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AbstractThere has been wide-spread use of plane wave theory in muffler design in industry. However, This has led to an underestimation of acoustical performances at higher frequencies. To overcome the above drawback, the finite element and boundary element methods have been developed. Nevertheless, the time consumed in calculating the noise level is unacceptable. Moreover, considering the acoustical effect and necessity of space-constrained situation in industry, a compact design of reverse mufflers which may improve the acoustical efficiency is then proposed.In this paper, a numerical assessment of rectangular mufflers hybridized with straight/reverse chambers using eigen function, four-pole matrix, and genetic algorithm under limited space is developed. Before the optimization is performed, an accuracy check of the mathematical models for the muffler will be carried out. Results reveal that the noise reduction will increase when the number of chambers increases. In addition, the acoustical performance of the mufflers is reversely proportional to the diameter of the inlet/outlet tubes. Also, the TL of the mufflers will be improved when using more number of target tones in the objective function. Consequently, a successful approach in searching optimal shaped rectangular straight/reverse mufflers using an eigen function and a genetic algorithm method within a constrained space has been demonstrated.

Objective:Body mass index (BMI) is commonly used to assess obesity, which is associated with numerous diseases and negative health outcomes. BMI has been shown to be a heritable, polygenic trait, with close to 100 loci previously identified and replicated in multiple populations. We aim to replicate known BMI loci and identify novel associations in a trans-ethnic study population.Subjects:Using eligible participants from the Population Architecture using Genomics and Epidemiology consortium, we conducted a trans-ethnic meta-analysis of 102?514 African Americans, Hispanics, Asian/Native Hawaiian, Native Americans and European Americans. Participants were genotyped on over 200?000 SNPs on the Illumina Metabochip custom array, or imputed into the 1000 Genomes Project (Phase I). Linear regression of the natural log of BMI, adjusting for age, sex, study site (if applicable), and ancestry principal components, was conducted for each race/ethnicity within each study cohort. Race/ethnicity-specific, and combined meta-analyses used fixed-effects models.Results:We replicated 15 of 21 BMI loci included on the Metabochip, and identified two novel BMI loci at 1q41 (rs2820436) and 2q31.1 (rs10930502) at the Metabochip-wide significance threshold (P<2.5 × 10-7). Bioinformatic functional investigation of SNPs at these loci suggests a possible impact on pathways that regulate metabolism and adipose tissue.Conclusion:Conducting studies in genetically diverse populations continues to be a valuable strategy for replicating known loci and uncovering novel BMI associations.

To better understand the influence of the microstructural characteristics on the mechanical properties of Fe-Cr22-Ni25-Nbxaustenitic stainless steel (ASS-Nbx), the mechanical properties were investigated. Nb addition was conducted with four different amounts: 0, 0.29, 0.58 and 0.86%. With the increasing Nb content, the mean grain size for the Fe-Cr-Ni-based alloys decreased, while the size of Nb precipitate increased. Owing to the different microstructural characteristics, their mechanical properties were altered. The highest tensile strength was obtained for ASS-Nb0.29alloy. However, with the increasing Nb content in ASS-Nb0.29–0.86alloys, the tensile strength decreases despite the grain refinement. The mechanical properties of the ASS-Nb alloys were influenced by the Nb precipitation hardening and the grain boundary cohesive strength, arising from the size of Nb precipitations.

To better understand the influence of the microstructural characteristics on the mechanical properties of Fe-Cr22-Ni25-Nbxaustenitic stainless steel (ASS-Nbx), the mechanical properties were investigated. Nb addition was conducted with four different amounts: 0, 0.29, 0.58 and 0.86%. With the increasing Nb content, the mean grain size for the Fe-Cr-Ni-based alloys decreased, while the size of Nb precipitate increased. Owing to the different microstructural characteristics, their mechanical properties were altered. The highest tensile strength was obtained for ASS-Nb0.29alloy. However, with the increasing Nb content in ASS-Nb0.29–0.86alloys, the tensile strength decreases despite the grain refinement. The mechanical properties of the ASS-Nb alloys were influenced by the Nb precipitation hardening and the grain boundary cohesive strength, arising from the size of Nb precipitations.

We present the investigations of interdiffusion in InGaAsP multiplequantumwell MQW structures using photoreflectance PR and photoluminescence PL measurements. It is found that the degree of compositional intermixing induced by the processes of ion implantation and rapid thermal annealing in MQW structures can be obtained through the energy shift of the 11H excitonic transition. Besides, the strain relaxation resulting from intermixing is studied through the high order excitonic transitions observed in PR spectra. It is found that the splitting energy between the 11H and 11L transitions decreases as a result of increasing the degree of intermixing. Based on the theoretical calculation considering the strain effect and the different diffusion ratios between the groupIII and groupV atoms, the data analysis have been done. It is pointed out that the diffusion coefficients and the ratio of diffusion rates between the groupV and groupIII atoms has been enhanced by the Pion implantation. © 2009 WILEYVCH Verlag GmbH & Co. KGaA, Weinheim

Estimating the effects of haplotypes on the age of onset of a disease is an important step toward the discovery of genes that influence complex human diseases. A haplotype is a specific sequence of nucleotides on the same chromosome of an individual and can only be measured indirectly through the genotype. We consider cohort studies which collect genotype data on a subset of cohort members through case–cohort or nested case–control sampling. We formulate the effects of haplotypes and possibly time-varying environmental variables on the age of onset through a broad class of semiparametric regression models. We construct appropriate nonparametric likelihoods, which involve both finite- and infinite-dimensional parameters. The corresponding nonparametric maximum likelihood estimators are shown to be consistent, asymptotically normal, and asymptotically efficient. Consistent variance–covariance estimators are provided, and efficient and reliable numerical algorithms are developed. Simulation studies demonstrate that the asymptotic approximations are accurate in practical settings and that case–cohort and nested case–control designs are highly cost-effective. An application to a major cardiovascular study is provided.

We present an optical study on three AlxGa1–xN/GaN high electron mobility transistor structures, which were grown by metalorganic chemical vapor deposition (MOCVD) on sapphire substrates, with different Al compositions using contactless electroreflectance (CER), piezoreflectance (PzR) and surface photovoltage spectroscopy (SPS). The Al composition x can be determined from the band gap energy of AlxGa1–xN layer observed in CER and PzR spectra. The determination of the built-in electric field strength in the barrier layer (F) has been done by the analysis of Franz–Keldysh oscillations (FKOs) above the AlxGa 1–xN band gap in CER spectra. A broad feature appeared at energies above the band gap of GaN was observed in each CER, PzR and SPS spectrum. We believe that it is related to the two-dimensional electron gas (2DEG). The energy of the broad 2DEG minimum roughly corresponds to the Fermi energy plus the band gap. The Hall-effect measurements have also been carried out in van der Pauw geometry at room temperature to reveal the sheet carrier density (ns). For the sample with lowest alloy composition (x = 0.07) the analysis of the FKOs yields F = 316 kV/cm at room temperature. When the temperature was cooled down to 50 K the electric field strength decreases to 188 kV/cm. This result can be explained by the change of piezoelectric polarization. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Variable air pressure tracking control has been studied as a means to ensure product quality in a casting furnace. A conventional PID controller, a fuzzy controller and a neural fuzzy controller have been designed and applied. Experimental results obtained with these control systems are shown and compared, allowing the choice of an optimal controller giving the best quality products in low pressure casting. IJCMR/344

Informative drop-out arises in longitudinal studies when the subject's follow-up time depends on the unobserved values of the response variable. We specify a semiparametric linear regression model for the repeatedly measured response variable and an accelerated failure time model for the time to informative drop-out. The error terms from the two models are assumed to have a common, but completely arbitrary joint distribution. Using a rank-based estimator for the accelerated failure time model and an artificial censoring device, we construct an asymptotically unbiased estimating function for the linear regression model. The resultant estimator is shown to be consistent and asymptotically normal. A resampling scheme is developed to estimate the limiting covariance matrix. Extensive simulation studies demonstrate that the proposed methods are suitable for practical use. Illustrations with data taken from two AIDS clinical trials are provided.

Owing to induced dependent censoring, estimating mean costs and quality‐adjusted survival in a cost‐effectiveness comparison of two groups using standard life‐table methods leads to biased results. In this paper we propose methods for estimating the difference in mean costs and the difference in mean effectiveness, together with their respective variances and covariance in the presence of dependent censoring. We consider the situation in which the measure of effectiveness is either the probability of surviving a duration of interest or mean quality‐adjusted survival time over a duration of interest. The methods are illustrated in an example using an incremental net benefit analysis. Copyright © 2003 John Wiley & Sons, Ltd.

Owing to induced dependent censoring, estimating mean costs and quality-adjusted survival in a cost-effectiveness comparison of two groups using standard life-table methods leads to biased results. In this paper we propose methods for estimating the difference in mean costs and the difference in mean effectiveness, together with their respective variances and covariance in the presence of dependent censoring. We consider the situation in which the measure of effectiveness is either the probability of surviving a duration of interest or mean quality-adjusted survival time over a duration of interest. The methods are illustrated in an example using an incremental net benefit analysis. Copyright © 2003 John Wiley & Sons, Ltd.

Summary. Residuals have long been used for graphical and numerical examinations of the adequacy of regression models. Conventional residual analysis based on the plots of raw residuals or their smoothed curves is highly subjective, whereas most numerical goodness‐of‐fit tests provide little information about the nature of model misspecification. In this paper, we develop objective and informative model‐checking techniques by taking the cumulative sums of residuals over certain coordinates (e.g., covariates or fitted values) or by considering some related aggregates of residuals, such as moving sums and moving averages. For a variety of statistical models and data structures, including generalized linear models with independent or dependent observations, the distributions of these stochastic processes under the assumed model can be approximated by the distributions of certain zero‐mean Gaussian processes whose realizations can be easily generated by computer simulation. Each observed process can then be compared, both graphically and numerically, with a number of realizations from the Gaussian process. Such comparisons enable one to assess objectively whether a trend seen in a residual plot reflects model misspecification or natural variation. The proposed techniques are particularly useful in checking the functional form of a covariate and the link function. Illustrations with several medical studies are provided.

There are three approaches to health economic evaluation for comparing two therapies. These are (i) cost minimization, in which one assumes or observes no difference in effectiveness, (ii) incremental cost-effectiveness, and (iii) incremental net benefit. The latter can be expressed either in units of effectiveness or costs. When analysing data from a clinical trial, expressing incremental net benefit in units of cost allows the investigator to examine all three approaches in a single graph, complete with the corresponding statistical inferences. Furthermore, if costs and effectiveness are not censored, this can be achieved using common two-sample statistical procedures. The above will be illustrated using two examples, one with censoring and one without. Copyright © 2001 John Wiley & Sons, Ltd.

There are three approaches to health economic evaluation for comparing two therapies. These are (i) cost minimization, in which one assumes or observes no difference in effectiveness, (ii) incremental cost‐effectiveness, and (iii) incremental net benefit. The latter can be expressed either in units of effectiveness or costs. When analysing data from a clinical trial, expressing incremental net benefit in units of cost allows the investigator to examine all three approaches in a single graph, complete with the corresponding statistical inferences. Furthermore, if costs and effectiveness are not censored, this can be achieved using common two‐sample statistical procedures. The above will be illustrated using two examples, one with censoring and one without. Copyright © 2001 John Wiley & Sons, Ltd.

Summary. This article deals with the problem of comparing two populations with respect to the distribution of the gap time between two successive events when each subject can experience a series of events and when the event times are potentially right censored. Several families of nonparametric tests are developed, all of which allow arbitrary distributions and dependence structures for the serial events. The asymptotic and small‐sample properties of the proposed tests are investigated. An illustration with data taken from a colon cancer study is provided. The related problem of testing the independence of two successive gap times is also studied.

Summary. The field of survival analysis emerged in the 20th century and experienced tremendous growth during the latter half of the century. The developments in this field that have had the most profound impact on clinical trials are the Kaplan‐Meier (1958, Journal of the American Statistical Association53, 457–481) method for estimating the survival function, the log‐rank statistic (Mantel, 1966, Cancer Chemotherapy Report50, 163–170) for comparing two survival distributions, and the Cox (1972, Journal of the Royal Statistical Society, Series B34, 187–220) proportional hazards model for quantifying the effects of covariates on the survival time. The counting‐process martingale theory pioneered by Aalen (1975, Statistical inference for a family of counting processes, Ph.D. dissertation, University of California, Berkeley) provides a unified framework for studying the small‐ and large‐sample properties of survival analysis statistics. Significant progress has been achieved and further developments are expected in many other areas, including the accelerated failure time model, multivariate failure time data, interval‐censored data, dependent censoring, dynamic treatment regimes and causal inference, joint modeling of failure time and longitudinal data, and Baysian methods.

Summary. The semiparametric proportional means model specifies that the mean function for the cumulative medical cost over time conditional on a set of covariates is equal to an arbitrary baseline mean function multiplied by an exponential regression function. We demonstrate how to estimate the vector‐valued regression parameter using possibly censored lifetime costs. The estimator is consistent and asymptotically normal with an easily estimable covariance matrix. Simulation studies show that the proposed methodology is appropriate for practical use. An application to AIDS is provided.

Summary. This article is concerned with the analysis of recurrent events in the presence of a terminal event such as death. We consider the mean frequency function, defined as the marginal mean of the cumulative number of recurrent events over time. A simple nonparametric estimator for this quantity is presented. It is shown that the estimator, properly normalized, converges weakly to a zero‐mean Gaussian process with an easily estimable covariance function. Nonparametric statistics for comparing two mean frequency functions and for combining data on recurrent events and death are also developed. The asymptotic null distributions of these statistics, together with consistent variance estimators, are derived. The small‐sample properties of the proposed estimators and test statistics are examined through simulation studies. An application to a cancer clinical trial is provided.

This paper deals with the problem of linear regression for medical cost data when some study subjects are not followed for the full duration of interest so that their total costs are unknown. Standard survival analysis techniques are ill-suited to this type of censoring. The familiar normal equations for the least-squares estimation are modified in several ways to properly account for the incompleteness of the data. The resulting estimators are shown to be consistent and asymptotically normal with easily estimated variance-covariance matrices. The proposed methodology can be used when the cost database contains only the total costs for those with complete follow-up. More efficient estimators are available when the cost data are recorded in multiple time intervals. A study on the medical cost for ovarian cancer is presented.

Summary. In this paper, we develop Poisson‐type regression methods that require the durations of exposure be measured only on a possibly nonrandom subset of the cohort members. These methods can be used to make inferences about the incidence density during exposure as well as the ratio of incidence densities during exposure versus not during exposure. Numerical studies demonstrate that the proposed methods yield reliable results in practical settings. We describe an application to a population‐based case‐control study assessing the transient increase in the risk of primary cardiac arrest during leisure‐time physical activity.

To elucidate the long‐term results of percutaneous ethanol injection (PEI) for hepatocellular carcinoma (HCC), 47 cirrhotic patients with HCC ≤5 cm after PEI were analysed. Thirty‐two of the patients were male. The age range was 37‐68 years. Thirty‐nine patients were seropositive either for hepatitis B surface antigen or antihepatitis C virus antibody. There were a total of 61 tumours, including solitary tumours in 35 patients, double tumours in 10 and triple tumours in two. The size of the main tumour was ≤3 cm in 29 patients and more than 3 cm in 18 patients. Seventeen, 27 and three patients were in Child's class A, B and C respectively; 5‐10 ml 95% ethanol was injected into the tumour every three to seven days until the echogenicity of the tumour changed to a hyperechoic or heterogeneous one. A booster PEI was given in 34 (56%) lesions with viable tumour, which was detected by dynamic computed tomography. The one, two, three and and four‐year survival rates were 85%, 75%, 61% and 39% respectively for all patients. Good liver reserve significantly improved the survival rate (p<0.01, Child's class A and B vsChild's class C). The one, two, three and four‐year recurrence rates were 24%, 55%, 69% and 79% for all patients. HCC recurred more frequently in patients with multiple tumours (p<0.02).

Summary. We use the semiparametric additive hazards model to formulate the effects of individual covariates on the capture rates in the continuous‐time capture–recapture experiment, and then construct a Horvitz–Thompson‐type estimator for the unknown population size. The resulting estimator is consistent and asymptotically normal with an easily estimated variance. Simulation studies show that the asymptotic approximations are adequate for practical use when the average capture probabilities exceed .5. Ignoring covariates would underestimate the population size and the coverage probability is poor. A wildlife example is provided.

In the competing risks problem, a useful quantity is the cumulative incidence function, which is the probability of occurrence by time t for a particular type of failure in the presence of other risks. The estimator of this function as given by Kalbfleisch and Prentice is consistent, and, properly normalized, converges weakly to a zero-mean Gaussian process with a covariance function for which a consistent estimator is provided. A resampling technique is developed to approximate the distribution of this process, which enables one to construct confidence bands for the cumulative incidence curve over the entire time span of interest and to perform Kolmogorov–Smirnov type tests for comparing two such curves. An AIDS example is provided. © 1997 by John Wiley & Sons, Ltd. Stat. Med., Vol. 16, 901–910 (1997).

Although expert systems are usually thought of as decision aids for human users, they may also serve as training aids for situations in which humans must make quick decisions and computer‐based decision aids would not be viable. This paper describes an exploratory study of the application of expert system‐based training for an emergency management of a hazardous chemical spill. Human factors methodologies are employed to define the training, control, and test conditions needed to quantify the significance of using an expert system for training human decision makers for an emergency management application. The results confirmed the hypothesis that the natural human tendency in processing rules would be to resort to a data‐driven strategy. The expert system‐based training can deter the human from employing such a strategy and can improve his performance, especially as the complexity in rule‐chaining increases. Overall, the results of this study are supportive of the use of artificial intelligence‐based techniques for training humans in the emergency management of risk.

In this paper, we measure the extent to which a biological marker is a surrogate endpoint for a clinical event by the proportional reduction in the regression coefficient for the treatment indicator due to the inclusion of the marker in the Cox regression model. We estimate this proportion by applying the partial likelihood function to two Cox models postulated on the same failure time variable. We show that the resultant estimator is asymptotically normal with a simple variance estimator. One can construct confidence intervals for the proportion by using the direct normal approximation to the point estimator or by using Fieller's theorem. Extensive simulation studies demonstrate that the proposed methods are appropriate for practical use. We provide applications to HIV/AIDS clinical trials. © 1997 John Wiley & Sons, Ltd.

Twenty chronic viral hepatitis patients, mainly with hepatitis B related with progression to liver cirrhosis were included for an assay of serum collagen markers: PICP (carboxy terminal propeptide of type I procollagen), PIIINP (amino terminal propeptide of type III procollagen), and 7S-IV (7S-domain type IV collagen). PICP is increased in 20% of chronic hepatitis patients with a mean of 190.3 ng/ml, which is not different from that of the follow-up concentration in liver cirrhosis, where 35% of cases were abnormal with a mean of 220.5 ng/ml. The serum level and percent of abnormality of PIIICP in chronic hepatitis and in liver cirrhosis are 23.5 ng/ml vs 14.8 ng/ml and 90% vs 100%, respectively (P>0.05). PICP/PIIINP is significantly higher during liver cirrhosis (15.11 vs 10.08,P<0.05). PICP during chronic hepatitis is not related to serum biochemical changes, while PICP during liver cirrhosis and PIIINP are correlated with hepatic enzymes. 7S-IV in chronic hepatitis and in liver cirrhosis is 14.0 ng/ml vs 10.9 ng/ml, respectively; both were positively correlated with hepatic enzymes. These results suggest that PICP/PIIINP is a better indicator of hepatic fibrogenesis than either PICP or PIIINP alone in viral hepatitis. A ratio of more than 12 is suggestive of liver cirrhosis.

In the competing risks problem, a useful quantity is the cumulative incidence function, which is the probability of occurrence by time tfor a particular type of failure in the presence of other risks. The estimator of this function as given by Kalbfleisch and Prentice is consistent, and, properly normalized, converges weakly to a zero‐mean Gaussian process with a covariance function for which a consistent estimator is provided. A resampling technique is developed to approximate the distribution of this process, which enables one to construct confidence bands for the cumulative incidence curve over the entire time span of interest and to perform Kolmogorov–Smirnov type tests for comparing two such curves. An AIDS example is provided. © 1997 by John Wiley & Sons, Ltd. Stat. Med., Vol. 16, 901–910 (1997).

In this paper, we measure the extent to which a biological marker is a surrogate endpoint for a clinical event by the proportional reduction in the regression coefficient for the treatment indicator due to the inclusion of the marker in the Cox regression model. We estimate this proportion by applying the partial likelihood function to two Cox models postulated on the same failure time variable. We show that the resultant estimator is asymptotically normal with a simple variance estimator. One can construct confidence intervals for the proportion by using the direct normal approximation to the point estimator or by using Fieller's theorem. Extensive simulation studies demonstrate that the proposed methods are appropriate for practical use. We provide applications to HIV/AIDS clinical trials. © 1997 John Wiley & Sons, Ltd.

Summary Fifteen patients with HBsAg-positive, severe chronic active heptatitis, nine DNA polymerase (DNAP)-positive and six negative were treated with intravenous adenine arabinoside (Ara-A) in a dose of 10 mg/kg/day for five consecutive days during each of two consecutive weeks. Of the DNAP-positive patients, two responded with histological and clinical remission as well as permanent loss of DNAP. However, histological and clinical remission were also observed in patients with unsatisfactory DNAP response and even in DNAP-negative patients. It is suggested that, in addition to its antiviral effect, Ara-A might have another mechanism, such as immunosuppression, that induced histological and clinical remission. Alternatively, the discrepancy of response might relate to the natural course of chronic type B hepatitis. Accordingly, controlled trial is mandatory for assessing the effect of Ara-A or any other agent in the treatment of chronic type B hepatitis.

Motivation: Multiple hypothesis testing is a common problem in genome research, particularly in microarray experiments and genomewide association studies. Failure to account for the effects of multiple comparisons would result in an abundance of false positive results. The Bonferroni correction and Holm's step-down procedure are overly conservative, whereas the permutation test is time-consuming and is restricted to simple problems. Results: We developed an efficient Monte Carlo approach to approximating the joint distribution of the test statistics along the genome. We then used the Monte Carlo distribution to evaluate the commonly used criteria for error control, such as familywise error rates and positive false discovery rates. This approach is applicable to any data structures and test statistics. Applications to simulated and real data demonstrate that the proposed approach provides accurate error control, and can be substantially more powerful than the Bonferroni and Holm methods, especially when the test statistics are highly correlated. Contact: lin@bios.unc.edu

Because of the difficulties in conducting studies of clinical efficacy of new therapies for human immunodeficiency virus infection and other diseases, there is increasing interest in using measures of biologic activity as surrogates for clinical end points. A widely used criterion for evaluating whether such measures are reliable as surrogates requires that the putative surrogate fully captures the “net effect”—the effect aggregated over all mechanisms of action—of the treatment on the clinical end point. The variety of proposed metrics for evaluating the degree to which this criterion is met are subject to misinterpretation because of the multiplicity of mechanisms by which drugs operate. Without detailed understanding of these mechanisms, metrics of “surrogacy” are not directly interpretable. Even when all of the mechanisms are understood, these metrics are associated with a high degree of uncertainty unless either treatment effects are large in moderate-size studies or sample sizes are large in studies of moderately effective treatments.

The optical transitions of the quasibound states at the above-barrier region in GaAs/Ga0.77Al0.23As multiple quantum wells have been observed at room temperature by photoreflectance measurement. It is found that the barrier-width dependence of the above-barrier transition energies can be described quite well by the modified Messiah's calculation. However, the simple calculation using the constructive interference condition can only explain the transitions at lower energies, and fails with increasing transition energy.

This paper presents a simple sequential method for comparing two treatments in randomized clinical trials which allows for the adjustment of other covariates with the accelerated life model. The new procedure is the same as the ordinary sequential log rank test except that the test statistic is calculated on an ‘adjusted’ time scale. This covariate adjustment can lead to more efficient designs of group sequential trials especially when the effects of covariates being adjusted for are strong. An aids example is provided.

In a multiple-armed clinical trial where one agent is administered at several dose levels or where each treatment regimen is formed by adding more agents to the preceding combination, it is desirable to use test statistics that are sensitive to alternatives of stochastically ordered distributions. Liu et al (1992) recently developed a class of such test statistics by taking linear combinations of the familiar two-sample weighted log rank statistics. In the present paper, we derive the asymptotic joint distributions of their test statistics calculated at different points in time. Applications to sequential survival studies with staggered patient entry are emphasized. A colon cancer example is provided.

In the presence of univariate censoring, the bivariate survival function of paired failure times can be expressed as the ratio of the bivariate at-risk probability to the survival function of the censoring time. The use of this natural representation yields a very simple nonparametric estimator for the bivariate survival curve. The estimator is strongly consistent and, upon proper normalization, converges weakly to a zero-mean Gaussian process with an easily estimated covariance function. Numerical studies demonstrate that both the survival curve estimator and its covariance function estimator perform markedly well for practical sample sizes. Applications to the correlation problem and to the interval estimation of the difference in median survival times are also studied.

This paper presents a new class of graphical and numerical methods for checking the adequacy of the Cox regression model. The procedures are derived from cumulative sums of martingale-based residuals over follow-up time and/or covariate values. The distributions of these stochastic processes under the assumed model can be approximated by zero-mean Gaussian processes. Each observed process can then be compared, both visually and analytically, with a number of simulated realizations from the approximate null distribution. These comparisons enable the data analyst to assess objectively how unusual the observed residual patterns are. Special attention is given to checking the functional form of a covariate, the form of the link function, and the validity of the proportional hazards assumption. An omnibus test, consistent against any model misspecification, is also studied. The proposed techniques are illustrated with two real data sets.

In this paper, we show how to construct simultaneous confidence bands for the subject-specific survival curve under the Cox proportional hazards model. The idea is to approximate the distribution of the normalized cumulative hazard estimator by a zero-mean Gaussian process whose distribution can be easily generated through simulation. Numerical studies indicate that the proposed bands are appropriate for practical use. A liver disease example is presented.

In contrast to the proportional hazards model, the additive risk model specifies that the hazard function associated with a set of possibly time-varying covariates is the sum of, rather than the product of, the baseline hazard function and the regression function of covariates. This formulation describes a different aspect of the association between covariates and the failure time than the proportional hazards model, and is more plausible than the latter for many applications. In the present paper, simple procedures with high efficiencies are developed for making inference about the regression parameters under the additive risk model with an unspecified baseline hazard function. The subject-specific survival estimation is also studied. The proposed techniques resemble the partial-likelihood-based methods for the proportional hazards model. A real example is provided.

Recently linear rank statistics with censored data have been used as the estimating functions for the regression parameters in the linear model with an unspecified error distribution. The resulting rank estimators are consistent and asymptotically normal. However, the asymptotic variances of these estimators are complicated and are difficult to estimate well with censored data. In this paper, we propose some simple methods for making inference about a subset of the regression coefficients while regarding others as nuisance parameters. A lack-of-fit test for the linear model is also presented. The proposed procedures are illustrated with an example.

This paper addresses sequential testing in randomized clinical trials with multiple endpoints. Patients enter treatments serially and are subject to random loss to followup. The endpoints of interest may be time-to-event variables or other quantitative measurements. The proposed test statistic at a given look is a weighted sum of the linear rank statistics with respect to the marginal distributions of the multiple endpoints. The weights can be chosen to maximize asymptotic power against certain local alternatives. Stopping boundaries are obtained from the asymptotic joint distribution of the proposed test statistics calculated at different looks. This new approach preserves a single preset overall significance level and can lead to quicker termination of the trial than sequential procedures based on single endpoints. An example taken from an aids clinical trial is presented.