Jackknifed random weighting for Cox proportional hazards model

The Cox proportional hazards model is the most used statistical model in the analysis of survival time data.Recently,a random weighting method was proposed to approximate the distribution of the maximum partial likelihood estimate for the regression coefficient in the Cox model.This method was shown not as sensitive to heavy censoring as the bootstrap method in simulation studies but it may not be second-order accurate as was shown for the bootstrap approximation.In this paper,we propose an alternative random weighting method based on one-step linear jackknife pseudo values and prove the second accuracy of the proposed method.Monte Carlo simulations are also performed to evaluate the proposed method for fixed sample sizes.     

Estimating Differences in Restricted Mean Lifetime Using Additive Hazards Models under Dependent Censoring

In epidemiological and clinical studies,the restricted mean lifetime is often of direct interest quantity.The differences of this quantity can be used as a basis of comparing several treatment groups with respect to their survival times.When the factor of interest is not randomized and lifetimes are subject to both dependent and independent censoring,the imbalances in confounding factors need to be accounted.We use the mixture of additive hazards model and inverse probability of censoring weighting method to estimate the differences of restricted mean lifetime.The average causal effect is then obtained by averaging the differences in fitted values based on the additive hazards models.The asymptotic properties of the proposed method are also derived and simulation studies are conducted to demonstrate their finite-sample performance.An application to the primary biliary cirrhosis(PBC)data is illustrated.     

BOOTSTRAP WAVELET IN THE NONPARAMETRIC REGRESSION MODEL WITH WEAKLY DEPENDENT PROCESSES

This paper introduces a method of bootstrap wavelet estimation in a nonparametric regression model with weakly dependent processes for both fixed and random designs. The asymptotic bounds for the bias and variance of the bootstrap wavelet estimators are given in the fixed design model. The conditional normality for a modified version of the bootstrap wavelet estimators is obtained in the fixed model. The consistency for the bootstrap wavelet estimator is also proved in the random design model. These results show that the bootstrap wavelet method is valid for the model with weakly dependent processes.     

Approximation by random weighting method for M-test in linear models

The M-test has been in common use and widely studied in testing the linear hypotheses in linear models. However, the critical value for the test is usually related to the quantities of the unknown error distribution and the estimate of the nuisance parameters may be rather involved, not only for the M-test method but also for the existing bootstrap methods. In this paper we suggest a random weighting resampling method for approximating the null distribution of the M-test statistic. It is shown that, under both the null and the local alternatives, the random weighting statistic has the same asymptotic distribution as the null distribution of the M-test. The critical values of the M-test can therefore be obtained by the random weighting method without estimating the nuisance parameters. A distinguished feature of the proposed method is that the approximation is valid even the null hypothesis is not true and the power evaluation is possible under the local alternatives.     

ESTIMATING OF ORDER-RESTRICTED LOCATION PARAMETERS OF TWO-EXPONENTIAL DISTRIBUTIONS UNDER MULTIPLE TYPE- Ⅱ CENSORING

In this article, Bayes estimation of location parameters under restriction is broughtforth. Since Bayes estimator is closely connected with the first value of order statistics that canbe observed, it is possible to consider “complete data” method, through which the pseudo-value of first order statistics and pseudo-right censored samples can he obtained. Thus the results under Type- Ⅱ right censoring can be used directly to get more accurate estimators by Bayes method.     

Bootstrap approximation of wavelet estimates in a semiparametric regression model

The inference for the parameters in a semiparametric regression model is studied by using the wavelet and the bootstrap methods. The bootstrap statistics are constructed by using Efron＇s resampling technique, and the strong uniform convergence of the bootstrap approximation is proved. Our results can be used to construct the large sample confidence intervals for the parameters of interest. A simulation study is conducted to evaluate the finite-sample performance of the bootstrap method and to compare it with the normal approximation-based method.     

Semiparametric analysis of longitudinal data with informative observation times

In many longitudinal studies,observation times as well as censoring times may be correlated with longitudinal responses.This paper considers a multiplicative random effects model for the longitudinal response where these correlations may exist and a joint modeling approach is proposed via a shared latent variable.For inference about regression parameters,estimating equation approaches are developed and asymptotic properties of the proposed estimators are established.The finite sample behavior of the methods is examined through simulation studies and an application to a data set from a bladder cancer study is provided for illustration.     

Hierarchically penalized additive hazards model with diverging number of parameters

In many applications,covariates can be naturally grouped.For example,for gene expression data analysis,genes belonging to the same pathway might be viewed as a group.This paper studies variable selection problem for censored survival data in the additive hazards model when covariates are grouped.A hierarchical regularization method is proposed to simultaneously estimate parameters and select important variables at both the group level and the within-group level.For the situations in which the number of parameters tends to∞as the sample size increases,we establish an oracle property and asymptotic normality property of the proposed estimators.Numerical results indicate that the hierarchically penalized method performs better than some existing methods such as lasso,smoothly clipped absolute deviation(SCAD)and adaptive lasso.     

Monotone rank estimation of transformation models with length-biased and right-censored data

This paper considers the monotonic transformation model with an unspecified transformation function and an unknown error function, and gives its monotone rank estimation with length-biased and rightcensored data. The estimator is shown to be√n-consistent and asymptotically normal. Numerical simulation studies reveal good finite sample performance and the estimator is illustrated with the Oscar data set. The variance can be estimated by a resampling method via perturbing the U-statistics objective function repeatedly.     

Quantile regression for right-censored and length-biased data

Length-biased data arise in many important fields, including epidemiological cohort studies, cancer screening trials and labor economics. Analysis of such data has attracted much attention in the literature. In this paper we propose a quantile regression approach for analyzing right-censored and length-biased data. We derive an inverse probability weighted estimating equation corresponding to the quantile regression to correct the bias due to length-bias sampling and informative censoring. This method can easily handle informative censoring induced by length-biased sampling. This is an appealing feature of our proposed method since it is generally difficult to obtain unbiased estimates of risk factors in the presence of length-bias and informative censoring. We establish the consistency and asymptotic distribution of the proposed estimator using empirical process techniques. A resampling method is adopted to estimate the variance of the estimator. We conduct simulation studies to evaluate its finite sample performance and use a real data set to illustrate the application of the proposed method.     

Regression analysis of right-censored failure time data with missing censoring indicators

This paper discusses regression analysis of right-censored failure time data when censoring indicators are missing for some subjects. Several methods have been developed for the analysis under different situations and especially, Goetghebeur and Ryan considered the situation where both the failure time and the censoring time follow the proportional hazards models marginally and developed an estimating equation approach. One limitation of their approach is that the two baseline hazard functions were assumed to be proportional to each other. We consider the same problem and present an efficient estimation procedure for regression parameters that does not require the proportionality assumption. An EM algorithm is developed and the method is evaluated by a simulation study, which indicates that the proposed methodology performs well for practical situations. An illustrative example is provided.     

Exact Confidence Limits for the Parameter of an Exponential Distribution in the Accelerated Life Tests under Type-ⅠCensoring

Life data frequently arise in many reliability studies,such as accelerated life tests studies.This paper considers the part of life data where failure and censoring observations may exist.To develop statistical methods and theory for the analysis of these data,a new approach was proposed to obtain the exact lower and upper confidence limits for the mean life of the exponential distribution with Type-I censoring data.It is assumed that the acceleration factor is a random variable,and that the distribution of the acceleration factor is known from some empirical information or the meta analysis.A method for constructing the lower and upper confidence limits for the parameter based on an ordering relation among the sample space was proposed.Simulation studies and analyses of two examples suggest that the proposed method performed well.     

Random Weighting Method

1.IntrOduction Since Efron's weIl known paper apPeared in 1979,there hasbeen enormous work8 0n resampling methods.Among all these techniques,bootstraP isconceptually the simplest and the most attractiye one. But for setting confidenceinterval, the confidenee level of the interval set by the boot8trap method, especi-ally for small sample size, is less than what we 0riginaIly exPected. The purPoseof this paPer is to discuss an alternatiVe method,the random weighting method,whichwas originally suggested by Rubin.Numirical study shows that the randomweighting method can reduce the level error of the confidence interVal for themeasure model. In section 2, the assymptotical behaVior of random weightingmethod for measure model is discussed. In 8ection 3, the random weighting me—     

EM algorithm and its application to testing hypotheses

The conventional method for testing hypotheses is to find an exact or asymptotic distributionof a test statistic But when the model is complex and the sample size is small,difficulty often arises. Thispaper aims to present a method for finding maximum probability with the help of EM algorithm. For any fixedsample size,this method can be used not only to obtain an accurate test but also to check the real level of     

Confidence Intervals of Variance Functions in Generalized Linear Model

In this paper we introduce an appealing nonparametric method for estimating variance and conditional variance functions in generalized linear models （GLMs）, when designs are fixed points and random variables respectively, Bias-corrected confidence bands are proposed for the （conditional） variance by local linear smoothers. Nonparametric techniques are developed in deriving the bias-corrected confidence intervals of the （conditional） variance. The asymptotic distribution of the proposed estimator is established and show that the bias-corrected confidence bands asymptotically have the correct coverage properties. A small simulation is performed when unknown regression parameter is estimated by nonparametric quasi-likelihood. The results are also applicable to nonparamctric autoregressive times series model with heteroscedastic conditional variance.     

One-step estimation for varying coefficient models

A one-step method is proposed to estimate the unknown functions in the varying coefficient models, in which the unknown functions admit different degrees of smoothness. In this method polynomials of different orders are used to approximate unknown functions with different degrees of smoothness. As only one minimization operation is employed, the required computation burden is much less than that required by the existing two-step estimation method. It is shown that the one-step estimators also achieve the optimal convergence rate. Moreover this property is obtained under conditions milder than that imposed in the two-step estimation method. More importantly, as only one minimization operation is employed, the full asymptotic properties, not only the asymptotic bias and variance, but also the asymptotic distributions of the estimators can be derived. The asymptotic distribution results will play a key role for making statistical inference.     

The computation of Buehler confidence limits

In medicine and industry, small sample size often arises owing to the high test cost. Then exact confidence inference is important. Buehler confidence limit is a kind of exact confidence limit for the function of parameters in a model. It can be always defined if the order in sample space is given. But the computing problem is often difficult, especially for the cases with high dimension parameter or with incomplete data. This paper presents an algorithm to compute the Buehler confidence limits by EM algorithm. This is the first-time usage of EM algorithm on Buehler confidence limits, but the algorithm is often used for maximum likelihood estimate in literatures. Three computation examples are given to illustrate the method.     

Statistical inference for right-censored data with nonignorable missing censoring indicators

We consider the statistical inference for right-censored data when censoring indicators are missing but nonignorable, and propose an adjusted imputation product-limit estimator. The proposed estimator is shown to be consistent and converges to a Gaussian process. Furthermore, we develop an empirical processbased testing method to check the MAR (missing at random) mechanism, and establish asymptotic properties for the proposed test statistic. To determine the critical value of the test, a consistent model-based bootstrap method is suggested. We conduct simulation studies to evaluate the numerical performance of the proposed method and compare it with existing methods. We also analyze a real data set from a breast cancer study for an illustration.     

ADDITIVE HAZARDS MODEL WITH TIME-VARYING REGRESSION COEFFICIENTS

This article discusses regression analysis of failure time under the additive hazards model, when the regression coefficients are time-varying. The regression coefficients are estimated locally based on the pseudo-score function [12] in a window around each time point. The proposed method can be easily implemented, and the resulting estimators are shown to be consistent and asymptotically normal with easily estimated variances. The simulation studies show that our estimation procedure is reliable and useful.     

Correcting for biases in affected sib-pair linkage analysis caused by uncertainty in sibling relationship

When there is uncertainty in sibling relationship,the classical affected sib-pair(ASP) linkage tests may be severely biased.This can happen,for example,if some of the half sib-pairs are mixed with full sib-pairs.The genomic control method has been used in association analysis to adjust for population structures.We show that the same idea can be applied to ASP linkage analysis with uncertainty in sibling relationship.Assuming that,in addition to the candidate marker,null markers that are unlinked to the disease locus are also genotyped,we may use the information on these loci to estimate the proportion of half sib-pairs and to correct for the bias and variance distortion caused by the heterogeneity of sibling relationship.Unlike in association studies,the null loci are not required to be matched with the candidate marker in allele frequency for ASP linkage analysis.This makes our approach flexible in selecting null markers.In our simulations,using a number of 30 or more null loci can effectively remove the bias and variance distortion.It is also shown that,even the null loci are weakly linked to the disease locus,the proposed method can also provide satisfactory correction.