to one are provided to obtain asymptotically Gaussian distributed kernel estimators. A Weissman-type estimator and kernel estimators of the conditional tail-index are derived, permitting to estimate extreme conditional quantiles of arbitrary order.Comment: arXiv admin note: text overlap with arXiv:1107.226

Vaginal hormone-free moisturising cream is not inferior to an estriol cream for treating symptoms of vulvovaginal atrophy: Prospective, randomised study.

This prospective, open-label, multicentre, multinational, randomised trial investigated the non-inferiority of treatment with a vaginal hormone-free moisturising cream compared to a vaginal estriol (0.1%) cream in a panel of post-menopausal women suffering from symptoms of vulvovaginal dryness in a parallel group design. In total, 172 post-menopausal women were randomly allocated to either one of the two treatments, each administered for 43 days. The primary endpoint was the total severity score of subjective symptoms (dryness, itching, burning and pain unrelated to sexual intercourse) of the respective treatment period. Secondary endpoints were severity of single subjective symptoms (including dyspareunia if sexually active), impairment of daily life, Vaginal Health Index, as well as assessment of safety. In both groups, women treated with hormone-free moisturising cream and those treated with estriol cream, total severity score improved significantly compared to baseline by 5.0 (from 6.1 to 1.1) and by 5.4 (from 6.0 to 0.6), respectively, after 43 days of treatment (p < 0.0001). One-sided test of baseline differences (for a clinically relevant difference Δ = 1.5) confirmed the hormone-free moisturising cream to be non-inferior to the estriol cream. Severity of dyspareunia as well as impairment of daily life due to subjective symptoms, significantly improved for both treatment groups (p<0.0001). Subgroup analysis of women with mild or moderate impairment of daily life at baseline caused by "vaginal dryness" symptoms benefited from both creams, while women with severe impairment showed a significantly greater benefit from the estriol cream (p = 0.0032). Both treatments were well tolerated with no serious adverse events occurring. This study provides clinical evidence that a hormone-free vaginal moisturising cream cannot only improve vaginal dryness compared to an 0.1% estriol cream but also can relieve dyspareunia as well as improve woman's impairment of daily life, justifying its use as a first choice for mild or moderate vulvovaginal dryness symptoms

Flow and sorption controls of groundwater arsenic in individual boreholes from bedrock aquifers in central Maine, USA

To understand the hydrogeochemical processes regulating well water arsenic (As) evolution in fractured bedrock aquifers, three domestic wells with [As] up to 478 μg/L are investigated in central Maine. Geophysical logging reveals that fractures near the borehole bottom contribute 70–100% of flow. Borehole and fracture water samples from various depths show significant proportions of As (up to 69%) and Fe (93–99%) in particulates (> 0.45 μm). These particulates and those settled after a 16-day batch experiment contain 560–13,000 mg/kg of As and 14–35% weight/weight of Fe. As/Fe ratios (2.5–20 mmol/mol) and As partitioning ratios (adsorbed/dissolved [As], 20,000–100,000 L/kg) suggest that As is sorbed onto amorphous hydrous ferric oxides. Newly drilled cores also show enrichment of As (up to 1300 mg/kg) sorbed onto secondary iron minerals on the fracture surfaces. Pumping at high flow rates induces large decreases in particulate As and Fe, a moderate increase in dissolved [As] and As(III)/As ratio, while little change in major ion chemistry. The δD and δ18O are similar for the borehole and fracture waters, suggesting a same source of recharge from atmospheric precipitation. Results support a conceptual model invoking flow and sorption controls on groundwater [As] in fractured bedrock aquifers whereby oxygen infiltration promotes the oxidation of As-bearing sulfides at shallower depths in the oxic portion of the flow path releasing As and Fe; followed by Fe oxidation to form Fe oxyhydroxide particulates, which are transported in fractures and sorb As along the flow path until intercepted by boreholes. In the anoxic portions of the flow path, reductive dissolution of As-sorbed iron particulates could re-mobilize As. For exposure assessment, we recommend sampling of groundwater without filtration to obtain total As concentration in groundwater

Remote Monitor Alarm System

A remote monitor alarm system monitors discrete alarm and analog power supply voltage conditions at remotely located communications terminal equipment. A central monitoring unit (CMU) is connected via serial data links to each of a plurality of remote terminal units (RTUS) that monitor the alarm and power supply conditions of the remote terminal equipment. Each RTU can monitor and store condition information of both discrete alarm points and analog power supply voltage points in its associated communications terminal equipment. The stored alarm information is periodically transmitted to the CMU in response to sequential polling of the RTUS. The number of monitored alarm inputs and permissible voltage ranges for the analog inputs can be remotely configured at the CMU and downloaded into programmable memory at each RTU. The CMU includes a video display, a hard disk memory, a line printer and an audio alarm for communicating and storing the alarm information received from each RTU

Semiparametric Multivariate Accelerated Failure Time Model with Generalized Estimating Equations

The semiparametric accelerated failure time model is not as widely used as the Cox relative risk model mainly due to computational difficulties. Recent developments in least squares estimation and induced smoothing estimating equations provide promising tools to make the accelerate failure time models more attractive in practice. For semiparametric multivariate accelerated failure time models, we propose a generalized estimating equation approach to account for the multivariate dependence through working correlation structures. The marginal error distributions can be either identical as in sequential event settings or different as in parallel event settings. Some regression coefficients can be shared across margins as needed. The initial estimator is a rank-based estimator with Gehan's weight, but obtained from an induced smoothing approach with computation ease. The resulting estimator is consistent and asymptotically normal, with a variance estimated through a multiplier resampling method. In a simulation study, our estimator was up to three times as efficient as the initial estimator, especially with stronger multivariate dependence and heavier censoring percentage. Two real examples demonstrate the utility of the proposed method

The universal Glivenko-Cantelli property

Let F be a separable uniformly bounded family of measurable functions on a standard measurable space, and let N_{[]}(F,\epsilon,\mu) be the smallest number of \epsilon-brackets in L^1(\mu) needed to cover F. The following are equivalent: 1. F is a universal Glivenko-Cantelli class. 2. N_{[]}(F,\epsilon,\mu)0 and every probability measure \mu. 3. F is totally bounded in L^1(\mu) for every probability measure \mu. 4. F does not contain a Boolean \sigma-independent sequence. It follows that universal Glivenko-Cantelli classes are uniformity classes for general sequences of almost surely convergent random measures.Comment: 26 page

Kernel based methods for accelerated failure time model with ultra-high dimensional data

<p>Abstract</p> <p>Background</p> <p>Most genomic data have ultra-high dimensions with more than 10,000 genes (probes). Regularization methods with <it>L</it>₁and <it>L_p</it>penalty have been extensively studied in survival analysis with high-dimensional genomic data. However, when the sample size <it>n </it>≪ <it>m </it>(the number of genes), directly identifying a small subset of genes from ultra-high (<it>m </it>> 10, 000) dimensional data is time-consuming and not computationally efficient. In current microarray analysis, what people really do is select a couple of thousands (or hundreds) of genes using univariate analysis or statistical tests, and then apply the LASSO-type penalty to further reduce the number of disease associated genes. This two-step procedure may introduce bias and inaccuracy and lead us to miss biologically important genes.</p> <p>Results</p> <p>The accelerated failure time (AFT) model is a linear regression model and a useful alternative to the Cox model for survival analysis. In this paper, we propose a nonlinear kernel based AFT model and an efficient variable selection method with adaptive kernel ridge regression. Our proposed variable selection method is based on the kernel matrix and dual problem with a much smaller <it>n </it>× <it>n </it>matrix. It is very efficient when the number of unknown variables (genes) is much larger than the number of samples. Moreover, the primal variables are explicitly updated and the sparsity in the solution is exploited.</p> <p>Conclusions</p> <p>Our proposed methods can simultaneously identify survival associated prognostic factors and predict survival outcomes with ultra-high dimensional genomic data. We have demonstrated the performance of our methods with both simulation and real data. The proposed method performs superbly with limited computational studies.</p