Adaptive design: estimation and inference with censored data in a semiparametric model

In this article, we provide a method of estimation for the treatment effect in the adaptive design for censored survival data with or without adjusting for risk factors other than the treatment indicator. Within the semiparametric Cox proportional hazards model, we propose a bias-adjusted parameter estimator for the treatment coefficient and its asymptotic confidence interval at the end of the trial. The method for obtaining an asymptotic confidence interval and point estimator is based on a general distribution property of the final test statistic from the weighted linear rank statistics at the interims with or without considering the nuisance covariates. The computation of the estimates is straightforward. Extensive simulation studies show that the asymptotic confidence intervals have reasonable nominal probability of coverage, and the proposed point estimators are nearly unbiased with practical sample sizes.     

Estimates of a Treatment Effect Based on Censored Data Rank Tests

Linear rank test statistics are applied to the problem of estimating a treatment effect if two sets of censored failure time data are compared and the distributions of the log-failure times of the two samples are assumed to differ only in location. Rank tests for this accelerated failure time model are reviewed and Hodges-Lehmann type estimates for the shift parameter are proposed. Properties of these estimates are investigated, computational aspects are discussed and an example is presented.     

Nonparametric Tests for Slope in Linear Regression Problems

In this paper some new, exactly distribution-free tests are offered for the hypothesis about the slope parameter in one-sample, two-sample, and several-sample simple linear regression problems. Asymptotic relative efficiencies of these test procedures are also studied.     

Testing for differentially expressed genes with microarray data

This paper compares the type I error and power of the one- and two-sample t-tests, and the one- and two-sample permutation tests for detecting differences in gene expression between two microarray samples with replicates using Monte Carlo simulations. When data are generated from a normal distribution, type I errors and powers of the one-sample parametric t-test and one-sample permutation test are very close, as are the two-sample t-test and two-sample permutation test, provided that the number of replicates is adequate. When data are generated from a t-distribution, the permutation tests outperform the corresponding parametric tests if the number of replicates is at least five. For data from a two-color dye swap experiment, the one-sample test appears to perform better than the two-sample test since expression measurements for control and treatment samples from the same spot are correlated. For data from independent samples, such as the one-channel array or two-channel array experiment using reference design, the two-sample t-tests appear more powerful than the one-sample t-tests.     

Comparing Two Samples of Response Curves by Nonparamètric Tests of Predicted Order

Starting from MOSTELLER'S (1955) one-sample test of predicted order, some two-sample versions are proposed for comparing nonparametrically a treatment group (m response curves) with a control group (n response curves) as to a predicted shape represented by a specified rank order. The tests are applied to two groups of learning curves.     

Exact,Distribution Free Confidence Intervals for Late Effects in Censored Matched Pairs

When comparing censored survival times for matched treated and control subjects, a late effect on survival is one that does not begin to appear until some time has passed. In a study of provider specialty in the treatment of ovarian cancer, a late divergence in the Kaplan–Meier survival curves hinted at superior survival among patients of gynecological oncologists, who employ chemotherapy less intensively, when compared to patients of medical oncologists, who employ chemotherapy more intensively; we ask whether this late divergence should be taken seriously. Specifically, we develop exact, permutation tests, and exact confidence intervals formed by inverting the tests, for late effects in matched pairs subject to random but heterogeneous censoring. Unlike other exact confidence intervals with censored data, the proposed intervals do not require knowledge of censoring times for patients who die. Exact distributions are consequences of two results about signs, signed ranks, and their conditional independence properties. One test, the late effects sign test, has the binomial distribution; the other, the late effects signed rank test, uses nonstandard ranks but nonetheless has the same exact distribution as Wilcoxon's signed rank test. A simulation shows that the late effects signed rank test has substantially more power to detect late effects than do conventional tests. The confidence statement provides information about both the timing and magnitude of late effects (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparing Survival Curves Using Rank Tests

Survival times of patients can be compared using rank tests in various experimental setups, including the two-sample case and the case of paired data. Attention is focussed on two frequently occurring complications in medical applications: censoring and tail alternatives. A review is given of the author's recent work on a new and simple class of censored rank tests. Various models for tail alternatives are discussed and the relation to censoring is demonstrated.     

删失数据下非线性半参数回归模型中参数的经验似然推断

考察了响应变量在随机删失情形下的非线性半参数回归模型,构造了未知参数的经验对数似然比统计量和调整经验对数似然比统计量,证明在一定条件下,所构造的经验似然比统计量渐近于X~2分布,并由此构造出未知参数的置信域.此外,又构造了未知参数的最小二乘估计量,证明了它的渐近性质.通过模拟研究表明,经验似然方法在置信域的覆盖概率以及精度方面要优于最小二乘法.     

One- and Two-Sample Tests of Kendall's τ

Several methods of testing general one-sample and two-sample hypotheses of Kendall's τ are discussed. The performance of these procedures in typical situations likely to occur in practice was investigated by numerous Monte Carlo experiments. The common one-sample test (H₀: τ = 0) based on the permutational variance performs very similar to bootstrap or jackknife testing for true τ near zero. For true |τ| perhaps greater than 0.4 and moderate sample sizes bootstrap techniques are the methods of choice.     

Generalized maximally selected statistics

SUMMARY: Maximally selected statistics for the estimation of simple cutpoint models are embedded into a generalized conceptual framework based on conditional inference procedures. This powerful framework contains most of the published procedures in this area as special cases, such as maximally selected chi(2) and rank statistics, but also allows for direct construction of new test procedures for less standard test problems. As an application, a novel maximally selected rank statistic is derived from this framework for a censored response partitioned with respect to two ordered categorical covariates and potential interactions. This new test is employed to search for a high-risk group of rectal cancer patients treated with a neo-adjuvant chemoradiotherapy. Moreover, a new efficient algorithm for the evaluation of the asymptotic distribution for a large class of maximally selected statistics is given enabling the fast evaluation of a large number of cutpoints.     

Weighted Kaplan-Meier statistics: a class of distance tests for censored survival data

A class of statistics based on the integrated weighted difference in Kaplan-Meier estimators is introduced for the two-sample censored data problem. With positive weight functions these statistics are intuitive for and sensitive against the alternative of stochastic ordering. The standard weighted log-rank statistics are not always sensitive against this alternative, particularly if the hazard functions cross. Qualitative comparisons are made between the weighted log-rank statistics and these weighted Kaplan-Meier (WKM) statistics. A statement of null asymptotic distribution theory is given and the choice of weight function is discussed in some detail. Results from small-sample simulation studies indicate that these statistics compare favorably with the log-rank procedure even under the proportional hazards alternative, and may perform better than it under the crossing hazards alternative.     

Nonparametric rank-based methods for group sequential monitoring of paired censored survival data

This research gives methods for nonparametric sequential monitoring of paired censored survival data in the two-sample problem using paired weighted log-rank statistics with adjustments for dependence in survival and censoring outcomes. The joint asymptotic closed-form distribution of these sequentially monitored statistics has a dependent increments structure. Simulations validating operating characteristics of the proposed methods highlight power and size consequences of ignoring even mildly correlated data. A motivating example is presented via the Early Treatment Diabetic Retinopathy Study.     

Space-time clustering tests for more than two samples.

The two-sample randomization tests for space-time clustering of Klauber are extended to cases with more than two samples. The approach is that of Mantel's one-sample test. The q-sample test provides the opportunity to test up to 2q-1 different models, depending on which of one or more of the q samples are considered random. A normal approximation is provided. An example using contrived data is used to illustrate the computations. An additional example using actual human, canine and feline leukemia and lymphoma is provided, and for this example an "analysis of clustering" table, comparable to tables for the analysis of variance is shown.     

Rank tests for survival analysis: a comparison by analogy with games

Several commonly used two-sample linear rank tests for censored data have been shown to be closely linked in mathematical structure. This pedagogical paper elucidates the relationships among the tests by introducing a videogame played between a boys' team and a girls' team with different rules of payment by the consecutive losers considered. Depending on the rule of payment, the total amount of money the girls win as a team becomes the Wilcoxon statistic, the Savage statistic, or their generalizations under censoring.     

Accounting for variability in the use of permutation testing to detect quantitative trait loci

Locating quantitative trait loci (QTL), or genomic regions associated with known molecular markers, is of increasing interest in a wide variety of applications ranging from human genetics to agricultural genetics. The hope of locating QTL (or genes) affecting a quantitative trait is that it will lead to characterization and possible manipulations of these genes. However, the complexity of both statistical and genetic issues surrounding the location of these regions calls into question the asymptotic statistical results supplying the distribution of the test statistics employed. Coupled with the power of current-day computing, permutation theory was reintroduced for the purpose of estimating the distribution of any test statistic used to test for the location of QTL. Permutation techniques have offered an attractive alternative to significance measures based on asymptotic theory. The ideas of permutation testing are extended in this application to include confidence intervals for the thresholds and p-values estimated in permutation testing procedures. The confidence intervals developed account for the Monte Carlo error associated with practical applications of permutation testing and lead to an effective method of determining an efficient permutation sample size.     

Constructing Confidence Intervals for Qtl Location

We describe a method for constructing the confidence interval of the QTL location parameter. This method is developed in the local asymptotic framework, leading to a linear model at each position of the putative QTL. The idea is to construct a likelihood ratio test, using statistics whose asymptotic distribution does not depend on the nuisance parameters and in particular on the effect of the QTL. We show theoretical properties of the confidence interval built with this test, and compare it with the classical confidence interval using simulations. We show in particular, that our confidence interval has the correct probability of containing the true map location of the QTL, for almost all QTLs, whereas the classical confidence interval can be very biased for QTLs having small effect.     

Nonparametric estimation and testing in a cure model.

Nonparametric generalized maximum likelihood product limit point estimators and confidence intervals are given for a cure model with random censorship. One-, two-, and K-sample likelihood ratio tests for inference on the cure rates are developed. In the two-sample case its power is compared to the power of several alternatives, including the log-rank and Gray and Tsiatis (1989, Biometrics 45, 899-904) tests. Implications for the use of the likelihood ratio test in a clinical trial designed to compare cure rates are discussed.     

A qualitative discrepancy between censored data rank tests.

Two popular censored data rank tests were used to compare cancer incidence rates between dogs receiving bone marrow transplantation and control dogs. The logrank test gave a significance level of 0.01. In contrast, Gehan's generalized Wilcoxon test gave a significance level of 0.76. The statistics are displayed in a manner that shows how such contrasting significance levels can arise. The Gehan statistic is shown to be subject to a serious criticism that does not apply to other Wilcoxon generalizations. Further insight into the data is obtained using a time-dependent logrank test and the proportional hazards regression model.     

Some Results on the Tukey-Mclaughlin and Yuen Methods for Trimmed Means when Distributions are Skewed

In applied work, distributions are often highly skewed with heavy tails, and this can have disastrous consequences in terms of power when comparing groups based on means. One solution to this problem in the one-sample case is to use the TUKEY and MCLAUGHLIN (1963) method for trimmed means, while in the two-group case YUEN's (1974) method can be used. Published simulations indicate that they yield accurate confidence intervals when distributions are symmetric. Using a Cornish-Fisher expansion, this paper extends these results by describing general circumstances under which methods based on trimmed means can be expected to give more accurate confidence intervals than those based on means. The results cover both symmetric and asymmetric distributions. Simulations are also used to illustrate the accuracy of confidence intervals using trimmed means versus means.     

Applications of the Mantel-Haenszel statistic to the comparison of survival distributions.

In comparing two survival distributions, a Mantel-Haenszel statistic can be computed after each death as a non-linear two-sample rank statistic. The distributions of both the maximum and terminal statistics in such a sequence are studied numerically, in the absence of censoring, and appropriate critical values are determined. The maximum statistic is applied to simultaneous inference, and both the maximum and terminal statistics are used as the basis for early stopping procedures (especially in the pseudo-sequential context). Procedures based on the two statistics are compared for power and for early decision properties such as stopping index and (for exponential distributions) stopping time.