The Lehmann Model with Time-dependent Covariates

Consider the Lehmann model with time-dependent covariates, which is different from Cox’s model. We find out that (1) the parameter space for β under the Lehmann model is restricted, and the maximum point of the parametric likelihood for β may lie outside the parameter space; (2) for some particular time-dependent covariate, under the standard generalized likelihood the semiparametric maximum likelihood estimator (SMLE) is inconsistent and we propose a modified generalized likelihood which leads to the consistent SMLE.     

Some sequential selection procedures for good regression models

In the past decade a number of fixed sampling methods have been developed for selecting the "best" or at least a "good" subset of vaiable in regression analysis. We are interested in deriving a sequential selection procedure to select a subset of a random size including equations. Tables for an example are given at the end of this paper     

Hamiltonicity of hypercubes with a constraint of required and faulty edges

Let R and F be two disjoint edge sets in an n-dimensional hypercube Q _n . We give two constructing methods to build a Hamiltonian cycle or path that includes all the edges of R but excludes all of F. Besides, considering every vertex of Q _n incident to at most n−2 edges of F, we show that a Hamiltonian cycle exists if (A) |R|+2|F|≤2n−3 when |R|≥2, or (B) |R|+2|F|≤4n−9 when |R|≤1. Both bounds are tight. The analogous property for Hamiltonian paths is also given. Dedicated to Professor Frank K. Hwang on the occasion of his 65th birthday. Lih-Hsing Hsu’s research project is partially supported by NSC 95-2221-E-233-002. Shu-Chung Liu’s research project is partially supported by NSC 90-2115-M-163-003 and 95-2115-M-163-002. Yeong-Nan Yeh’s research project is partially supported by NSC 95-2115-M-001-009.     

Missing genetic information in case-control family data with general semi-parametric shared frailty model

Case-control family data are now widely used to examine the role of gene-environment interactions in the etiology of complex diseases. In these types of studies, exposure levels are obtained retrospectively and, frequently, information on most risk factors of interest is available on the probands but not on their relatives. In this work we consider correlated failure time data arising from population-based case-control family studies with missing genotypes of relatives. We present a new method for estimating the age-dependent marginalized hazard function. The proposed technique has two major advantages: (1) it is based on the pseudo full likelihood function rather than a pseudo composite likelihood function, which usually suffers from substantial efficiency loss; (2) the cumulative baseline hazard function is estimated using a two-stage estimator instead of an iterative process. We assess the performance of the proposed methodology with simulation studies, and illustrate its utility on a real data example.     

Statistical analysis of firm interdependence using duration data—parametric approach

A pioneer first enters the market as the monopolist and later experiences the competition when a similar product is brought to the market by the competitor. In 2012, Wang and Xie suggested to decompose the pioneer survival to “monopoly” and “competition” durations and estimate the two survivals of the pioneer individually with the competitor's survival via regression analysis. In their article, several regression analyses were performed to study the effect of order entry to the pioneer and the later entrant in different market status. Using the same datasets from their study, our main interest is to investigate the interdependent relationship between two competitive firms and study whether the market pioneer and the later entrant can benefit from the competition. The major contribution of this article is that the interdependence between two competitive firms is explicitly expressed and three survival durations can be estimated in one model. The proposed method relates the survival times of two competitive firms to pioneer's monopoly time and some observable covariates via proportional hazard model, and incorporates frailty variables to capture the interdependence in the competition. This article demonstrates a new method that formulates the interdependence between competitive firms and shows data analyses in the industries of newspapers and high technology.     

Evidence for significant polydrug use among ecstasy-using college students

Ecstasy (MDMA) has been added to the spectrum of illicit drugs used by college students. In this study, the authors estimated the prevalence of ecstasy use within a large college student sample and investigated the polydrug-use history of those ecstasy users. They administered an anonymous questionnaire to college students (N = 1,206) in classrooms at a large university in the mid-Atlantic United States. The overall student response rate was 91%. Nine percent of the sample reported lifetime ecstasy use. Because 98% of ecstasy users had used marijuana, the authors compared polydrug use between ecstasy users and individuals who had used marijuana but not ecstasy. Ecstasy users, as compared with these marijuana users, were significantly more likely to have used inhalants (38% vs. 10%), LSD (38% vs. 5%), cocaine (46% vs 2%), and heroin (17% vs 1%) in the past year. Significant polydrug use among college student ecstasy users has important implications for their substance abuse treatment.     

A single-machine learning effect scheduling problem with release times

In this paper, we investigate a single-machine problem with the learning effect and release times where the objective is to minimize the makespan. A branch-and-bound algorithm incorporating with several dominance properties and lower bounds is developed to derive the optimal solution. A heuristic algorithm is proposed to obtain a near-optimal solution. The computational experiments show that the branch-and-bound algorithm can solve instances up to 36 jobs, and the average error percentage of the proposed heuristic is less than 0.11%.     

Testing the Unconfoundedness Assumption via Inverse Probability Weighted Estimators of (L)ATT

We propose inverse probability weighted estimators for the local average treatment effect (LATE) and the local average treatment effect for the treated (LATT) under instrumental variable assumptions with covariates. We show that these estimators are asymptotically normal and efficient. When the (binary) instrument satisfies one-sided noncompliance, we propose a Durbin–Wu–Hausman-type test of whether treatment assignment is unconfounded conditional on some observables. The test is based on the fact that under one-sided noncompliance LATT coincides with the average treatment effect for the treated (ATT). We conduct Monte Carlo simulations to demonstrate, among other things, that part of the theoretical efficiency gain afforded by unconfoundedness in estimating ATT survives pretesting. We illustrate the implementation of the test on data from training programs administered under the Job Training Partnership Act in the United States. This article has online supplementary material.     

A two-phase method for controlling Erlang-failure processes with high reliability

Monitoring a failure process and measuring its performance are important issues for complex nonrepairable and repairable systems. For a highly reliable process, traditional methods for reliability monitoring and performance measuring become inapplicable. This paper proposes a new two-phase controlling method for monitoring and measuring an Erlang-failure process (EFP). In the first-phase controlling method, a control chart is used to monitor the EFP condition. When special causes of variation have been removed from the EFP and all of the failure times plotted on the control chart lie within the control limits, the EFP is considered to be in control. However, the in-control EFP still likely carries out bad or out-of-lifetime-specification conditions. Thus, its lifetime-specification limit is taken into consideration as the second-phase controlling method for measuring the in-control EFP performance. We propose a lifetime-capability index. Its value has a one-to-one corresponding relationship with the lifetime-conforming rate, which indicates the lifetime performance of this EFP. Without collecting additional data efforts, in-control data gathered from the control chart in the first phase is employed to estimate the lifetime-capability index. To realize main lifetime-capability of the EFP impacting on downstream customers, the lower confidence bound of the estimate of the lifetime-capability index, capturing its minimum lifetime capability, is considered. The advantage of this two-phase method for controlling the failure processes can motivate the manufacturer to develop a reliability-monitoring technique, establish an adequate reliability improvement program and implement an appropriate analysis to ensure its lifetime performance meeting the customers requirement.