An exact test for trend among binomial proportions based on a modified Baumgartner-Weiß-Schindler statistic

The Cochran-Armitage test is the most frequently used test for trend among binomial proportions. This test can be performed based on the asymptotic normality of its test statistic or based on an exact null distribution. As an alternative, a recently introduced modification of the Baumgartner-Weiß-Schindler statistic, a novel nonparametric statistic, can be used. Simulation results indicate that the exact test based on this modification is preferable to the Cochran-Armitage test. This exact test is less conservative and more powerful than the exact Cochran-Armitage test. The power comparison to the asymptotic Cochran-Armitage test does not show a clear winner, but the difference in power is usually small. The exact test based on the modification is recommended here because, in contrast to the asymptotic Cochran-Armitage test, it guarantees a type I error rate less than or equal to the significance level. Moreover, an exact test is often more appropriate than an asymptotic test because randomization rather than random sampling is the norm, for example in biomedical research. The methods are illustrated with an example data set.     

A new two-sample test for choosing between log-rank and Wilcoxon tests with right-censored data

When differences of survival functions are located in early time, a Wilcoxon test is the best test, but when differences of survival functions are located in late time, using a log-rank test is better. Therefore, a researcher needs a stable test in these situations. In this paper, a new two-sample test is proposed and considered. This test is distribution-free. This test is useful for choosing between log-rank and Wilcoxon tests. Its power is roughly the maximal power of the log-rank test and Wilcoxon test.     

A weighted log-rank test and associated effect estimator for cancer trials with delayed treatment effect

The standard log-rank test has been extended by adopting various weight functions. Cancer vaccine or immunotherapy trials have shown a delayed onset of effect for the experimental therapy. This is manifested as a delayed separation of the survival curves. This work proposes new weighted log-rank tests to account for such delay. The weight function is motivated by the time-varying hazard ratio between the experimental and the control therapies. We implement a numerical evaluation of the Schoenfeld approximation (NESA) for the mean of the test statistic. The NESA enables us to assess the power and to calculate the sample size for detecting such delayed treatment effect and also for a more general specification of the non-proportional hazards in a trial. We further show a connection between our proposed test and the weighted Cox regression. Then the average hazard ratio using the same weight is obtained as an estimand of the treatment effect. Extensive simulation studies are conducted to compare the performance of the proposed tests with the standard log-rank test and to assess their robustness to model mis-specifications. Our tests outperform the G^ρ,γ class in general and have performance close to the optimal test. We demonstrate our methods on two cancer immunotherapy trials.     

Exact power computation for stratified dose-response studies

Toxicological and pharmaceutical studies often use the stratified dose-response design. This paper deals with the problem of exact power computation for such a design. Recourse to exact methods is advised in study with sparse data. We give three algorithms for exact power calculation and apply them to three data sets. The algorithms include an exact power computation approach and two alternatives to further reduce the computation time: a -precision approach and Monte Carlo approach. Four exact and two asymptotic tests are used for illustration.     

Robust test for independence in high dimensions

This article develops a new test based on Spearman’s rank correlation coefficients for total independence in high dimensions. The test is robust to the non normality and heavy tails of the data, which is a merit that is not shared by the existing tests in literature. Simulation results suggest that the new test performs well under several typical null and alternative hypotheses. Besides, we employ a real data set to illustrate the use of the new test.     

An exact two-sample test based on the baumgartner-weiss-schindler statistic and a modification of lepage's test

It is shown that the nonparametric two-saniDle test recently proposed by Baumgartner, WeiB, Schindler (1998, Biometrics, 54, 1129-1135) does not control the type I error rate in case of small sample sizes. We investigate the exact permutation test based on their statistic and demonstrate that this test is almost not conservative. Comparing exact tests, the procedure based on the new statistic has a less conservative size and is, according to simulation results, more powerful than the often employed Wilcoxon test. Furthermore, the new test is also powerful with regard to less restrictive settings than the location-shift model. For example, the test can detect location-scale alternatives. Therefore, we use the test to create a powerful modification of the nonparametric location-scale test according to Lepage (1971, Biometrika, 58, 213-217). Selected critical values for the proposed tests are given.     

The two-sample problem with multivariate censored data: a new rank test family

A new rank test family is proposed to test the equality of two multivariate failure times distributions with censored observations. The tests are very simple: they are based on a transformation of the multivariate rank vectors to a univariate rank score and the resulting statistics belong to the familiar class of the weighted logrank test statistics. The new procedure is also applicable to multivariate observations in general, such as repeated measures, some of which may be missing. To investigate the performance of the proposed tests, a simulation study was conducted with bivariate exponential models for various censoring rates. The size and power of these tests against Lehmann alternatives were compared to the size and power of two other tests (Wei and Lachin, 1984 and Wei and Knuiman, 1987). In all simulations the new procedures provide a relatively good power and an accurate control over the size of the test. A real example from the National Cooperative Gallstone Study is given     

右删失数据风险函数直方图估计

鉴于生存分析中风险函数较生存函数更能反映生存数据内在失效机制,基于累计风险函数的Nelson-Aalen估计量,构造了右删失数据风险函数的新直方图估计量,并对该估计量的偏差、方差、积分均方误差等统计性质进行了论证,对该估计量的使用注意事项进行了说明,通过数值模拟进一步说明了新估计量的合理性。     

Goodness of Fit Tests for Multivariate Counting Process Models with Applications

In this paper, we develop some distribution-free tests for checking the adequacy of the parametric forms of the intensity processes of a multivariate counting process model. The proposed tests, based in Khmaladze's transformations, are derived from the transforms of weighted aggregated martingale residual processes. The transformed processes converge weakly to independent Gaussian martingales under the assumed model. The distribution-free tests, such as Kolmogorov–Smirnov and Cramer–von Mises type tests, are appropriately defined to account for deviations in each of the transformed aggregated martingale residual processes. Consistency of the tests are discussed. The tests are applicable to multiplicative intensity models such as a competing risks model as well as to non-multiplicative intensity models such as a constant relative or excess mortality model. A small simulation study is conducted and an illustration to a real data example is provided.     

A Class of Permutation Tests for the Equality of Two Marginal Survival Functions Using Paired Censored Data

We studied several test statistics for testing the equality of marginal survival functions of paired censored data. The null distribution of the test statistics was approximated by permutation. These tests do not require explicit modeling or estimation of the within-pair correlation, accommodate both paired data and singletons, and the computation is straightforward with most statistical software. Numerical studies showed that these tests have competitive size and power performance. One test statistic has higher power than previously published test statistics when the two survival functions under comparison cross. We illustrate use of these tests in a propensity score matched dataset.     

Estimation of conditional mode with truncated,censored, and dependent data

In this paper, we studied the uniform convergence with rates for the kernel estimator of the conditional mode function for a left truncated and right censored model. It is assumed that the lifetime observations with multivariate covariates form a stationary α-mixing sequence. Also, the asymptotic normality of the estimator is established.     

A resampling‐based test for two crossing survival curves

The area between two survival curves is an intuitive test statistic for the classical two‐sample testing problem. We propose a bootstrap version of it for assessing the overall homogeneity of these curves. Our approach allows ties in the data as well as independent right censoring, which may differ between the groups. The asymptotic distribution of the test statistic as well as of its bootstrap counterpart are derived under the null hypothesis, and their consistency is proven for general alternatives. We demonstrate the finite sample superiority of the proposed test over some existing methods in a simulation study and illustrate its application by a real‐data example.     

Rank tests for independence based on partially right-censored pairs

Linear rank procedures are developed for testing independence with right-censored matched pairs. It is assumed that censoring Is Independent of the random variables under study. The test statistics are derived as score statistics (Hajek and Sidak, 1967) based on the probability of the generalised rank vectors (Prentice, 1978). Applications to survival data analysis are also discussed.     

Modifying the exact test for a binomial proportion and comparisons with other approaches

In this note we provide a simple continuity and tail-corrected approach to the standard exact test for a single binomial proportion commonly used in practice. We redefine the p-value for the two-sided alternative by noting the skewed distribution of the sample proportion under the null hypothesis. We illustrate that for both one and two-sided alternatives the coverage probabilities of the new methodology approaches more closely the desired type I error α and thus recommend these modifications to the applied statistician for consideration.     

Inefficiency of inferences with the partial likelihood

In two-sample semiparametric survival models other than the Cox proportional-hazards regression model, it is shown that partial-likelihood inference of structural parameters in the presence of fully nonpararnetric nuisance-hazards typically has relative efficiency zero compared with fuii-Iikelihood infer -ence. The practical Interpretation of efficiencies in the pres-ence of infinite-dimensional nuisance-parameters is discussed, with reference to two important examples, namely a recent sur-vival regression-model of Clayton and Cuzick and a class of additive excess-risk models. Under the excess-risk models, a formula is derived for the large-sample information [which here is the same as the limiting Fisher information when the nuisance-parameter dimension gets large] for estimating the parameter of difference between two samples, as the nuisance function becomes fully nonpararnetric.     

Logrank test for bivariate survival data

The logrank test procedure for testing bivariate symmetry against asymmetry in matched-pair data is proposed. The presented test statistic is based on Mantel-Haenszel type statistics evaluated at diagonal grid points on the plane obtained from distinct uncensored failure times. The asymptotic results of the proposed test are derived and an example is shown to illustrate the methodology.     

Transform methods for the hypergeometric distribution

Two new methods for computing with hypergeometric distributions on lattice points are presented. One uses Fourier analysis, and the other uses Gröbner bases in the Weyl algebra. Both are very general and apply to log-linear models that are graphical or non-graphical.     

Extension of two-sided test to multiple treatment trials

In a two-treatment trial, a two-sided test is often used to reach a conclusion, Usually we are interested in doing a two-sided test because of no prior preference between the two treatments and we want a three-decision framework. When a standard control is just as good as the new experimental treatment (which has the same toxicity and cost), then we will accept both treatments. Only when the standard control is clearly worse or better than the new experimental treatment, then we choose only one treatment. In this paper, we extend the concept of a two-sided test to the multiple treatment trial where three or more treatments are involved. The procedure turns out to be a subset selection procedure; however, the theoretical framework and performance requirement are different from the existing subset selection procedures. Two procedures (exclusion or inclusion) are developed here for the case of normal data with equal known variance. If the sample size is large, they can be applied with unknown variance and with the binomial data or survival data with random censoring.     

Marshall-Olkin extended weibull distribution and its application to censored data

In this paper we show that the Marshall-Olkin extended Weibull distribution can be obtained as a compound distribution with mixing exponential distribution. In addition, we provide simple sufficient conditions for the shape of the hazard rate function of the distribution. Moreover, we extend the considered distribution to accommodate randomly right censored data. Finally, application of the extended distribution to a data set representing the remission times of bladder cancer patients is given and its goodness-of-fit is demonstrated.     

A circular test of association between a point process and a continuous time series

A test of association between a point process and a continuous time series is proposed. The test is exact for a general class of point processes, including Poisson processes. Simulation results for a Poisson point process are reported.