Flexible weighted log-rank tests optimal for detecting early and/or late survival differences

At the present time, many AIDS clinical trials compare drug therapies by a time-to-event primary endpoint that measures the durability of suppression of HIV replication. For such studies, survival differences tend to occur early and/or late in the follow-up period due to drug differences in initial potency and/or durability of efficacy, and detecting these differences is of primary interest. We propose a weighted log-rank statistic that emphasizes early and/or late survival differences. We also consider some versatile tests that also emphasize these differences but are sensitive to a wider range of alternatives. The performances of the new tests are evaluated in numerical studies. For the alternatives of interest, the new tests show greater power and flexibility than commonly used weighted log-rank tests and related versatile tests. When the main interest is in detecting early and/or late survival differences, these tests may be preferable to the other versatile and weighted log-rank tests that have been studied.     

Taste sensitivities to PROP and PTC vary independently in mice

Mammals use common mechanisms to detect, transduce and process taste stimulus information. For example, they share families of receptors that respond to amino acids, and sweet- and bitter-tasting stimuli. Nonetheless, it also clear that different species exhibit unique taste sensitivities that may reflect specific genetic variations. In humans, sensitivities to the chemically similar, bitter-tasting compounds 6-n-propylthiouracil (PROP) and phenylthiocarbamide (PTC) are heritable and strongly correlated, suggesting a common genetic basis. However, it is unknown whether PROP and PTC taste sensitivities are similarly correlated in mice. Here we report that PROP and PTC taste sensitivities vary independently between two inbred strains of mice. In brief-access taste tests C3HeB/FeJ (C3) and SWR/J (SW) mice possess similar taste sensitivity to PTC, while SW mice are significantly more sensitive to PROP than are C3 mice. In two-bottle preference tests, however, SW mice display greater aversion to both compounds. This discrepancy may be explained by the observation that SW mice consumed taste solutions at a greater rate during the intake test than did C3 mice. Therefore, PTC avoidance is correlated with the amount of PTC consumed in the intake tests rather than the concentration of PTC tested. These findings suggest that post-ingestive factors play a significant role in PTC avoidance during intake tests and highlight an important advantage of brief-access tests over intake tests in resolving the gustatory and post-ingestive contributions to taste-related behaviors. Most strikingly, these results demonstrate that in mice, unlike in humans, PTC and PROP taste sensitivities vary independently, thereby suggesting a subtle functional diversity of bitter-taste mechanisms across mammalian species.     

UMPU and Alternative Tests for Association in 2 × 2 Tables

The use of the uniformly most powerful among the unbiased (UMPU) test was recently suggested for the study of gametic association between two polymorphic loci as an alternative to the Fisher's exact test (Zapata and Alvarez, 1997, Annals of Human Genetics 61, 71-77). However, the proposed test is not UMPU for two-sided alternatives. In this study, we present the UMPU test, discuss criticisms against the use of randomized tests, and compare the power of several tests. We show that, in many practical cases, the use of the UMPU test is less than desirable and propose the alternative adjusted-more extreme tables (A-MET) and the equal-tails (ET) tests. We suggest that some of the general arguments against the use of randomized tests can be alleviated by a newly proposed extended p-value definition.     

Analysis of Randomized Dose-Finding-Studies: Closure Test Modifications Based on Multiple Contrast Tests

The power of single contrast tests strongly depends on the a priori unknown shape of the dose response relationship. Two approaches can be used to overcome this major disadvantage: the likelihood ratio test for order restriction or multiple contrast tests. Within the closure principle, the shape for the different hyptheses varies. Therefore multiple contrast tests are used as trend tests. Based on a simulation study the power advantage of this approach in comparison with single contrast tests is demonstrated.     

Adjusting O'Brien's test to control type I error for the generalized nonparametric Behrens-Fisher problem

O'Brien (1984, Biometrics 40, 1079-1087) introduced a simple nonparametric test procedure for testing whether multiple outcomes in one treatment group have consistently larger values than outcomes in the other treatment group. We first explore the theoretical properties of O'Brien's test. We then extend it to the general nonparametric Behrens-Fisher hypothesis problem when no assumption is made regarding the shape of the distributions. We provide conditions when O'Brien's test controls its error probability asymptotically and when it fails. We also provide adjusted tests when the conditions do not hold. Throughout this article, we do not assume that all outcomes are continuous. Simulations are performed to compare the adjusted tests to O'Brien's test. The difference is also illustrated using data from a Parkinson's disease clinical trial.     

Is the Exact Test Better than the Asymptotic Test for Testing Marginal Homogeneity in 2 × 2 Tables?

McNemar test is commonly used to test for the marginal homogeneity in 2 × 2 contingency tables. McNemar test is an asymptotic test based either on standard normal distribution or on the chi‐square distribution. When the total sample size is small, an exact version of McNemar test is available based on the binomial probabilities. The example in the paper came from a clinical study to investigate the effect of epidermal growth factor for children who had microvillus inclusion diseases. There were only six observations available. The test results differ between the exact test and the asymptotic test. It is a common belief that with this small sample size the exact test be used. However, we claim that McNemar test performs better than the exact test even when the sample size is small. In order to investigate the performances of McNemar test and the exact test, we identify the parameters that affect the test results and then perform sensitivity analysis. In addition, through Monte Carlo simulation studies we compare the empirical sizes and powers of these tests as well as other asymptotic tests such as Wald test and the likelihood ratio test.     

The use of score tests for inference on variance components

Whenever inference for variance components is required, the choice between one-sided and two-sided tests is crucial. This choice is usually driven by whether or not negative variance components are permitted. For two-sided tests, classical inferential procedures can be followed, based on likelihood ratios, score statistics, or Wald statistics. For one-sided tests, however, one-sided test statistics need to be developed, and their null distribution derived. While this has received considerable attention in the context of the likelihood ratio test, there appears to be much confusion about the related problem for the score test. The aim of this paper is to illustrate that classical (two-sided) score test statistics, frequently advocated in practice, cannot be used in this context, but that well-chosen one-sided counterparts could be used instead. The relation with likelihood ratio tests will be established, and all results are illustrated in an analysis of continuous longitudinal data using linear mixed models.     

Wald Tests of Location for Symmetric Nonnormal Data

For nonnormal data we suggest a test of location based on a broader family of distributions than normality. Such a test will in a sense fall between the standard parametric and non parametric tests. We see that the Wald tests based on this family of distributions have some advantages over the score tests and that they perform well in comparison to standard parametric and nonparametric tests in a variety of situations. We also consider when and how to apply such tests in practice.     

A class of permutation tests for stratified survival data

We propose a class of permutation tests for stratified survival data. The tests are derived using the framework of Fay and Shih (1998, Journal of the American Statistical Association 93, 387-396), which creates tests by permuting scores based on a functional of estimated distribution functions. Here the estimated distribution function for each possibly right-, left-, or interval-censored observation is based on a shrinkage estimator similar to the nonparametric empirical estimator of Ghosh, Lahiri, and Tiwari (1989, Communications in Statistics--Theory and Methods 18, 121-146), and permutation is carried out within strata. The proposed test with a weighted Mann-Whitney functional is similar to the permutation form of the stratified log-rank test when there is a large strata effect or the sample size in each stratum is large and is similar to the permutation form of the ordinary log-rank test when there is little strata effect. Thus, the proposed test unifies the advantages of both the stratified and ordinary log-rank tests. By changing the functional, we may obtain a stratified Prentice-Wilcoxon test or a difference in means test with similar unifying properties. We show through simulations the advantage of the proposed test over existing tests for uncensored and right-censored data.     

Trend Test for Overdispersed Proportions

The Cochran-Armitage test has commonly been used for a trend test in binomial proportions. The quasi-likelihood method provides a simple approach to model extra-binomial proportions. Two versions of the score and Wald tests using different parameterizations for the extra-binomial variance were investigated: one in terms of intercluster correlation, and another in terms of variance. The Monte Carlo simulation was used to evaluate the performance of the each version of the score test and the Wald test, and the Cochran-Armitage test. The simulation shows that the Cochran-Armitage test has the proper size only for the binomial sample data, and the test is no longer valid when applied to the extra-binomial data. The Wald test is more likely to exceed the nominal level than the score test under either intercluster correlation model or variance model. Both score tests performed very well even with the binomial data; the tests control the type I error and in the meantime maintain the power of detecting the dose effects. Based on the design considered in this paper, the two scores test are comparable. The score test based on the intercluster correlations model seems better controlling the Type I error but appears less powerful than that based on the variance model. An example from a developmental toxicity experiment is given.