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We propose a two-stage estimation procedure for a copula-based model with semi-competing risks data, where the non-terminal event is subject to dependent censoring by the terminal event, and both events are subject to independent censoring. With a copula-based model, the marginal survival functions of individual event times are specified by semiparametric transformation models, and the dependence between the bivariate event times is specified by a parametric copula function. For the estimation procedure, in the first stage, the parameters associated with the marginal of the terminal event are estimated using only the corresponding observed outcomes, and in the second stage, the marginal parameters for the non-terminal event time and the copula parameter are estimated together via maximizing a pseudo-likelihood function based on the joint distribution of the bivariate event times. We derived the asymptotic properties of the proposed estimator and provided an analytic variance estimator for inference. Through simulation studies, we showed that our approach leads to consistent estimates with less computational cost and more robustness than the one-stage procedure developed in Chen (2012), where all parameters were estimated simultaneously. In addition, our approach demonstrates more desirable finite-sample performances over another existing two-stage estimation method proposed in Zhu et al. (2021). An R package PMLE4SCR is developed to implement our proposed method., Comment: 23 pages, 1 figure

Various goodness-of-fit tests are designed based on the so-called information matrix equivalence: if the assumed model is correctly specified, two information matrices that are derived from the likelihood function are equivalent. In the literature, this principle has been established for the likelihood function with fully observed data, but it has not been verified under the likelihood for censored data. In this manuscript, we prove the information matrix equivalence in the framework of semiparametric copula models for multivariate censored survival data. Based on this equivalence, we propose an information ratio (IR) test for the specification of the copula function. The IR statistic is constructed via comparing consistent estimates of the two information matrices. We derive the asymptotic distribution of the IR statistic and propose a parametric bootstrap procedure for the finite-sample $P$-value calculation. The performance of the IR test is investigated via a simulation study and a real data example., Comment: 39 pages, 5 figures

Nested case-control (NCC) is a sampling method widely used for developing and evaluating risk models with expensive biomarkers on large prospective cohort studies. The biomarker values are typically obtained on a sub-cohort, consisting of all the events and a subset of non-events. However, when the number of events is not small, it might not be affordable to measure the biomarkers on all of them. Due to the costs and limited availability of bio-specimens, only a subset of events is selected to the sub-cohort as cases. For these "untypical" NCC studies, we propose a new weighting method for the inverse probability weighted (IPW) estimation. We also design a perturbation method to estimate the variance of the IPW estimator with our new weights. It accounts for between-subject correlations induced by the sampling processes for both cases and controls through perturbing their sampling indicator variables, and thus, captures all the variations. Furthermore, we demonstrate, analytically and numerically, that when cases consist of only a subset of events, our new weight produces more efficient IPW estimators than the weight proposed in Samuelsen (1997) for a standard NCC design. We illustrate the estimating procedure with a study that aims to evaluate a biomarker-based risk prediction model using the Framingham cohort study., Comment: 27 pages,3 figures, 5 tables

Incremental value (IncV) evaluates the performance change from an existing risk model to a new model. It is one of the key considerations in deciding whether a new risk model performs better than the existing one. Problems arise when different IncV metrics contradict each other. For example, compared with a prescribed-dose model, an ovarian-dose model for predicting acute ovarian failure has a slightly lower area under the receiver operating characteristic curve (AUC) but increases the area under the precision-recall curve (AP) by 48%. This phenomenon of conflicting conclusions is not uncommon, and it creates a dilemma in medical decision making. In this article, we examine the analytical connections and differences between two IncV metrics: IncV in AUC (IncV-AUC) and IncV in AP (IncV-AP). Additionally, since they are both semi-proper scoring rules, we compare them with a strictly proper scoring rule: the IncV of the scaled Brier score (IncV-sBrS), via a numerical study. We demonstrate that both IncV-AUC and IncV-AP are weighted averages of the changes (from the existing model to the new one) in separating the risk score distributions between events and non-events. However, IncV-AP assigns heavier weights to the changes in the high-risk group, whereas IncV-AUC weights the changes equally. In the numerical study, we find that IncV-AP has a wide range, from negative to positive, but the size of IncV-AUC is much smaller. In addition, IncV-AP and IncV-sBr Sare highly consistent, but IncV-AUC is negatively correlated with IncV-sBrS and IncV-AP at a low event rate. IncV-AUC and IncV-AP are the least consistent among the three pairs, and their differences are more pronounced as the event rate decreases., Comment: 25 pages, 6 figures, 1 table. Compared to Version 1, the title and overall structure of the manuscript have been changed significantly

Metals and alloys fabricated by fusion-based additive manufacturing (AM), or 3D printing, undergo complex dynamics of melting and solidification, presenting challenges to the effective control of grain structure. Herein, we report on the use of high-intensity ultrasound that controls the process of solidification during AM of 316L stainless steel. We find that the use of ultrasound favours the columnar-to-equiaxed transition, promoting the formation of fine equiaxed grains with random crystallographic texture. Moreover, the use of ultrasound increases the number density of grains from 305 mm-2 to 2748 mm-2 despite an associated decrease in cooling rate and temperature gradient in the melt pool during AM. Our assessment of the relationship between grain size and cooling rate indicates that the formation of crystallites during AM is enhanced by ultrasound. Furthermore, the use of ultrasound increases the amount of constitutional supercooling during solidification by lowering the temperature gradient in the bulk of the melt pool, thus creating an environment that favours nucleation, growth, and survival of grains. This new understanding provides opportunities to better exploit ultrasound to control grain structure in AM-fabricated metal products., Comment: Paper published in Additive Manufacturing

Backoff algorithms are used in many distributed systems where multiple devices contend for a shared resource. For the classic balls-into-bins problem, the number of singletons -- those bins with a single ball -- is important to the analysis of several backoff algorithms; however, existing analyses employ advanced probabilistic tools to obtain concentration bounds. Here, we show that standard Chernoff bounds can be used instead, and the simplicity of this approach is illustrated by re-analyzing some well-known backoff algorithms., Comment: Corrections to first version

A popular technique for tolerating malicious faults in open distributed systems is to establish small groups of participants, each of which has a non-faulty majority. These groups are used as building blocks to design attack-resistant algorithms. Despite over a decade of active research, current constructions require group sizes of $O(\log n)$, where $n$ is the number of participants in the system. This group size is important since communication and state costs scale polynomially with this parameter. Given the stubbornness of this logarithmic barrier, a natural question is whether better bounds are possible. Here, we consider an attacker that controls a constant fraction of the total computational resources in the system. By leveraging proof-of-work (PoW), we demonstrate how to reduce the group size exponentially to $O(\log\log n)$ while maintaining strong security guarantees. This reduction in group size yields a significant improvement in communication and state costs., Comment: This work is supported by the National Science Foundation grant CCF 1613772 and a C Spire Research Gift

Prediction performance of a risk scoring system needs to be carefully assessed before its adoption in clinical practice. Clinical preventive care often uses risk scores to screen asymptomatic population. The primary clinical interest is to predict the risk of having an event by a pre-specified future time $t_0$. Prospective accuracy measures such as positive predictive values have been recommended for evaluating the predictive performance. However, for commonly used continuous or ordinal risk score systems, these measures require a subjective cutoff threshold value that dichotomizes the risk scores. The need for a cut-off value created barriers for practitioners and researchers. In this paper, we propose a threshold-free summary index of positive predictive values that accommodates time-dependent event status. We develop a nonparametric estimator and provide an inference procedure for comparing this summary measure between competing risk scores for censored time to event data. We conduct a simulation study to examine the finite-sample performance of the proposed estimation and inference procedures. Lastly, we illustrate the use of this measure on a real data example, comparing two risk score systems for predicting heart failure in childhood cancer survivors., Comment: 17 pages, 2 figures, 3 tables

We report on radiation properties of extreme nulling pulsar J1502-5653, by analyzing the data acquired from the Parkes 64-m telescope at 1374 MHz. The radio emission from this pulsar exhibits sequences of several tens to several hundreds consecutive burst pulses, separated by null pulses, and the appearance of the emission seems quasi-periodic. The null fraction from the data is estimated to be 93.6%. No emission is detected in the integrated profile of all null pulses. Systematic modulations of pulse intensity and phase are found at the beginning of burst-pulse sequences just after null. The intensity usually rises to a maximum for the first few pulses, then declines exponentially afterwards, and becomes stable after few tens of pulse periods. The peak phase appears at later longitudes for the first pulse, then drifts to earlier longitudes rapidly, and then systematic drifting gradually vanishes while the intensity becomes stable. In this pulsar, the intensity variation and phase modulation of pulses are correlated in a short duration after the emission starts following a null. Observed properties of the pulsar are compared with other nulling pulsars published previously, and the possible explanation for phase modulation is discussed., Comment: 5 pages, 7 figures. Accepted by MNRAS

We propose and investigate the properties of a digital ferromagnetic heterostructure (DFH) consisting of a $\delta$-doped layer of Mn in Si, using \textit{ab initio} electronic-structure methods. We find that (i) ferromagnetic order of the Mn layer is energetically favorable relative to antiferromagnetic, and (ii) the heterostructure is a two-dimensional half metallic system. The metallic behavior is contributed by three majority-spin bands originating from hybridized Mn-$d$ and nearest-neighbor Si-$p$ states, and the corresponding carriers are responsible for the ferromagnetic order in the Mn layer. The minority-spin channel has a calculated semiconducting gap of 0.25 eV. Analysis of the total and partial densities of states, band structure, Fermi surfaces and associated charge density reveals the marked two-dimensional nature of the half metallicity. The band lineup is found to be favorable for retaining the half metal character to near the Curie temperature ($T_{C}$). Being Si based and possibly having a high $T_{C}$ as suggested by an experiment on dilutely doped Mn in Si, the heterostructure may be of special interest for integration into mature Si technologies for spintronic applications., Comment: 4 pages, 4 figures, Revised version, to appear in Phys. Rev. Lett