Comparison of two independent life tests subject to type II censoring

The problem of comparing two life distributions is considered. It Is assumed that each life test Is stopped after a predetermined number of failures without regard to the number of failures which have occurred in the other life test. A generalized Wilcoxon-rlann-Whitney test is proposed. Small and large sample distributional results are obtained for the test statistic. Under the assumption that the life distributions differ by at most a scale parameter an exact confidence interval for that parameter is obtained. An algorithm for computing the interval is given.     

Rate of consistency of one sample tests of location

Let X₁,…,X_n be a sample from a population with continuous distribution function F(x?θ) such that F(x)+F(-x)=1 and 0<F(x)<1, x?R¹. It is shown that the power- function of a monotone test of H: θ=θ₀ against K: θ>θ₀ cannot tend to 1 as θ?θ₀ → ∞ more than n times faster than the tails of F tend to 0. Some standard as well as robust tests are considered with respect to this rate of convergence.     

Young chains and rank orders

Savage (1956) obtained an easily applied necessary condition for the admissibility of two-sample rank tests under alternatives having a monotone likelihood ratio. This condition is: rank order Z is more likely than rank order Z' if the Z-path is above the Z'-path in Young's lattice. This condition is easily applied and allows not only the proof of the inadmissibility of the Wilcoxon test under Lehmann alternatives but it can also be used to construct explicitly uniformly better tests. For Lehmann alternatives, we obtain another necessary criterion on rank orders which makes use of dominance.     

Rank Tests for Clustered Survival Data

In a clinical trial, we may randomize subjects (called clusters) to different treatments (called groups), and make observations from multiple sites (called units) of each subject. In this case, the observations within each subject could be dependent, whereas those from different subjects are independent. If the outcome of interest is the time to an event, we may use the standard rank tests proposed for independent survival data, such as the logrank and Wilcoxon tests, to test the equality of marginal survival distributions, but their standard error should be modified to accommodate the possible intracluster correlation. In this paper we propose a method of calculating the standard error of the rank tests for two-sample clustered survival data. The method is naturally extended to that for K-sample tests under dependence.     

Nonparametric confidence intervals for location in time series data

We extend the confidence interval construction procedure for location for symmetric iid data using the one-sample Wilcoxon signed rank statistic (T⁺) to stationary time series data. We propose a normal approximation procedure when explicit knowledge of the underlying dependence structure/distribution is unknown. By conducting extensive simulations from linear and nonlinear time series models, we show that the extended procedure is a strong contender for use in the construction of confidence intervals in time series analysis. Finally we demonstrate real application implementations in two case studies.     

On the three-way equivalence of AUC in credit scoring with tied scores

In credit scoring, it is well known that AUC (the area under curve) can be calculated geometrically, by the probability of a correct ranking of a good and bad pair, and by the Wilcoxon Rank-Sum statistic. This three-way equivalence was first present by Hanley and McNeil in 1982 without considering tied scores and without giving analytical proofs. In this paper, we extend the three-way equivalence to the case with tied scores and provide analytic proofs for the three-way equivalence.     

Nonparametric Two‐Sample Tests of the Marginal Mark Distribution with Censored Marks

Occasionally, investigators collect auxiliary marks at the time of failure in a clinical study. Because the failure event may be censored at the end of the follow‐up period, these marked endpoints are subject to induced censoring. We propose two new families of two‐sample tests for the null hypothesis of no difference in mark‐scale distribution that allows for arbitrary associations between mark and time. One family of proposed tests is a nonparametric extension of an existing semi‐parametric linear test of the same null hypothesis while a second family of tests is based on novel marked rank processes. Simulation studies indicate that the proposed tests have the desired size and possess adequate statistical power to reject the null hypothesis under a simple change of location in the marginal mark distribution. When the marginal mark distribution has heavy tails, the proposed rank‐based tests can be nearly twice as powerful as linear tests.     

Approximated non parametric confidence regions for the ratio of two percentiles

In the wood industry, it is common practice to compare in terms of the ratio of the same-strength properties for lumber of two different dimensions, grades, or species. Because United States lumber standards are given in terms of population fifth percentile, and strength problems arise from the weaker fifth percentile rather than the stronger mean, so the ratio should be expressed in terms of the fifth percentiles rather than the means of two strength distributions. Percentiles are estimated by order statistics. This paper assumes small samples to derive new non parametric methods such as percentile sign test and percentile Wilcoxon signed rank test, construct confidence intervals with covergage rate 1 – αx for single percentiles, and compute confidence regions for ratio of percentiles based on confidence intervals for single percentiles. Small 1 – αx is enough to obtain good coverage rates of confidence regions most of the time.     

A comparative study of tests for paired lifetime data

In this paper, we investigate different procedures for testing the equality of two mean survival times in paired lifetime studies. We consider Owen’s M-test and Q-test, a likelihood ratio test, the paired t-test, the Wilcoxon signed rank test and a permutation test based on log-transformed survival times in the comparative study. We also consider the paired t-test, the Wilcoxon signed rank test and a permutation test based on original survival times for the sake of comparison. The size and power characteristics of these tests are studied by means of Monte Carlo simulations under a frailty Weibull model. For less skewed marginal distributions, the Wilcoxon signed rank test based on original survival times is found to be desirable. Otherwise, the M-test and the likelihood ratio test are the best choices in terms of power. In general, one can choose a test procedure based on information about the correlation between the two survival times and the skewness of the marginal survival distributions.