arXiv subjects

Qian M. Zhou

Publications and source records attributed to Qian M. Zhou.

8 recordsLinked to original sources

arXiv2025

Analysis of multivariate event times under informative censoring using vine copula

The study of times to nonterminal events of different types and their interrelation is a compelling area of interest. The primary challenge in analyzing such multivariate event times is the presence of informative censoring by the terminal event. While numerous statistical methods have been proposed for a single nonterminal event, i.e., semi-competing risks data, there remains a dearth of tools for analyzing times to multiple nonterminal events. This article introduces a novel analysis framework that leverages the vine copula to directly estimate the joint density of multivariate times to nonterminal and terminal events. Unlike the few existing methods based on multivariate or nested copulas, the developed approach excels in capturing the heterogeneous dependence between each pair of event times (nonterminal-terminal and between-nonterminal) in terms of strength and structure. We propose a likelihood-based estimation and inference procedure, which can be implemented efficiently in sequential stages. Through extensive simulation studies, we demonstrate the satisfactory finite-sample performance of our proposed stage-wise estimators and analytical variance estimators, as well as their advantages over existing methods. We apply the developed approach to data from a crowdfunding platform to investigate the relationship between various types of creator-backer interactions and a creator's lifetime on the platform.

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arXiv2024

Two-Stage Pseudo Maximum Likelihood Estimation of Semiparametric Copula-based Regression Models for Semi-Competing Risks Data

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.

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arXiv2023

Information matrix equivalence in the presence of censoring: A goodness-of-fit test for semiparametric copula models with multivariate survival data

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.

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arXiv2022

Singletons for Simpletons: Revisiting Windowed Backoff using Chernoff Bounds

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.

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arXiv2021

A new weighting method when not all the events are selected as cases in a nested case-control study

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.

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arXiv2020

Is the new model better? One metric says yes, but the other says no. Which metric do I use?

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.

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arXiv2018

Tiny Groups Tackle Byzantine Adversaries

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.

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arXiv2016

A Threshold-free Prospective Prediction Accuracy Measure for Censored Time to Event Data

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.

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