Significance Levels of Randomization Trend Tests in the Event of Rare Occurrences

In the statistical evaluation of data from a dose-response experiment, it is frequently of interest to test for dose-related trend: an increasing trend in response with increasing dose. The randomization trend test, a generalization of Fisher's exact test, has been recommended for animal tumorigenicity testing when the numbers of tumor occurrences are small. This paper examines the type I error of the randomization trend test, and the Cochran-Armitage and Mantel-Haenszel tests. Simulation results show that when the tumor incidence rates are less than 10%, the randomization test is conservative; the test becomes very conservative when the incidence rate is less than 5%. The Cochran-Armitage and Mantel-Haenszel tests are slightly anti-conservative (liberal) when the incidence rates are larger than 3%. Further, we propose a less conservatived method of calculating the p-value of the randomization trend test by excluding some permutations whose probabilities of occurrence are greater than the probability of the the observed outcome.     

Prolonged conservative care versus early surgery in patients with sciatica caused by lumbar disc herniation: two year results of a randomised controlled trial

Objectives To evaluate the effects of early lumbar disc surgery compared with prolonged conservative care for patients with sciatica over two years of follow-up.Design Randomised controlled trial.Setting Nine Dutch hospitals.Participants 283 patients with 6-12 weeks of sciatica.Interventions Early surgery or an intended six months of continued conservative treatment, with delayed surgery if needed.Main outcome measures Scores from Roland disability questionnaire for sciatica, visual analogue scale for leg pain, and Likert self rating scale of global perceived recovery.Results Of the 141 patients assigned to undergo early surgery, 125 (89%) underwent microdiscectomy. Of the 142 patients assigned to conservative treatment, 62 (44%) eventually required surgery, seven doing so in the second year of follow-up. There was no significant overall difference between treatment arms in disability scores during the first two years (P=0.25). Improvement in leg pain was faster for patients randomised to early surgery, with a significant difference between “areas under the curves” over two years (P=0.05). This short term benefit of early surgery was no longer significant by six months and continued to narrow between six months and 24 months. Patient satisfaction decreased slightly between one and two years for both groups. At two years 20% of all patients reported an unsatisfactory outcome.Conclusions Early surgery achieved more rapid relief of sciatica than conservative care, but outcomes were similar by one year and these did not change during the second year.Trial Registry ISRCT No 26872154.     

Choice of Scores in Trend Tests for Case‐Control Studies of Candidate‐Gene Associations

When applying the Cochran‐Armitage (CA) trend test for an association between a candidate allele and a disease in a case‐control study, a set of scores must be assigned to the genotypes. Sasieni (1997, Biometrics 53 , 1253–1261) suggested scores for the recessive, additive, and dominant models but did not examine their statistical properties. Using the criteria of minimizing the required sample size of the CA trend test to achieve prespecified type I and type II errors, we show that the scores given by Sasieni (1997) are optimal for the recessive and dominant models and locally optimal for the additive one. Moreover, the additive scores are shown to be locally optimal for the multiplicative model. The tests are applied to a real dataset.     

A note on P-values for two-sided tests

Based on uniformly most powerful unbiased (UMPU) tests for two-sided hypotheses and a short note in Lehmann (1959) on critical levels for randomized tests, Meulepas (1998, 1999) proposed (two-tailed) P -values taking into account the randomization constant(s) of the UMPU-tests. While UMPU-tests need an extra uniform observation if randomization is required, the P -values proposed by Meulepas need no extra uniform observation. At first glance, his idea looks very promising in order to define a suitable and powerful P -value. Unfortunately, such P -values are generally too conservative.     

An analysis of preliminary and post-discussion priority scores for grant applications peer reviewed by the Center for Scientific Review at the NIH

There has been the impression amongst many observers that discussion of a grant application has little practical impact on the final priority scores. Rather the final score is largely dictated by the range of preliminary scores given by the assigned reviewers. The implication is that the preliminary and final scores are the same and the discussion has little impact. The purpose of this examination of the peer review process at the National Institutes of Health is to describe the relationship between preliminary priority scores of the assigned reviewers and the final priority score given by the scientific review group. This study also describes the practical importance of any differences in priority scores. Priority scores for a sample of standard (R01) research grant applications were used in this assessment. The results indicate that the preliminary meeting evaluation is positively correlated with the final meeting outcome but that they are on average significantly different. The results demonstrate that discussion at the meeting has an important practical impact on over 13% of the applications.     

Non-inferiority of new procedure to standard procedure in stratified matched-pair design

We consider the statistical testing for non-inferiority of a new treatment compared with the standard one under matched-pair setting in a stratified study or in several trials. A non-inferiority test based on the efficient scores and a Mantel-Haenszel (M-H) like procedure with restricted maximum likelihood estimators (RMLEs) of nuisance parameters and their corresponding sample size formulae are presented. We evaluate the above tests and the M-H type Wald test in level and power. The stratified score test is conservative and provides the best power. The M-H like procedure with RMLEs gives an accurate level. However, the Wald test is anti-conservative and we suggest caution when it is used. The unstratified score test is not biased but it is less powerful than the stratified score test when base-line probabilities related to strata are not the same. This investigation shows that the stratified score test possesses optimum statistical properties in testing non-inferiority. A common difference between two proportions across strata is the basic assumption of the stratified tests, we present appropriate tests to validate the assumption and related remarks.     

Sequentially Rejective Test Procedures for Detecting Outlying Cells in One- and Two-Sample Multinomial Experiments

For multiple testing of multinomial models in the case of one or two samples we propose using test procedures based on the principle described by MARCUS, PERITZ and GABRIEL (1976). These methods are based in each step of the sequentially rejective strategy on tests which exhaust the full α level (i.e. which are not conservative). The tests can be performed in a finite or asymptotic version.     

Testing the Intraclass Version of Kappa Coeffcient of Agreement with Binary Scale and Sample Size Determination

The intraclass version of kappa coefficient has been commonly applied as a measure of agreement for two ratings per subject with binary outcome in reliability studies. We present an efficient statistic for testing the strength of kappa agreement using likelihood scores, and derive asymptotic power and sample size formula. Exact evaluation shows that the score test is generally conservative and more powerful than a method based on a chi‐square goodness‐of‐fit statistic (Donner and Eliasziw , 1992, Statistics in Medicine 11 , 1511–1519). In particular, when the research question is one directional, the one‐sided score test is substantially more powerful and the reduction in sample size is appreciable.     

Drawbacks to noninteger scoring for ordered categorical data

A proposal to improve trend tests by using noninteger scores is examined. It is concluded that despite improved power such tests are usually inferior to the simpler integer scored approach.     

Testing for multiple species in fossil samples: an evaluation and comparison of tests for equal relative variation

Tests for equal relative variation are valuable and frequently used tools for evaluating hypotheses about taxonomic heterogeneity in fossil hominids. In this study, Monte Carlo methods and simulated data are used to evaluate and compare 11 tests for equal relative variation. The tests evaluated include CV-based parametric bootstrap tests, modifications of Levene's test, and modified weighted scores tests. The results of these simulations show that a modified version of the weighted scores test developed by Fligner and Killeen ([1976] J. Am. Stat. Assoc. 71:210-213) is the only test that maintains an acceptable balance of type I and type II errors, even under conditions where all other tests have extraordinarily high type I error rates or little power.     

Comparison of independent samples of high-dimensional data by pairwise distance measures

Pairwise distance or association measures of sample elements are often used as a basis for hierarchical cluster analyses. They can also be used in tests for the comparison of pre-defined subgroups of the total sample. Usually this is done with permutation tests In this paper, we compare such a procedure with alternative tests for high-dimensional data based on spherically distributed scores in simulation experiments and with real data. The tests based on the pairwise distance or similarity measures perform quite well in this comparison. As the number of possible permutations is small in very small samples, this might restrict the use of the test. Therefore, we propose an exact parametric small sample version of the test using randomly rotated samples.     

A Simple Method to Obtain all the Sample-Values and their Probabilities of the Wald-Wolfowitz Test Statistics in the Existence of Ties

In order to carry out non-conservative tests in the general two-sample problem with ties, we want to know all possible sample-values of the used test statistics and their occurrence probabilities as well. But this knowledge can be acquired only after very protracted attempts. In the present paper we depict a simple technique for obtaining that without any exertion in the case of the Wald-Wolfowitz test statistic. With that, we then are able to lead the Wald-Wolfowitz test easily and effortlessly in any manner conservative or non-conservative and in the existence of any number and any length of ties.     

Analysis of ordered categorical data: two score-independent approaches

SUMMARY: A trend test is often employed to analyze ordered categorical data, in which a set of increasing scores is assigned a priori. There is a drawback in this approach, because how to choose a set of scores is not clear. There have been debates on which scores should be used (e.g., Graubard and Korn, 1987, Biometrics 43, 471-476; Ivanova and Berger, 2001, Biometrics 57, 567-570; Senn, 2007, Biometrics 63, 296-298). Conflicting conclusions are often obtained with different sets of scores. Two approaches, which have been applied to genetic case-control studies, are appealing for ordered categorical data, because they take into account the natural order in the data, are score independent, and not contingent on asymptotic theory. These two approaches are applied to a prospective study for detecting association between maternal drinking and congenital malformations.     

Allele-sharing models: LOD scores and accurate linkage tests.

Starting with a test statistic for linkage analysis based on allele sharing, we propose an associated one-parameter model. Under general missing-data patterns, this model allows exact calculation of likelihood ratios and LOD scores and has been implemented by a simple modification of existing software. Most important, accurate linkage tests can be performed. Using an example, we show that some previously suggested approaches to handling less than perfectly informative data can be unacceptably conservative. Situations in which this model may not perform well are discussed, and an alternative model that requires additional computations is suggested.     

Carcinogens in the diet vs. overnutrition. Individual dietary habits, malnutrition, and genetic susceptibility modify carcinogenic potency and cancer risk.

Chemical carcinogens in the diet cannot explain the cancer incidence attributed by epidemiologists to dietary factors when the calculation is based on average exposure levels and conservative estimates of carcinogenic potencies. In a previous review, the discrepancy was explained primarily by overnutrition to which a carcinogenic potency was assigned from dietary restriction experiments and the associated reduction in spontaneous tumor incidence (W.K. Lutz and J. Schlatter, Chemical carcinogens and overnutrition in diet-related cancer, Carcinogenesis 13 [1992] 2211-2216). Here, additional aspects are introduced. They focus on using individual rather than averaged data, both for exposure and susceptibility. First, under conditions of a sublinear (convex) dose-response, the cancer incidence obtained by using an average exposure level is lower than if individual exposure levels associated with particular dietary habits are taken into account. Second, carcinogenic factors, including those unrelated to the diet (e.g., smoking), can act synergistically. Third, the potency of dietary carcinogens is increased under conditions of malnutrition in the sense of a deficiency of protective factors, such as those available with fruits, vegetables, and fibers. Quantitatively, this aspect may be particularly important because it simultaneously increases the efficacy of a multitude of carcinogens. It is concluded that chemical carcinogens could be as important as overnutrition for diet-related cancer.     

Bayesian inference on order-constrained parameters in generalized linear models

In biomedical studies, there is often interest in assessing the association between one or more ordered categorical predictors and an outcome variable, adjusting for covariates. For a k-level predictor, one typically uses either a k-1 degree of freedom (df) test or a single df trend test, which requires scores for the different levels of the predictor. In the absence of knowledge of a parametric form for the response function, one can incorporate monotonicity constraints to improve the efficiency of tests of association. This article proposes a general Bayesian approach for inference on order-constrained parameters in generalized linear models. Instead of choosing a prior distribution with support on the constrained space, which can result in major computational difficulties, we propose to map draws from an unconstrained posterior density using an isotonic regression transformation. This approach allows flat regions over which increases in the level of a predictor have no effect. Bayes factors for assessing ordered trends can be computed based on the output from a Gibbs sampling algorithm. Results from a simulation study are presented and the approach is applied to data from a time-to-pregnancy study.     

Testing for group effect in a 2 x k heteroscedastic ANOVA model

It is natural to want to relax the assumption of homoscedasticity and Gaussian error in ANOVA models. For a two-way ANOVA model with 2 x k cells, one can derive tests of main effect for the factor with two levels (referred to as group) without assuming homoscedasticity or Gaussian error. Empirical likelihood can be used to derive testing procedures. An approximate empirical likelihood ratio test (AELRT) is derived for the test of group main effect. To approximate the distributions of the test statistics under the null hypothesis, simulation from the approximate empirical maximum likelihood estimate (AEMLE) restricted by the null hypothesis is used. The homoscedastic ANOVA F -test and a Box-type approximation to the distribution of the heteroscedastic ANOVA F -test are compared to the AELRT in level and power. The AELRT procedure is shown by simulation to have appropriate type I error control (although possibly conservative) when the distribution of the test statistics are approximated by simulation from the constrained AEMLE. The methodology is motivated and illustrated by an analysis of folate levels in the blood among two alcohol intake groups while accounting for gender.     

A computer program for testing average partial association in three-way contingency tables (PARCAT).

PARCAT is a computer program which implements alternative tests for average partial association in three-way contingency tables within the framework of the product multiple hypergeometric probability model. Primary attention is directed at the relationship between two of the variables, controlling for the effects of a covariable. This approach is essentially a multivariate extension of the Cochran/Mantel-Haenszel test to sets of (s x r) tables. A set of scores such as uniform, ridits, or probits can be assigned to categories which are ordinally scaled. In particular, if ridit scores with midranks assigned for ties are utilized, this procedure is equivalent to a partial Kruskal-Wallis test when one variable is ordinally scaled, and is equivalent to a partial Spearman rank correlation test when both variables are ordinally scaled.     

THE ZHOUKOUDIAN UPPER CAVE DENTITION

Much has been written in the last ten years about the origin of anatomically modernEast Asians and their derived populations(Akazawa etal.,1 992 ;Brown,1 998,1 999?;Hanihara,1 994 ;Howells,1 995;Neves,1 998;Omoto,1 995;Pope,1 992 ;Turner,1 992 a,1 992 b;Wu,1 998;many others) .In mostarticles,some consideration is given to the remainsof the seven or more largely incomplete late Pleistocene individuals found in the Zhouk-oudian Upper Cave(Black,1 93 4;Pei,1 93 4;Weidenreich,1 93 8— 1 93 9…     

Neonatal behavioral scoring of common marmosets (Callithrix jacchus): relation to physical condition and survival

A seven-task behavioral test was performed on 86 common marmoset (Callithrix jacchus) infants, 24-36 h following birth. This report describes the test outcome and its relation to physical condition and survival of the infants. The percentage of infants receiving a perfect score on a given task ranged from 30.6 (rooting) to 70.6% (grasping). Heavier infants were more likely to have perfect scores for crawling (F=4.20, P=0.044) and infants with a longer knee-heel length tended to be more likely to have a perfect grasping score (F=3.63, P=0.06). While the modal score was a perfect score for most individual tasks, the modal number of total perfect scores that a given infant received was 3-4 and only 4.7% of infants received perfect scores on all seven tasks. These results suggest that this group of behavioral tasks will produce a variable response within a population of neonates. While no individual behavioral score predicted survival during week 1, the number of perfect scores across all tasks was predictive of survival outcome; infants with a higher total number of perfect scores were more likely to survive (F=6.02, P=0.018). When all combinations of tests were compared, the best predictor of survival was outcome on four of the seven tests, all related to motor skills (F=7.46, P=0.009).